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[[Image:Splash-mom.jpg|right|720px]]<strong><font color="#06569f" size="4">3D Wire MoM And Surface MoM Solvers For Simulating Free-Space Structures</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

[[EM.Libera ]] is a 3D free-space structure simulator for modeling metallic structures. It features a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) engine for analyzing wire frequency domain modeling of free-space structures made up of metal and dielectric regions or wire-frame models a combination of metallic surfaces and solidsthem. Many RF systems utilize wire antennas like dipolesIt features two separate simulation engines, monopolesa Surface MoM solver and a Wire MoM solver, loops, or arrays that work independently and provide different types of wire antennassolutions to your numerical problem. The [[3D Method of Moments|3D method of moments]] (Surface MoM) based on Pocklington's integral solver utilizes a surface integration equation can accurately model such antennas formulation of the metal and their coupling effectsdielectric objects in your physical structure. Moreover, in many applications, The Wire MoM solver can only handle metallic surface or wireframe structures. [[Solid Objects|solid objects]] can be approximately modeled as wire-frame structures. EM.Libera's Wire MoM simulator can provide an adequate numerical solution ]] selects the simulation engine automatically based on the types of wire-frame structures. Examples of this sort are wire antennas objects present in the presence of large reflectors or scatterers. Wire-frame models also make a good approximation of metallic target structures for radar cross section (RCS) analysisyour project workspace.

EM.Libera's Wire MoM simulator is seamlessly interfaced with [[EM.Cube|EM.CUBELibera]]'s other offers two distinct 3D MoM simulation engines. The solution of a wire-frame structure can be imported to [[EMWire MoM solver is based on Pocklington's integral equation.Cube]]The Surface MoM solver uses a number of surface integral equation formulations of Maxwell's equations. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions. On the other modules as a set hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions. Equivalent electric and magnetic currents are assumed on the surface of short dipole sources with proper amplitudes the dielectric objects to formulate their assocaited interior and phasesexterior boundary value problems.

=== A {{Note|In general, [[EM.Libera]] uses the surface MoM solver to analyze your physical structure. If your project workspace contains at least one line or curve object, [[EM.Libera]] switches to the Wire MoM solver.}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of the '''[[Basic Principles of The Method of Moments | 3D Method Of of Moments Primer ===]]'''.

The Method of Moments (MoM) is a rigorous, full<table><tr><td>[[Image:Yagi Pattern.png|thumb|500px|3D far-wave, numerical technique for solving open boundary electromagnetic problems. Using this technique, you can analyze electromagnetic field radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method pattern of moments is an integral equation technique; it solves the integral form of Maxwell’s equations as opposed to their differential forms used in the finite element or finite difference time domain methodsexpanded Yagi-Uda antenna array with 13 directors.]] </td></tr></table>

In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem=== EM. The given structure is immersed in the free space. These currents or fields are discretized Libera as a collection of elementary currents or fields with small finite spatial extents. Such elementary currents or fields are called basis functions. They obviously have a vectorial nature and must satisfy Maxwell's equations and relevant boundary conditions individually. The actual currents or fields on the surface MoM3D Module of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields with initially unknown amplitudes. Through the MoM solution, you find these unknown amplitudes, from which you can then calculate the currents or fields everywhere in the structureEM.Cube ===

You can use [[EM.CubeLibera]]’s [[MoM3D Module|MoM3D module]] offers two distinct either for simulating arbitrary 3D MoM simulation engine. The first one is a Wire MoM solver that can be used to simulate wireframe models of metallic , dielectric and composite surfaces and volumetric structures. This solver is particularly useful or for modeling wire-type antennas objects and arraysmetallic wireframe structures. The second engine features a powerful surface MoM solver[[EM. It can model metallic surfaces and solids Libera]] also serves as well as solid dielectric objects. The Surface MoM solver uses a surface integral equation formulation the frequency-domain, full-wave '''MoM3D Module''' of Maxwell's equations''[[EM. In Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Libera]] shares the case of solid dielectric objectsvisual interface, 3D parametric CAD modeler, data visualization tools, equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior many more utilities and exterior boundary value problemsfeatures collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[3D Method of MomentsGetting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

== Physical Structure = Advantages &amp; 3D Mesh Generation Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===

=== The method of moments uses an open-boundary formulation of Maxwell's equations which does not require a discretization of the entire computational domain, but only the finite-sized objects within it. As a result, [[EM.Libera]]'s typical mesh size is typically much smaller that that of a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[EM.Libera]]'s triangular surface mesh provides a more accurate representation of your physical structure than [[EM.Tempo]]'s staircase brick volume mesh, which often requires a fairly high mesh density to capture the geometric details of curved surfaces. These can be Defining Groups Of PEC Objects === serious advantages when deciding on which solver to use for analyzing highly resonant structures. In that respect, [[EM.Libera]] and [[EM.Picasso]] are similar as both utilize MoM solvers and surface mesh generators. Whereas [[EM.Picasso]] is optimized for modeling multilayer planar structures, [[EM.Libera]] can handle arbitrarily complex 3D structures with high geometrical fidelity.

[[EM.CubeLibera]]'s [[MoM3D Module]] features two different simulation engines: Wire MoM solver can be used to simulate thin wires and Surface MoM. Both simulation engines can handle metallic wireframe structuresvery fast and accurately. The Wire MoM engine models metallic objects as wireframe structures, while This is particularly useful for modeling wire-type antennas and arrays. One of the Surface MoM engine treats them as perfect electric conductor (PEC) surfacescurrent limitations of [[EM. The PEC objects can be linesLibera]], curveshowever, surfaces or solidsis its inability to mix wire structures with dielectric objects. All If your physical structure contains one ore more wire objects, then all the PEC surface and solid CAD objects are created under of the '''PEC''' node project workspace are reduced to wireframe models in order to perform a Wire MoM simulation. Also note that Surface MoM simulation of composite structures containing conjoined metal and dielectric parts may take long computation times due to the '''Physical Structure''' section slow convergence of the Navigation Treeiterative linear solver for such types of numerical problems. Objects are grouped together by their colorSince [[EM. You Libera]] uses a surface integral equation formulation of dielectric objects, it can insert different PEC groups with different colorsonly handle homogeneous dielectric regions. A new PEC group can be defined by simply right clicking on the '''PEC''' item in the Navigation Tree For structures that involve multiple interconnected dielectric and selecting '''Insert New PECmetal regions such as planar circuits, it is highly recommended that you use either [[EM...''' from the contextual menu. A dialog for setting up the PEC properties opens up. From this dialog you can change the name of the group Tempo]] or its color[[EM. Note that PEC object do not have any material properties that can be editedPicasso]] instead.

<table><tr><td>[[FileImage:wire_pic1Hemi current.png]] [[File:wire_pic2|thumb|500px|The computed surface current distribution on a metallic dome structure excited by a plane wave source.png]]</td></tr></table>

Figure 1: [[MoM3D Module]]'s Navigation Tree and its PEC dialog== EM.Libera Features at a Glance ==

=== Defining Dielectric Objects Physical Structure Definition ===

Of the two simulation engines of [[EM.Cube]]'s [[MoM3D Module]] only the Surface MoM solver can handle dielectric objects as dielectric materials cannot be modeled by wireframe structures. Dielectric objects are created under the '''Dielectric''' node in the '''Physical Structure''' section of the Navigation Tree. They are grouped together by their color and material properties. You can insert different dielectric groups with different colors and different permittivity e_r and electric conductivity s. Note that a PEC object is the limiting cases of a lossy dielectric material when === Sources, Loads &sigmaamp; &rarr; &infin;.Ports ===

To define a new Dielectric group<ul> <li> Gap sources on wires (for Wire MoM) and gap sources on long, follow these steps:narrow, metal strips (for Surface MoM)</li> <li> Gap arrays with amplitude distribution and phase progression</li> <li> Multi-port port definition for gap sources</li> <li> Short dipole sources</li> <li> Import previously generated wire mesh solution as collection of short dipoles</li> <li> RLC lumped elements on wires and narrow strips with series-parallel combinations</li> <li> Plane wave excitation with linear and circular polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li> <li> Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li></ul>

=== <ul> <li> Wireframe and electric and magnetic current distributions</li> <li> Near Field intensity plots (vectorial - amplitude &amp; phase)</li> <li> Huygens surface data generation for use in MoM3D or other [[EM.Cube]] modules</li> <li> Far field radiation patterns: 3D MoM Mesh Types === pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li> <li> Radiation pattern of an arbitrary array configuraition of the wire structure</li> <li> Bi-static and mono-static radar cross section: 3D visualization and 2D graphs</li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

Coming Soon..== Building the Physical Structure in EM.Libera ==

The {| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[MoM3D ModuleFile:pec_group_icon.png]]'s method | style="width:150px;" | [[Glossary of moments solver assumes an infinite open boundary for your projectEM.Cube's structure Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and uses the free space Greencurve objects| None|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's functions for the background structure. As a resultMaterials, the extents of the computational domain are infinite in all directionsSources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only |-| style="width:30px;" | [[File:diel_group_icon. The mesh generation process in png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |EMDielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface MoM solver only |-| style="width:30px;" | [[File:Virt_group_icon.CUBEpng]]'s | style="width:150px;" | [[MoM3D ModuleGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]] involves three steps| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects| None |}

# Setting Click on each category to learn more details about it in the mesh properties[[Glossary of EM.# Generating the mesh.# Verifying the meshCube's Materials, Sources, Devices & Other Physical Object Types]].

The commercial release Both of [[EM.Cube|EM.CUBELibera]]'s [[MoM3D Module]] provides a two simulation engines, Wire MoM solver. In this simulation engineand Surface MoM, all the can handle metallic objects are discretized as a wire-frame structurestructures. Wires, line You define wires under '''Thin Wire''' groups and curves are discretized as polylines made up of small linear cells (segments).Surface surface and [[Solid Objects|solid volumetric metal objects]] are discretized as a wire-frame mesh with triangular cells. The MoM3D mesh generator meshes the wires based on a specified mesh sampling rate expressed in cells/&lambda₀. Curves are first polygonized and converted into under '''PolylinePEC Objects''' Objects, whose edge lengths follow the specified mesh sampling rate. In the case of [[Solid Objects|solid objects]]other words, only their surface you can draw lines, polylines and faces are discretized using a triangular wireframe meshother curve objects as thin wires, which is regarded as have a grid of interconnected wiresradius parameters expressed in project units. Two algorithms are offered for generation All types of solid and surface CAD objects can be drawn in a triangular wireframe meshPEC group. The default algorithm is Only solid CAD objects can be drawn under '''Regular WireframeDielectric Objects'''. This mesh generator creates wireframe elements that have almost equal edge lengths. The other algorithm is '''Structured Wireframe''', which usually creates a very structured wireframe with a large number of aligned wireframe elements.

To view the <table><tr><td>[[MoM3D Module]]'s wire-frame mesh, click on the [[FileImage:mesh_tool_tnwire_pic1.png]] button of the '''Compute Toolbar''' or select '''Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Shoe Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the wire-frame mesh is displayed in the Project Workspace, [[EM.Cube|thumb|350px|EM.CUBE]]Libera's mesh view mode is enabledNavigation Tree. In this mode, you can perform view operations like rotate view, pan, zoom, etc. However, you cannot select or move or edit objects. While the mesh view is enabled, the '''Show Mesh''' [[File:mesh_tool.png]] button remains depressed. To get back to the Normal View mode, click this button one more time, or deselect '''Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Show Mesh''' to remove its check mark or simply click the '''Esc Key''' of the keyboard.&quot;Show Mesh&quot; generates a new mesh and displays it if there is none in the memory, or it simply displays an existing mesh in the memory. This is a useful feature because generating a wire-frame mesh may take a long time depending on the complexity and size of objects. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore the mesh in the memory and force [[EM.Cube|EM.CUBE]] to generate a mesh from the ground up by selecting '''Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu. </td></tr></table>

Once a new object group node has been created on the navigation tree, it becomes the "Active" group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active group. There is only one object group that is active at any time. Any object type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create object groups, and then draw new CAD objects under the active object group. However, if you start a new [[File:wire_pic5_tnEM.pngLibera]]project from scratch, and start drawing a new object without having previously defined any object groups, a new default PEC object group is created and added to the navigation tree to hold your new CAD object.

The regular wireframe mesh of a PEC sphere[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

=== Customizing {{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]. From [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], you can then move the Mesh === imported objects to [[EM.Libera]].}}

[[File:wire_pic4== EM.png|thumb|300px|[[MoM3D Module]]Libera's mesh settings dialog]]Excitation Sources ==

To set the wire-frame mesh propertiesYour 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, click electric surface currents on metal surface and both electric magnetic surface currents on the [[File:mesh_tool_tn.png]] button surface of the '''Compute Toolbar''' or select '''Menu [[File:larrow_tndielectric objects.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Mesh Settings...'''or right click The excitation source you choose depends on the '''3-D Mesh''' item observables you seek in the '''Discretization''' section or the Navigation Tree and select '''Mesh Settingsyour project...''' from the contextual menu. The MoM3D Mesh Settings Dialog opens up. You can change the mesh generation algorithm from the drop-down list labeled '''Mesh Type''' and select one of the two options: '''Regular Wireframe''' or '''Structured Wireframe'''. You can also set the '''Mesh Sampling Rate''', whose default value is 20 Cells/&lambda;₀.By default, [[Surface Objects|surface objects]] or solids are wire-framed at the mesh cell sizeEM. Therefore, each wire segment of the wire-frame mesh contains one cell. Another parameter that can affect the shape of the mesh especially in the case of [[Solid Objects|solid objectsLibera]] is provides the '''Curvature Angle Tolerance'''. This parameter expressed in degrees determines the apex angle of the triangular cells of the structured mesh. Lower values of the angle tolerance will results in more pointed triangular cells.following source types for exciting your physical structure:

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:wire_pic6_tngap_src_icon.png]]|800px[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source | style="width:300px;" | Associated with a PEC rectangle strip, works only with SMOM solver|-| style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source| style="width:300px;" | Associated with an PEC or thin wire line or polyline, works only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

Four-port view of Click on each category to learn more details about it in the structured wireframe mesh [[Glossary of a PEC sphereEM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

=== Mesh For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera]] provides two types of Connected Objects === lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current and is used to define an ideal voltage source. Wire gap sources must be placed on '''Thin Wire Line''' and '''Thin Polyline''' objects to provide excitation for the Wire MoM solver. The gap splits the wire into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Strip gap sources must be placed on long, narrow, '''PEC Rectangle Strip''' objects to provide excitation for the Surface MoM solver. The gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source.

All the [[Solid Objects{{Note|solid objects]] belonging If you want to the same PEC group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected excite a curved wire antenna such as a circular loop or overlapping [[Solid Objects|solid objects]]helix with a wire gap source, their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the [[Surface Objects|surface objects]] belonging first you have to convert the same PEC group are merged together before meshing. However, following curve object into a polyline using [[EM.Cube|EM.CUBECubeCAD]]'s union rules, a solid and a surface object cannot not be &quot;unioned&quot; together. Therefore, their meshes will not connect even if the two objects belong to the same PEC groupPolygonize Tool.}}

A short dipole provides another simple way of exciting a 3D structure in [[EM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. You can connect also use an incident plane wave to excite your physical structure in [[EM.Libera]]. In particular, you need a line object plane wave source to compute the radar cross section of a touching surfacetarget. To connect lines to surfaces The direction of incidence is defined by the &theta; and allow for current continuity, you must make sure that &phi; angles of the box labeled '''Connect Lines to Touching Surfaces''' is checked unit propagation vector in the '''Mesh Settings Dialog'''spherical coordinate system. If the end The default values of the incidence angles are &theta; = 180° and &phi; = 0° corresponding to a line lies on normally incident plane wave propagating along the -Z direction with a flat surface, [[EM+X-polarized E-vector.Cube|EM.CUBE]] will detect Huygens sources are virtual equivalent sources that and create capture the connection automatically. However, this may not always be the case if the surface is not flat radiated electric and has curvature. In such cases, you have to specifically instruct magnetic fields from another structure that was previously analyzed in another [[EM.Cube|EM.CUBE]] to enforce the connection. An example of this case is shown in the figure belowcomputational module.

[[FileImage:wire_pic7_tnInfo_icon.png|260px40px]] Click here to learn more about '''[[File:wire_pic8_tn.pngPreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays |260pxUsing Source Arrays in Antenna Arrays]] [[File:wire_pic9_tn'''.png|260px]]

The line object at the top <table><tr><td> [[Image:wire_pic14_tn.png|thumb|left|640px|A wire gap source placed on one side of a PEC sphere and the structure's mesh without and with proximity mesh connection enforcedpolyline representing a polygonized circular loop.]] </td></tr><tr></table>

=== Local Mesh Control === <table><tr>[[EM.Cube|EM.CUBE]] applies the global mesh sampling rate to discretize all the objects in the Project Workspace. However, you can lock the mesh sampling rate of any PEC group to a desired value different than the global rate. To do so, open the property dialog of a PEC group by right clicking on its name in the Navigation Tree and select '''Properties...''' from the contextual menu. At the bottom of the dialog, check the box labeled '''Lock Mesh'''. This will enable the '''Sampling Rate''' box, where you can set a desired value. The default value is equal to the global mesh sampling rate. Keep in mind that objects that belong to different PEC groups are not merged during the mesh generation even if they overlap or are intended to be connected to one another.<br /td>  [[FileImage:wire_pic10po_phys16_tn.png]] Locking the mesh sampling rate of |thumb|left|420px|Illuminating a PEC group. == Excitation Sources == === Gaps Sources On Wires ===  A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current. In [[EM.Cube]]'s [[MoM3D Module]], a gap is used to define an excitation source in the form of an ideal voltage source. Gap sources can be placed only on '''Line''' and '''Polyline''' objects. '''If you want to excite a curved wire antennas such as a circular loop or helix metallic sphere with a gap source, first you have to convert the curve object into a polyline using [[EM.Cube]]'s Polygonize Tool.''' The gap splits the wire into two segment with a an infinitesimally small spacing between them, across which the ideal voltage obliquely incident plane wave source is connected. To define a new gap source, follow these steps: * Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Gap Source Dialog opens up.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A gap symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction for the source. This parameter is obviously relevant only for lumped elements of active type.* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees. [[File:wire_pic14_tn.png]]</td></tr>A gap source placed on one side of a polyline representing a polygonized circular loop.</table>

[[File:wire_pic15.png|thumb|300px|[[MoM3D Module]]'s lumped element dialog]] In [[EM.Cube]]'s [[MoM3D ModuleLibera]], you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance. Unlike the [[FDTD Module]]'s single-device lumped loads that connect between two adjacent nodes, the [[MoM3D ModuleEM.Libera]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below: [[File:image106.png]] [[File:wire_pic16_tn.png|thumb|200px|Active lumped element with a voltage gap in series with an RC circuit placed on a dipole wire]]

To define a new lumped element, follow these steps[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.

* Right click on the '''Lumped Elements''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Lumped Element Dialog opens up.* In the '''Lumped Circuit Type''' select one of the two options[[Image: '''Passive RLC''' or '''Active with Gap Source'''Info_icon. Choosing the latter option enables the '''Source Properties''' section of the dialog.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A lumped element symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction png|40px]] Click here for the source.* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance general discussion of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side26_Nonlinear_Passive_. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* In the '''Load Properties''' section, the series and shunt resistance values Rs and Rp are specified in Ohms, the series and shunt inductance values Ls and Lp are specified in nH (nanohenry), and the series and shunt capacitance values Cs and Cp are specified in pF (picofarad). The impedance of the circuit is calculated at the operating frequency of the project. Only the elements that have been checked are taken into account. By default, only the series resistor has a value of 50&Sigma; and all other circuit elements are initially grayed out.* If the lumped element is active and contains a gap source, the '''Source Properties''' section of the dialog becomes enabled. Here you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degrees.* If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A lumped element will be placed on each element of the array. All the lumped elements will have identical direction, offset, resistance, inductance and capacitance values. If you define an active lumped element, you can prescribe certain amplitude and/or phase distribution to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression26_Active_Devices | Linear Passive Devices]]''' in degrees along all three principal axes.

Ports are used to order and index gap sources for S parameter calculation. They are defined in the '''Observables''' section of the Navigation Tree. Right click on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the total number of existing sources in the workspacenavigation tree. By default, as many ports as the total number of sources are created. You can define any number of ports equal to or less than the total number of sources. This includes both gap sources and active lumped elements (which contain gap sources). In the '''Port Association''' section of this dialog, you can go over each one of the sources and associate them with a desired port. Note that you can associate more than one source with same given port. In this case, you will have a coupled port. All the coupled sources are listed as associated with a single port. However, you cannot associate the same source with more than one port. Finally, you can assign '''Port Impedance''' in Ohms. By default, all port impedances are 50&SigmaOmega;. The table titled '''Port Configuration''' lists all the ports and their associated sources and port impedancesby default.

{{Note|In [[EMImage:Info_icon.Cubepng|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|EM.CUBE40px]]]]]]]]]]]]]]]]]]]]]]]]]] you cannot assign ports Click here to an array object, even if it contains sources on its elements. To calculate learn more about the S '''[[parametersGlossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]] of an antenna array, you have to construct it using individual elements, not as an array object'''.}}

<table><tr><td> [[FileImage:port-definitionMOM7A.png|thumb|360px|Two metallic strips hosting a gap source and a lumped element.]] </td><td> [[Image:MOM7B.png|thumb|360px|The surface mesh of the two strips with a gap source and a lumped element.]]</td></tr></table>

The [[MoM3D Module]]== EM.Libera's port definition dialog.Simulation Data & Observables ==

At the end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the computed simulation data. The primary solution of the Wire MoM simulation engine consists of the linear electric currents on the wires and wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables: {| class="wikitable"|-! scope="col"| Icon! scope= Sources "col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables &ampGraph Types#Current Distribution |Current Distribution]]| style="width:300px; Loads On Arrays Of Wire Radiators " | Computing electric surface current distribution on metal and dielectric objects, magnetic surface current distribution on dielectric objects and linear current distribution on wires| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style= "width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}

If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A gap source will be placed Click on each element of the array. All the gap sources will have identical direction and offset. However, you can prescribe certain amplitude and/or phase distributions. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need category to set a value for maximum side lobe level ('''SLL''') learn more details about it in dBthe [[Glossary of EM. You can also define Cube'''Phase Progression''' in degrees along all three principal axess Simulation Observables & Graph Types]].

Depending on the types of objects present in your project workspace, [[File:wire_pic12EM.pngLibera]] performs either a Surface MoM simulation or a Wire MoM simulation. In the former case, the electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized. In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted. [[File:wire_pic13_tn.png]]

The <table><tr><td> [[MoM3D ModuleImage:wire_pic26_tn.png|thumb|360px|A monopole antenna connected above a PEC plate.]]'s gap source dialog and gaps sources defined on an array of dipole wires with binomial weight </td><td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution and 90° phase progressionplot of the monopole antenna connected above the PEC plate.]] </td></tr></table>

<table><tr><td> [[FileImage:wire_pic17wire_pic32_tn.png|thumb|300px360px|The short dipole source dialogElectric field plot of the circular loop antenna.]] </td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]]</td></tr></table>

A short dipole provides You need to define a simple way far field observable if you want to plot radiation patterns of exciting a your physical structure in the [[MoM3D ModuleEM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. To define After a short dipole source3D MoM simulation is finished, follow these steps:three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field.

* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source[[Image:Info_icon...''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section of the dialog, you can set the coordinate of the center of the short dipole. By default, the source is placed at the origin of the world coordinate system at (0,0,0).You can type in new coordinates or use the spin buttons png|30px]] Click here to move learn more about the dipole around.* In the '''Source Properties''' section, you can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' theory of the dipole in project units.* In the '''Direction Unit Vector[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes the vector components upon closure even if your component values do not satisfy a unit magnitude.

When you simulate a wire structure in the <table><tr><td> [[MoM3D Module]], you can define a '''Current Distribution Observable''' in your project. This is used not only to visualize the current distribution in the project workspace but also to save the current solution into an ASCII data file. This data file is called &quot;MoM.IDI&quot; by default and has a '''.IDI''' file extensionImage:wire_pic38_tn. png|thumb|230px|The current data are saved as line segments representing each 3D radiation pattern of the wire cells together with the complex current at the center of each cellcircular loop antenna: Theta component. In the ]] </td><td> [[MoM3D Module]], you can import the current data from an existing '''Image:wire_pic39_tn.IDI''' file to serve as a set png|thumb|230px|The 3D radiation pattern of short dipoles for excitation. To import a wire current solution, right click on '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Import Dipole Sourcecircular loop antenna: Phi component...''' from the contextual menu. This opens up the standard [[Windows]] Open dialog with the file type set to '''.IDI'''. Browse your folders to find the right current data file. Once you find it, select it and click the '''Open''' button of the dialog. This will create as many short dipole sources on the </td><td> [[PO Module]]'s Navigation Tree as the Image:wire_pic40_tn.png|thumb|230px|The total number radiation pattern of mesh cells in the Wire MoM solutioncircular loop antenna. From this point on, each of the imported dipoles behave like a regular short dipole source. You can open the property dialog of each individual source and modify its [[parameters]].</td></tr></table>

[[File:po_phys15To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the navigation tree.png|thumb|300px|plane wave dialog]]

{{Note| The wire-frame structure in 3D RCS plot is always displayed at the [[MoM3D Module]] can be excited by an incident plane wave. In particularorigin of the spherical coordinate system, a plane wave source can be used (0,0,0), with respect to compute which the radar cross section of a metallic target. A plane wave far radiation zone is defined by its propagation vector indicating . Oftentimes, this might not be the direction scattering center of incidence and its polarizationyour physical structure. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides the following polarization options:}}

<table><tr><td> [[Image:wire_pic51_tn.png|thumb|230px|The direction RCS of incidence is defined through the a metal plate structure: &thetasigma; and _{&phitheta; angles of the unit propagation vector in the spherical coordinate system}. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi''']] </td><td> [[Image:wire_pic52_tn. png|thumb|230px|The default values are RCS of a metal plate structure: &thetasigma; = 180° and _{&phi; = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM}z.]] </subtd> and TE<subtd>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively[[Image:wire_pic53_tn. png|thumb|230px|The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case total RCS of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfieda metal plate structure: '''ê . ê''' = 1 and '''ê × k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (&thetasigma; = 180°)_tot.]] </td></tr></table>

* Right click === A Note on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source..EM.Libera''' The Plane wave Dialog opens up.* In the Field Definition section of the dialog, you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selected, you also need to enter the X, Y, Z components of the '''E-Field Vector'''.s Mesh Types ===

{{Note|In the spherical coordinate system[[EM.Libera]] features two simulation engines, normal plane wave incidence from Wire MoM and Surface MoM, which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to a mesh density criterion. Curved wires are first converted to multi-segment polylines and then subdivided further if necessary. At the top of the domain downward corresponds connection points between two or more wires, junction basis functions are generated to &theta; of 180&deg;ensure current continuity. }}

On the other hands, [[File:po_phys16_tnEM.pngLibera]]'s Surface MoM solver requires a triangular surface mesh of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.

Figure[[Image: Illuminating a metallic sphere Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with an obliquely incident plane wave sourceMesh Generator]]'''.

Once you have set up your metal structure in You can analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Cube|EM.CUBELibera]]'s [[MoM3D Module]], have defined sources and observables and have examined the quality of the Wire MoM simulator. When you structure's wire-frame meshcontains at least one PEC line, you are ready to run a simulation. To open the Run Simulation Dialogpolyline or any curve CAD object, click the '''Run''' [[File:run_iconEM.pngLibera]] button will automatically invoke its linear wireframe mesh generator. This mesh generator subdivides straight lines and linear segments of polyline objects into or linear elements according to the '''Compute Toolbar''' or select Menu [[File:larrow_tnspecified mesh density.png]] Compute It also polygonizes rounded [[File:larrow_tn.pngCurve Objects|curve objects]] Run...or use into polylines with side lengths that are determined by the keyboard shortcut '''Ctrl+R'''specified mesh density. To start the simulation click the '''Run''' button of this dialog. Once the Wire MoM simulation starts, a new dialog called '''Output Window''' opens up Note that reports the various stages of Wire MoM simulation, displays the running time polygonizing operation is temporary and shows the percentage of completion solely for certain tasks during the Wire MoM simulation process. A prompt announces the completion he purpose of the Wire MoM simulationmesh generation. At this timeAs for surface and solid CAD objects, [[EM.Cube|EM.CUBE]] generates a wireframe mesh of these objects is created which consists of a large number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections interconnected linear (RCSwire) if the structure is excited by a plane wave sourceelements.

You have the choice to run a '''Fixed Frequency''' simulation, which is the default choice, or run a '''Frequency Sweep''{{Note| The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. In the former case, the simulation will be carried out at the It also discretizes surface and solid CAD objects temporarily using CubeCAD'''Center Frequency''' of the project. This frequency can be changed from the Frequency Dialog of the project or you can click the Frequency Settings button of the Run Dialog to open up the Frequency Settings dialog. You can change the value of Center Frequency from this dialog, toos Polymesh tool.}}

In case you choose Frequency Sweep, the Frequency Settings dialog gives two options for '''Sweep Type<table><tr><td> [[Image: Adaptive''' or '''Uniform'''Mesh6. In png|thumb|200px|The geometry of an expanding helix with a uniform sweep, equally spaced samples circular ground.]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the frequency are used between helix with the Start and End frequencies. These are initially set by the project Bandwidth, but you can change their values from the Frequency Settings dialog. The default '''Number mesh density of Samples''' is 10cells/&lambda;₀.In the case ]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of adaptive sweep, you have to specify the '''Maximum Number of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts helix with a few initial frequency samples, where the Wire MoM engine is runmesh density of 25 cells/&lambda;₀. Then, the intermediary samples are calculated in a progressive manner]] </td><td> [[Image:Mesh9. At each iteration, png|thumb|200px|Wireframe mesh of the frequency samples are used to calculate helix with a rational approximation mesh density of the S parameter response over the specified frequency range. The process stops when the error criterion is met50 cells/&lambda;₀.]] </td></tr></table>

[[File:wire_pic20.png]] Figure: The output window. === Setting Wire MoM Numerical Parameters ===  A Wire MoM simulation involves a number Mesh of numerical [[parameters]] that normally take default values unless you change them. You can access these [[parameters]] and change their values by clicking on the '''Settings''' button next to the &quot;Select Engine&quot; drop-down list in the '''Run Dialog'''. This opens up the Wire MoM Engine Settings Dialog. In the '''Solver''' section of the dialog, you can choose the type of linear solver. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the [[MoM3D Module]]. The BiCG solver is iterative. Once selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''. The Wire MoM simulator is based on Pocklington's integral equation method. In this method, the wires are assumed to have a very small radius. The basis functions are placed on the axis of the &quot;wire cylinder&quot;, while the Galerkin testing is carried out on its surface to avoid the singularity of the Green's functions. In the &quot;Source Singularity&quot; section of the dialog, you can specify the '''Wire Radius''' . [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] assumes an identical wire radius for all wires and wireframe structures. This radius is expressed in free space wavelengths and its default value is 0.001&lambda;₀. The value of the wire radius has a direct influence on the wire's computed reactance. [[File:wire_pic21.png]] The wire MoM engine settings dialog. Connected Objects == More 3D MoM Simulation Types == === 3D MoM Sweep Simulations ===  You can run [[EM.Cube|EM.CUBE]]'s MoM3D simulation engine in the sweep mode, whereby a parameter like frequency, plane wave angles of incidence or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data file for visualization and plotting. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] currently offers three types of sweep: # Frequency Sweep# Angular Sweep# Parametric Sweep To run a MoM3D sweep, open the '''Run Simulation Dialog''' and select one of the above sweep types from the '''Simulation Mode''' drop-down list in this dialog. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode drop-down list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the project's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep: # Fix mesh at the highest frequency.# Fix mesh at the center frequency.# Re-mesh at each frequency. The [[MoM3D Module]] offers two types of frequency sweep: adaptive or uniform. In a uniform sweep, equally spaced frequency samples are generated between the start and end frequencies. In the case of an adaptive sweep, you must specify the '''Maximum Number of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts with a few initial frequency samples, where the Wire MoM engine is initially run. Then, the intermediary frequency samples are calculated and inserted in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation of the scattering parameter response over the specified frequency range. The process stops when the specified error criterion is met in a mean-square sense. The adaptive sweep simulation results are always continuous and smooth. This is due to the fact that a rational function curve is fitted through the discrete frequency data points. This usually captures frequency response characteristics such as resonances with much fewer calculated data points. However, you have to make sure that the process converges. Otherwise, you might get an entirely wrong, but still perfectly smooth, curve at the end of the simulation. [[File:wire_pic22.png]] [[File:wire_pic24.png]] The [[MoM3D Module]]'s run simulation dialog with frequency sweep selected and the frequency settings dialog. You can run an angular sweep only if your project has a plane wave excitation. In this case, you have to define a plane wave source with the default settings. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range. The other angle remains fixed at the value that is specified in the '''Plane Wave Dialog'''. You have to select either '''Theta''' or '''Phi''' as the '''Sweep Angle''' in the Angle Settings Dialog. Then you can set the start and end angles as well as the number of angle samples. [[File:wire_pic23.png]] [[File:po_phys54.png]] The [[PO Module]]'s run simulation dialog with angular sweep selected and the angle settings dialog. In a parametric sweep, one or more user defined [[variables]] are varied at the same time over their specified ranges. This creates a parametric space with the total number of samples equal to the product of the number of samples for each variable. The user defined [[variables]] are defined using [[EM.Cube|EM.CUBE]]'s '''[[Variables]] Dialog'''. For a description of [[EM.Cube|EM.CUBE]] [[variables]], please refer to the [[CubeCAD|CUBECAD]] manual or the &quot;Parametric Sweep&quot; sections of the FDTD or [[Planar Module]] manuals. == Working with 3D MoM Simulation Data == === Visualizing Wire Current Distributions ===  [[File:wire_pic25.png|thumb|300px|[[MoM3D Module]]'s current distribution dialog]] At the end of a MoM3D simulation, [[EM.Cube|EM.CUBE]]'s Wire MoM engine generates a number of output data files that contain all the computed simulation data. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots of current distributions in the Project Workspace. Current distributions are visualized on all the wires and the magnitude and phase of the electric currents are plotted for all the PEC objects. In order to view these currents, you must first define current sensors before running the Wire MoM simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the [[MoM3D Module]] you can define only one current distribution node in the Navigation Tree, which covers all the PEC object in the Project Workspace. After a Wire MoM simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of the linear wire currents. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -&pi; and &pi;. Current distribution maps are displayed with some default settings and options. You can customize the individual maps (total, magnitude, phase, etc.). To do so, open the '''Output Plot Settings Dialog''' by right clicking on the specific plot entry in the Navigation Tree and selecting '''Properties...''' or by double clicking on the surface of the plot's legend box. Two '''scale''' options are available: '''Linear''' and '''dB'''. With the '''Linear''' (default) option selected, the current value is always normalized to the maximum total current in that plane, and the normalized scale is mapped between the minimum and maximum values. If the '''dB''' option is selected, the normalized current is converted to dB scale. The plot limits (bounds) can be set individually for every current distribution plot. In the '''Limits''' section of the plot's property dialog, you see four options: '''Default''', '''User Defined''', '''95% Conf.''' and '''95% Conf.'''. Select the user defined option and enter new values for the '''Lower''' and '''Upper''' limits. The last two options are used to remove the outlier data within the 95% and 99% confidence intervals, respectively. In other words, the lower and upper limits are set to ? ± 1.96? and ? ± 2.79? , respectively, assuming a normal distribution of the data. Three color maps are offered: '''Default''', '''Rainbow''' and '''Grayscale'''. You can hide the legend box by deselecting the box labeled '''Show Legend Box'''. You can also change the foreground and background colors of the legend box. [[File:wire_pic26_tn.png|400px]] [[File:wire_pic27_tn.png|400px]] Figure: A monopole antenna connected above a PEC plate and its current distribution with the default plot settings. [[File:wire_pic28.png|360px]] [[File:wire_pic29_tn.png|440px]] Figure: The output plot settings dialog, and the current distribution of the monopole-plate structure with a user defined upper limit. === Scattering Parameters and Port Characteristics ===  If the project structure is excited by gap sources, and one or more ports have been defined, the Wire MoM engine calculates the scattering (S) [[parameters]] of the selected ports, all based on the port impedances specified in the project's &quot;Port Definition&quot;. If more than one port has been defined in the project, the scattering matrix of the multiport network is calculated. The S [[parameters]] are written into output ASCII data files. Since these data are complex, they are stored as '''.CPX''' files. Every file begins with a header starting with &quot;#&quot;. The admittance (Y) and impedance (Z) [[parameters]] are also calculated and saved in complex data files with '''.CPX''' file extensions. The voltage standing wave ratio of the structure at the first port is also computed and saved to a real data '''.DAT''' file. You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]]. Keep in mind that in multi-port structures, each individual port parameter has its own graph. You can also see a list of all the port characteristics data files in [[EM.Cube|EM.CUBE]]'s data manager. To open data manager, click the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[File:larrow_tn.png]]Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You change the format of complex data plots. In general complex data can be plotted in three forms: # Magnitude and Phase# Real and Imaginary Parts# Smith Chart In particular, it may be useful to plot the S_ii [[parameters]] on a Smith chart. To change the format of a data plot, go to the row in the '''Data Manager Dialog''' that contains a specific complex data file's name and click on the fourth column under the title '''Graph Type'''. The selected table cell turns into a dropdown list that contains the above three formats. Select the desired format and click the '''Plot''' button of the data manager dialog to plot the data in the new format. [[File:wire_pic56.png]] [[EM.Cube|EM.CUBE]]'s data manager showing the port characteristics data files for a two-port structure consisting of two adjacent dipoles. The magnitude and phase graphs of the S₁₁ parameter. The real and imaginary part graphs of the Z₂₁ parameter. The Smith chart. === Near Field Visualization ===  [[File:wire_pic30.png|thumb|300px|[[MoM3D Module]]'s field sensor dialog]] [[EM.Cube|EM.CUBE]] allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps: * Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''* The '''Label''' box allows you to change the sensor’s name. you can also change the color of the field sensor plane using the '''Color''' button.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBE]] creates a field sensor plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''. You can also changes these coordinates using the spin buttons. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe the sensor plane moving along that direction in the Project Workspace.* The initial size of the sensor plane is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation times. After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once a Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -&pi; and &pi;. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc. [[File:wire_pic31_tn.png]] Figure: A circular loop antenna fed by a gap source. [[File:wire_pic32_tn.png|400px]] [[File:wire_pic33_tn.png|400px]] Electric and magnetic field plots of the circular loop antenna. == Visualizing 3D Radiation Patterns == [[File:wire_pic37.png|thumb|300px|[[MoM3D Module]]'s radiation pattern dialog]] Unlike the FDTD method, in the [[MoM3D Module]] you do not need a far field box to perform near-to-far-field transformations. Nonetheless, you still need to define a far field observable if you want to plot radiation patterns. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output Settings section allows you to change the '''Angle Increment''' in the degrees, which indeed sets the resolution of far field calculations. The default value is 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree and can be right clicked for further editing. After a Wire MOM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field. The 3-D plots can be viewed by clicking on their name in the navigation tree. They are displayed in the Project Workspace and overlaid on the project's structure. The view of a 3-D radiation pattern plot can be changed with the available view operations such as rotate view, pan, zoom, etc. If the structure blocks the view of the pattern, you can simply hide the whole structure or parts of it. The fields are always normalized to the maximum of the total far field: [[File:farfieldformula.gif]] A legend box appears in the upper right corner of the 3-D radiation plot, which can be moved around by clicking and dragging with the left mouse button. The calculated Directivity of the (antenna) structure is displayed at the bottom of the legend box. It is important to note that if the wire-frame structure is excited by an incident plane wave, the radiation patterns indeed represent the far-zone scattered field data. {{Note|If you do not define a far field observable in your project, no radiation patterns will be calculated at the end of a wire MoM simulation.}} {{Note|Every time you change the angle increment of the far field, you have to start a new simulation, even if your structure has not changed.}} [[File:wire_pic38_tn.png|260px]] [[File:wire_pic39_tn.png|260px]] [[File:wire_pic40_tn.png|260px]] 3-D radiation pattern of the circular loop antenna: (Left) Theta component, (Center) Phi components, and (Right) total far field. === Modeling Antenna Arrays ===  In view of far field characteristics, [[EM.Cube|EM.CUBE]] can handle antenna arrays in two different ways. The first approach is full-wave and requires building an array of radiating elements using the '''Array Tool''' and feeding individual array elements using some type of excitation. This method is very accurate and takes into account all the inter-element coupling effects. At the end of the Wire MoM simulation of the array structure, you can plot the radiation patterns and other far field characteristics of the antenna array just like any other wire-frame structure. The second approach is based on the &quot;Array Factor&quot; concept and ignores any inter-element coupling effects. In this approach, you can regard the structure in the project workspace as a single radiating element. A specified array factor can be calculated and multiplied by the element pattern to estimate the radiation pattern of the overall radiating array. To define an array factor, open the '''Radiation Pattern Dialog''' of the project. In the section titled '''Impose Array Factor''', you will see a default value of 1 for the '''Number of Elements''' along the three X, Y and Z directions. This implies a single radiator, which is your structure in the project workspace. There are also default zero values for the '''Element Spacing''' along the X, Y and Z directions. You should change both the number of elements and element spacing in the X, Y or Z directions to define any desired finite array lattice. For example, you can define a linear array by setting the number of elements to 1 in two directions and entering a larger value for the number of elements along the third direction. The radiation patterns of antenna arrays usually have a main beam and several side lobes. Some [[parameters]] of interest in such structures include the '''Half Power Beam Width (HPBW)''', '''Maximum Side Lobe Level (SLL)''' and '''First Null [[Parameters]]''' such as first null level and first null beam width. You can have [[EM.Cube|EM.CUBE]] calculate all such [[parameters]] if you check the relevant boxes in the &quot;Additional Radiation Characteristics&quot; section of the '''Radiation Pattern Dialog'''. These quantities are saved into ASCII data files of similar names with '''.DAT''' file extensions. In particular, you can plot such data files at the end of a sweep simulation.

{{Note|Defining an array factor in All the objects belonging to the radiation pattern dialog simply performs a post-processing calculationsame PEC or dielectric group are merged together using the Boolean union operation before meshing. The resulting far field obviously do not take into account any inter-element coupling effects as [[EMIf your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and only the surface of the external faces is meshed.Cube|[[EMSimilarly, all the surface objects belonging to the same PEC group are merged together and their internal edges are removed before meshing.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|[[EM.Cube|EM.CUBE]]]]]]]]]]]]]]]]]]]]]]]]]] does not construct Note that a real physical array in solid and a surface object belonging to the project workspacesame PEC group might not always be merged properly.}}

{{Note|Using When two objects belonging to two different material groups overlap or intersect each other, [[EM.Libera]] has to determine how to designate the overlap or common volume or surface. As an array factor for far field calculationexample, you cannot assign non-uniform amplitude the figure below shows a dielectric cylinder sitting on top of a PEC plate. The two object share a circular area at the base of the cylinder. Are the cells on this circle metallic or phase distribution do they belong to the array elementsdielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. For To address problems of this purposekind, [[EM.Libera]] does provide a "Material Hierarchy" table, which you can modify. To access this table, select '''Menu > Simulate > discretization > Mesh Hierarchy...'''. The PEC groups by default have to define an array objectthe highest priority and reside at the top of the table.You can select an group from the table and change its hierarchy using the {{key|Move Up}}or {{key|Move Down}} buttons of the dialog. You can also change the color of junction cells that belong to each group.

<table><tr><td> [[FileImage:wire_pic47MOM3.png|thumb|300px|EM.Libera's Mesh Hierarchy dialog.]] </td></tr></table>

Defining <table><tr><td> [[Image:MOM1.png|thumb|360px|A dielectric cylinder attached to a finite-sized 4-element array factor in PEC plate.]] </td><td> [[Image:MOM2.png|thumb|360px|The surface mesh of the radiation pattern dialogdielectric cylinder and PEC plate.]] </td></tr></table>

Radiation pattern of If the project workspace contains a 4-element dipole array: (Left) computed using array factor and (Right) computed by simulating an array line object, the wireframe mesh generator is used to discretize your physical structure. From the point of view of this mesh generator, all PEC surface objects and PEC solid objects are treated as wireframe objects. If you want to model a wire radiator connected to a metal surface, you have to make sure that the resulting wireframe mesh of the surface has a node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[EM.Cube]]'s polymesh objects to accomplish this objective.

[[File:wire_pic49.png|thumb|300px|[[MoM3D Module]]You can convert any surface object or solid object to a polymesh using CubeCAD's RCS dialog]] '''Polymesh Tool'''.

When the wire-frame structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields[[Image:Info_icon. png|30px]] Click here to learn more about '''[[EMGlossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool |Converting Object to Polymesh]]''' in [[EM.CUBECube]] calculates the radar cross section (RCS) of a target, which is defined in the following manner:.

:<math> \sigma = 4\pi R^2 \cdot \frac{|E_{scat}|^2}{|E_{inc}|^2} </math><!--Once an object is converted to a polymesh, you can place your wire at any of its nodes. In that case, [[File:rcs_equationEM.pngLibera]]-->'s Wire MoM engine will sense the coincident nodes between line segments and will create a junction basis function to ensure current continuity.

[[EM.Cube|EM.CUBE]] calculates three RCS quantities: the &phi; and &theta; components of the radar cross section as well as the total radar cross section: &sigma;<subtable>&theta;</subtr>, &sigma;<subtd>&phi;</sub>, and &sigma;_tot. In addition, [[EMImage:MOM4.Cubepng|thumb|EM360px|Geometry of a monopole wire connected to a PEC plate.CUBE]] [[MoM3D Module]] calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;_{0</subtd> and &phi;<subtd>0} and the RCS is measured and plotted at all &theta; and &phi; angles[[Image:MOM5. In mono-static RCS, png|thumb|360px|Placing the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀ and wire on the RCS is measured and plotted at polymesh version of the echo angles 180°-&theta;<sub>0PEC plate.]] </subtd> and &phi;<sub>0</subtr>.It is clear that in the case of mono-static RCS, the Wire MoM simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &theta;<sub>0</subtable> and &phi;₀ are varied over the intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. Right click on the '''Far Fields''' item == Running 3D MoM Simulations in the '''Observables''' section of the Navigation Tree and select '''Insert New RCSEM...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''. The former is the default choice. The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By default, the &theta; and &phi; angles are incremented by 5 degrees. At the end of a Wire MoM simulation, besides calculating the RCS data over the entire (spherical) 3-D space, a number of 2-D RCS graphs are also generated. These are RCS cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant &phi;-cut. This latter cut is at &phi;Libera ==45° by default. You can assign another phi angle in degrees in the box labeled '''Non-Principal Phi Plane'''.

At the end of a Wire MoM simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_totare added under the far field section of the Navigation Tree. These plots are very similar to the three 3-D radiation pattern plots. You can view them by clicking on their names in the navigation tree. The RCS values are expressed in m². For visualization purposes, the 3-D plots are normalized to the maximum RCS value, which is also displayed in the legend box. The 2-D RCS graphs can be plotted from [[=== EM.Cube|EM.CUBE]]Libera's data manager exactly in the same way that you plot 2-D radiation pattern graphs. A total of eight 2-D RCS graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, [[EM.Cube|EM.CUBE]] calculates some other quantities including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable). In this case, the RCS needs to be computed at a fixed pair of phi and theta angles. These angles are specified in degrees as '''User Defined Azimuth &amp; Elevation''' in the &quot;Output Settings&quot; section of the '''Radar Cross Section Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith.Simulation Modes ===

{{Note|Computing Once you have set up your structure in [[EM.Libera]], have defined sources and observables and have examined the 3-D mono-static RCS may take an enormous amount quality of computation timethe structure's mesh, you are ready to run a 3D MoM simulation. [[EM.}}Libera]] offers five simulation modes:

{| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[File#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:wire_pic50_tn270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|}

Figure: You can set the simulation mode from [[EM.Libera]]'s "Simulation Run Dialog". A halfsingle-wave wire connected to frequency analysis is a metal plate illuminated by an obliquely incident plane wavesingle-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

The RCS of the wireIn a single-plate structure: (Left) &sigma;_&theta;frequency analysis, (Center) &sigma;_&phi; the structure of your project workspace is meshed at the center frequency of the project and (Right) total RCSanalyzed by one of [[EM.Libera]]'s two MoM solvers. If your project contains at least one line or curve object, the Wire MoM solver is automatically selected. Otherwise, the Surface MoM solver will always be used to simulate your numerical problem. In either case, the engine type is set automatically.

=== Customizing To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, the Surface MoM solver is selected as your simulation engine. To start the simulation, click the {{key|Run}} button of this dialog. Once the 3D Plots === MoM simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of MoM simulation, displays the running time and shows the percentage of completion for certain tasks during the MoM simulation process. A prompt announces the completion of the MoM simulation.

Similar to the current distribution and field sensor plots, <table><tr><td> [[EMImage:Libera L1 Fig13.Cubepng|thumb|left|480px|EM.CUBE]]Libera's 3-D radiation pattern plots are interactive. When you move Simulation Run dialog showing Wire MoM engine as the mouse over a pattern plot, tiny dots appear on its surfacesolver. These dots correspond to the theta-phi angle pairs on the surface of the unit sphere where the far field data have been calculated]] </td></tr><tr><td> [[Image:MOM3D MAN10. Upon mouse-over, you can highlight one of these pointspng|thumb|left|480px|EM. A small tooltip appears on Libera's Simulation Run dialog showing Surface MoM engine as the plot that shows the normalized far field value in that directionsolver.]] </td></tr></table>

Reading far field values from MoM simulations involve a 3-D radiation pattern plot number of numerical parameters that normally take default values unless you change them. You can access these parameters and change their values by mouse-overclicking on the '''Settings''' button next to the &quot;Select Engine&quot; dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.

You can change First we discuss the type of the 3-D radiation pattern plot through Wire MoM Engine Settings dialog. In the '''Radiation Pattern DialogSolver'''. The plot type change applies to all the three nodes: theta component, phi component and total field patterns. In the 3D Display Type section of this dialog , you can choose from three options: the type of '''3D PolarLinear Solver''', which is the default choice, . The current options are '''Spherical MapLU''' and '''ConeBi-Conjugate Gradient (BiCG)'''. In the last two cases, the far field values are plotted on the surface of the unit sphere, where each point correspond to The LU solver is a (&theta;, &phi;) pair. In direct solver and is the spherical map, the curved cells default option of the unit sphere are colored based on their field valueWire MoM solver. In the cone-type plot, a vectorial visualization of the far fields The BiCG solver is generatediterative. In the last caseIf BiCG is selected, you have to set a '''Tolerance''' for its convergence. You can also set change the size maximum number of the cones that represent the far field vectorsBiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''.

<table><tr><td> [[FileImage:wire_pic42_tnMOM9B.png]] [[File:wire_pic43_tn|thumb|left|480px|EM.Libera's Wire MoM Engine Settings dialog.png]]</td></tr></table>

The spherical map Surface MoM Engine Settings dialog is bit more extensive and cone provides more options. In the "Integral Equation" section of the dialog, you can choose among the three PEC formulations: EFIE, MFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is &alpha; = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional parameters: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, [[EM.Libera]] uses an acceleration technique called the Adaptive Integral Method (vectorialAIM) versions of to speed up the radiation pattern show linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05&lambda;₀. [[EM.Libera]]'s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the previous figureinstaller program also installs the Windows MPI package on your computer. If you are using a multicore CPU, taking advantage of the MPI-parallelized solver can speed up your simulations significantly. In the "MPI Settings" of the dialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.

Just like current distribution For both Wire MoM and field sensor plotsSurface MoM solvers, each individual 3-D radiation pattern plots has an you can instruct [[EM.Libera]] to write the contents of the MoM matrix and excitation and solutions vectors into data files with '''.DAT1''' file extensions. These files can be accessed from the '''Input/Output Settings DialogFiles'''tab of the Data Manager. In both case, from which you can further customize have the option to uncheck the check box labeled "Superpose Incident plane Wave Fields". This option applies when your structure is excited by a plane wave source. When checked, the field sensors plot's scale (linear vsthe total electric and magnetic field distributions including the incident field. dB)Otherwise, lower only the scattered electric and upper limits and color map typemagnetic field distributions are visualized.

At the end of a Wire MoM simulation, the radiation pattern data E_&theta;, E_&phi;, and E<sub>tot<br /sub> in the three principal XY, YZ and ZX planes as well as an additional user defined phi plane cut are available for plotting on 2-D graphs. There are a total of eight 2D pattern graphs in the data manager: 4 polar graphs and 4 Cartesian graphs of the same pattern data. To open data manager, click the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[File:larrow_tn.png]]Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. In the Data manager Dialog, you will see a list of all the data files available for plotting. These include the four polar pattern data files with a '''.ANG''' file extension and the four Cartesian pattern data file with a '''.DAT''' file extension. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph.

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The data manager dialog showing a list of 2-D polar and Cartesian radiation pattern graphs[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Tutorial Gateway]]'''

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