[[Image:Splash-mom.jpg|right|800px720px]]
<strong><font color="#06569f" size="4">3D Wire MoM And Surface MoM Solvers For Simulating Free-Space Structures</font></strong>
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<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=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:postatic-ico.png | link=EM.IlluminaFerma]] [[image:staticplanar-ico.png | link=EM.FermaPicasso]] [[image:planarpo-ico.png | link=EM.PicassoIllumina]] </td>
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[[Image:Tutorial_icon.png|40px30px]] '''[[EM.Cube#EM.Libera_Tutorial_Lessons Libera_Documentation | EM.Libera Tutorial Gateway]]'''
[[Image:Back_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==
[[Image:MOMTUT4 17.png|thumb|500px|3D far-field radiation pattern of the expanded Yagi-Uda antenna array with 13 directors.]]
=== EM.Libera in a Nutshell ===
[[EM.Libera ]] is a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structures made up of metal and dielectric regions or a combination of them. It features two separate simulation engines, a Surface MoM solver and a Wire MoM solver, that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric objects in your physical structure. The Wire MoM solver can only handle metallic wireframe structures. [[EM.Libera ]] selects the simulation engine automatically based on the types of objects present in your project workspace.
[[Image:Tutorial_iconEM.png|40pxLibera]] Click here to access offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's integral equation. The Surface MoM solver uses a number of surface integral equation formulations of Maxwell''[[EMs equations.Cube#EMIn particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions.Libera_Tutorial_Lessons | EMOn the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions.Libera Tutorial Gateway]]'''Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.
=== {{Note|In general, [[EM.Tempo as Libera]] uses the FDTD Module of surface MoM solver to analyze your physical structure. If your project workspace contains at least one line or curve object, [[EM.Cube ===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 Moments]]'''.
Note<table><tr><td>[[Image:Yagi Pattern.png|thumb|500px|You can use EM.Libera either for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structures. EM.Libera also serves as the frequencyfar-domain, full-wave '''[[MoM3D Module]]''' field radiation pattern of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Libera shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCAD]]''' expanded Yagi-Uda antenna array with all of [[EM13 directors.Cube]]'s other computational modules.</td></tr></table>
[[Image:Info_icon=== EM.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.CUBE | Libera as the MoM3D Module of EM.Cube Modeling Environment]]'''.===
You can use [[EM.Libera]] either for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structures. [[EM.Libera]] also serves as the frequency-domain, full-wave '''MoM3D Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Libera]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules. [[Image:Info_icon.png|40px30px]] Click here to learn more about the basic functionality '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''. === Advantages & 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 [[CubeCADEM.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 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.Libera]]'s Wire MoM solver can be used to simulate thin wires and wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of the current limitations of [[EM.Libera]], however, is its inability to mix wire structures with dielectric objects. If your physical structure contains one ore more wire objects, then all the PEC surface and solid CAD objects of the 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 slow convergence of the iterative linear solver for such types of numerical problems. Since [[EM.Libera]] uses a surface integral equation formulation of dielectric objects, it can only handle homogeneous dielectric regions. For structures that involve multiple interconnected dielectric and metal regions such as planar circuits, it is highly recommended that you use either [[EM.Tempo]] or [[EM.Picasso]] instead. <table><tr><td>[[Image:Hemi current.png|thumb|500px|The computed surface current distribution on a metallic dome structure excited by a plane wave source.]] </td></tr></table>
== EM.Libera Features at a Glance ==
Metal surfaces and solids in free space</li>
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Homogeneous dielectric [[Solid Objects|solid objects]] in free space</li>
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Import STL CAD files as native polymesh structures</li>
Export wireframe structures as STL CAD files</li>
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Â
[[Image:MOMTUT5 28.png|thumb|500px|The surface electric current distribution on a pyramidal horn antenna.]]
=== Sources, Loads & Ports ===
Plane wave excitation with linear and circular polarizations</li>
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Multi-Ray excitation capability (ray data imported from [[Propagation ModuleEM.Terrano]] or external files)</li>
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Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li>
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== A 3D Mom Simulation Primer ==Â === An Overview of 3D Method Of Moments =Building the Physical Structure in EM.Libera ==
The Method All the objects in your project workspace are organized into object groups based on their material composition and geometry type in the "Physical Structure" section of Moments (MoM) is a rigorous, full-wave, numerical technique for solving open boundary electromagnetic problemsthe navigation tree. Using this techniqueIn [[EM.Libera]], you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method create three different types of moments is an integral equation technique; it solves the integral form of Maxwellâs equations as opposed to their differential forms used in the finite element or finite difference time domain methods.objects:
In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns {| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:150px;" | [[Glossary of the problemEM. The given structure is immersed in the free spaceCube's 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 the unbounded background medium is modeled using the freecurve objects| None|-space Green's functions| style="width:30px;" | [[File:thin_group_icon. The unknown physical or equivalent currents are discretized as a collection png]]| style="width:150px;" | [[Glossary of elementary currents with small finite spatial extentsEM. Such elementary currents are called basis functionsCube's Materials, Sources, 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. They obviously have a vectorial nature and must satisfy png]]| style="width:150px;" | [[MaxwellGlossary of EM.Cube's EquationsMaterials, Sources, Devices & Other Physical Object Types#Dielectric Material |Maxwell's equationsDielectric Material]] and the relevant boundary conditions individually| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface MoM solver only |-| style="width:30px;" | [[File:Virt_group_icon. The actual currents on the surface png]]| style="width:150px;" | [[Glossary of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents with initially unknown amplitudesEM. Through the MoM solutionCube's Materials, you find these unknown amplitudesSources, from which you can then calculate the currents or fields everywhere in the structure.Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects| None |}
EM.Libera offers two distinct 3D MoM simulation engines. The Wire MoM solver is based Click on Pocklington's integral equation. The Surface MoM solver uses a number of surface integral equation formulations of each category to learn more details about it in the [[MaxwellGlossary of EM.Cube's Equations|Maxwell's equationsMaterials, Sources, Devices & Other Physical Object Types]]. 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 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 the dielectric objects to formulate their assocaited interior and exterior boundary value problems.
{{Note|In general, Both of [[EM.Libera uses the surface ]]'s two simulation engines, Wire MoM and Surface MoM solver to analyze your physical structure. If your project workspace contains at least one line or curve object, EMcan handle metallic structures.Libera switches to the You define wires under '''Thin Wire MoM solver''' groups and surface and volumetric metal objects under '''PEC Objects'''.}} [[Image:Info_iconIn other words, you can draw lines, polylines and other curve objects as thin wires, which have a radius parameters expressed in project units.png|40px]] Click here to learn more about the theory All types of solid and surface CAD objects can be drawn in a PEC group. Only solid CAD objects can be drawn under '''[[3D Method of Moments]]Dielectric Objects'''.
=== Advantages & Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===<table><tr>The method of moments uses an open-boundary formulation of [[Maxwell's Equations|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 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.Libera's Wire MoM solver can be used to simulate thin wires and wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of the current limitations of EM.Libera, however, is its inability to mix wire structures with dielectric objects. If your physical structure contains one ore more wire objects, then all the PEC surface and solid CAD objects of the 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 slow convergence of the iterative linear solver for such types of numerical problems. Since EM.Libera uses a surface integral equation formulation of dielectric objects, it can only handle homogeneous dielectric regions. For structures that involve multiple interconnected dielectric and metal regions such as planar circuits, it is highly recommended that you use either [[EM.Tempo]] or [[EM.Picasso]] instead. == Building the Physical Structure in EM.Libera ==<td>[[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] All the objects in your project workspace are organized into object groups based on their material composition and geometry type in the "Physical Structure" section of the navigation tree. In EM.Libera, you can create three different types of objects (click on each type to learn more about it):</td></tr>* '''[[Defining_Materials_in_EM.Cube#Perfect_Electric_Conductors_.26_Metal_Traces | Perfect Electric Conductor (PEC) Objects]]'''* '''[[Defining_Materials_in_EM.Cube#Thin_Wires | Thin Wires]]'''* '''[[Defining_Materials_in_EM.Cube#Defining_Dielectric_Materials | Dielectric Objects]]''' Both of EM.Libera's two simulation engines, Wire MoM and Surface MoM, can handle metallic structures. You define wires under '''Thin Wire''' groups and surface and volumetric metal objects under '''PEC Objects'''. In other words, you can draw lines, polylines and other [[Curve Objects|curve objects]] as thin wires, which have a radius [[parameters]] expressed in project units. All types of solid and surface CAD objects can be drawn in a PEC group. Only solid CAD objects can be drawn under '''Dielectric Objects'''.  [[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Defining Materials in EM.Cube]]'''.</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 [[EM.Libera]] 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.
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Defining_Materials_in_EM.CubeBuilding Geometrical Constructions in CubeCAD#Defining_a_New_Material_Group Transferring Objects Among Different Groups or Modules | Defining a New Object GroupMoving Objects among Different Groups]]'''.
{{Note|In [[Image:Info_iconEM.png|40pxCube]] Click here , you can import external CAD models (such as STEP, IGES, STL models, etc.) only to learn more about '''[[Defining_Materials_in_EMBuilding_Geometrical_Constructions_in_CubeCAD | CubeCAD]].Cube#Moving_Objects_among_Material_Groups From [[Building_Geometrical_Constructions_in_CubeCAD | Moving Objects among Material GroupsCubeCAD]], you can then move the imported objects to [[EM.Libera]]'''.}}
{{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[CubeCAD]]. From [[CubeCAD]], you can then move the imported objects to == EM.Libera.}}'s Excitation Sources ==
== Your 3D Mesh Generation ==physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, electric surface currents on metal surface and both electric magnetic surface currents on the surface of dielectric objects. The excitation source you choose depends on the observables you seek in your project. [[EM.Libera]] provides the following source types for exciting your physical structure:
{| class="wikitable"|-! scope="col"| Icon! scope= A Note on "col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of EM.LiberaCube's Mesh 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|}
Click on each category to learn more details about it in the [[Glossary of EM.Libera features two simulation enginesCube's Materials, Wire MoM and Surface MoMSources, 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 connection points between two or more wires, junction basis functions are generated to ensure current continuityDevices & Other Physical Object Types]].
On the other handsFor antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera's Surface MoM solver requires a triangular surface mesh ]] provides two types of surface lumped sources: strip gap and [[Solid Objects|solid 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 mesh generating algorithm tries to generate regularized triangular cells gap splits the wire into two lines with almost equal surface areas a an infinitesimally small spacing between them, across which the entire structureideal voltage source is connected. You can control Strip gap sources must be placed on long, narrow, '''PEC Rectangle Strip''' objects to provide excitation for the cell size using the "Mesh Density" parameterSurface MoM solver. By defaultThe gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the mesh density ideal voltage source is expressed in terms of the free-space wavelengthconnected. The default mesh density is 10 cells per wavelength. For meshing surfaces, Only narrow rectangle strip object that have a single mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you cell across their width can base the definition of the mesh density on "Cell Edge Length" expressed in project unitsbe used to host a gap source.
[[Image:Info_icon.png{{Note|40px]] Click here If you want to learn more about '''excite a curved wire antenna such as a circular loop or helix with a wire gap source, first you have to convert the curve object into a polyline using [[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator CubeCAD]]'''s Polygonize Tool.}}
A short dipole provides another simple way of exciting a 3D structure in [[Image:Info_iconEM.png|40pxLibera]] Click here . A short dipole source acts like an infinitesimally small ideal current source. You can also use an incident plane wave to learn more about excite your physical structure in [[EM.Libera's ''']]. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[Mesh_Generation_Schemes_in_EMEM.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator ]]'''computational module.
[[Image:Info_icon.png|40px]] Click here to learn more about EM.Libera's '''[[Mesh_Generation_Schemes_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#The_Linear_Wireframe_Mesh_Generator Modeling_Finite-Sized_Source_Arrays | Linear Wireframe Mesh Generator Using Source Arrays in Antenna Arrays]]'''.
=== Mesh of Connected Objects === <table><tr><td> [[Image:MOM3wire_pic14_tn.png|thumb|300pxleft|EM.Libera's Mesh Hierarchy dialog.]] All the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping [[Solid Objects640px|solid objects]], their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the [[Surface Objects|surface objects]] belonging to the same PEC group are merged together and their internal edges are removed before meshing. Note that a solid and a surface object belonging to the same PEC group might not always be merged properly. Â 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 example, the figure below shows a dielectric cylinder sitting A wire gap source placed on top one side of a PEC plate. The two object share polyline representing a polygonized circular area at the base of the cylinderloop. Are the cells on this circle metallic or do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, EM.Libera does provide a "Material Hierarchy" table, which you can modify. To access this table, select '''Menu ]] </td> Simulate < discretization /tr>< Mesh Hierarchy...'''. The PEC groups by default have the highest priority and reside at the top of the tr></table. You can select an group from the table and change its hierarch 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> [[Image:MOM1po_phys16_tn.png|thumb|360pxleft|A dielectric cylinder attached to 420px|Illuminating a PEC plate.]] </td><td> [[Image:MOM2.png|thumb|360px|The surface mesh of the dielectric cylinder and PEC platemetallic sphere with an obliquely incident plane wave source.]] </td>
</tr>
</table>
=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces Modeling Lumped Circuits ===
If the project workspace contains a line object, the wireframe mesh generator is used to discretize your physical structure. From the point of view of this mesh generator, all PEC In [[Surface Objects|surface objectsEM.Libera]] and PEC [[Solid Objects|solid objects]] are treated , you can define simple lumped elements in a similar manner as wireframe objectsgap sources. If you want to model In fact, a wire radiator connected lumped element is equivalent to a metal surface, you have to make sure an infinitesimally narrow gap that is placed in the resulting wireframe mesh path of the surface has current, across which Ohm's law is enforced as a node exactly at the location where you want 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 connect your excite a wirestructure or metallic strip and model a non-ideal voltage source with an internal resistance. This is not guaranteed automatically. However, you can use [[EM.CubeLibera]]'s polymesh objects to accomplish this objectivelumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:
{{Note|In [[EMImage:Info_icon.Cubepng|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]], polymesh objects are regards as already-meshed objects and are not re-meshed again during a simulation'''.}}
You can convert any surface object or solid object to a polymesh using [[CubeCADImage:Info_icon.png|40px]]Click here for a general discussion of 's '''Polymesh Tool[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''.
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Discretizing_Objects#Converting_Objects_to_Polymesh | Converting Object to Polymesh]]''' in [[EM.Cube]].=== Defining Ports ===
Once an object is converted Ports are used to a polymeshorder and index gap sources for S parameter calculation. They are defined in the '''Observables''' section of the navigation tree. By default, you as many ports as the total number of sources are created. You can place your wire at define any number of its nodesports equal to or less than the total number of sources. In that case, EMAll port impedances are 50Ω by default.Libera's Wire MoM engine will sense the coincident nodes between line segments and will create a junction basis function  [[Image:Info_icon.png|40px]] Click here to ensure current continuitylearn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''.
<table>
<tr>
<td> [[Image:MOM4MOM7A.png|thumb|360px|Geometry of Two metallic strips hosting a monopole wire connected to gap source and a PEC platelumped element.]] </td><td> [[Image:MOM5MOM7B.png|thumb|360px|Placing the wire on the polymesh version The surface mesh of the PEC platetwo strips with a gap source and a lumped element.]] </td>
</tr>
</table>
== Excitation Sources EM.Libera's Simulation Data & Observables ==
At the end of a 3D MoM simulation, [[ImageEM.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:MOM6B {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]|thumbstyle="width:150px;" |320pxCurrent Distribution Maps|style="width:150px;" | [[Glossary of EM.LiberaCube's Strip Gap Source dialog.Simulation Observables & Graph Types#Current Distribution |Current Distribution]] Your 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, | style="width:300px;" | Computing electric surface currents current distribution on metal surface and both electric dielectric objects, magnetic surface currents current distribution on the surface of dielectric objectsand linear current distribution on wires| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon. The excitation source you choose depends 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 the observables you seek a specified plane in your projectthe 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.Libera provides Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the following 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 types for exciting your physical structure |-| 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 (click 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 each type a box to learn more about it)be used later as a Huygens source in other [[EM.Cube]] modules| style="width: 250px;" | None|}
* '''Click on each category to learn more details about it in the [[Common_Excitation_Source_Types_in_EMGlossary of EM.Cube#Lumped_.26_Gap_Sources | Strip Gap Sources]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Lumped_.26_Gap_Sources | Wire Gap Sourcess Simulation Observables & Graph Types]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Hertzian_Dipole_Sources |Short Dipole Sources]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Plane_Wave_Sources | Plane Wave Sources]]'''* '''[[Hybrid_Modeling_using_Multiple_Simulation_Engines#Working_with_Huygens_Sources | Huygens Sources]]'''
For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. EM.Libera provides two types of lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed Depending on the path types 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 solverpresent in your project workspace, [[EM. The gap splits the wire into two lines with Libera]] performs either 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.  {{Note|If you want to excite a curved wire antenna such as a circular loop simulation or helix with a wire gap source, first you have to convert the curve object into a polyline using [[CubeCAD]]'s Polygonize 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 also use an incident plane wave to excite your physical structure in EM.LiberaWire MoM simulation. In particularthe former case, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ electric and φ angles of magnetic surface current distributions on the unit propagation vector in the spherical coordinate system. The default values surface of the incidence angles are θ = 180° PEC and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vectordielectric objects can be visualized. Huygens sources are virtual equivalent sources that capture In the latter case, the radiated linear electric currents on all the wires and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.  [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.Cube#Defining_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'''wireframe objects can be plotted.
<table>
<tr>
<td> [[Image:wire_pic14_tnwire_pic26_tn.png|thumb|600px360px|A wire gap source placed on one side of monopole antenna connected above a polyline representing a polygonized circular loopPEC plate.]] </td><td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate.]] </td>
</tr>
<tr>
</table>
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{{Note|Keep in mind that since [[EM.Libera]] uses MoM solvers, the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}
<table>
<tr>
<td> [[Image:MOM8wire_pic32_tn.png|thumb|360px|EM.Libera's Plane Wave dialogElectric field plot of the circular loop antenna.]] </td><td> [[Image:po_phys16_tnwire_pic33_tn.png|thumb|360px|Illuminating a metallic sphere with an obliquely incident plane wave sourceMagnetic field plot of the circular loop antenna.]] </td>
</tr>
</table>
=== Modeling Lumped Circuits === You need to define a far field observable if you want to plot radiation patterns of your physical structure in [[EM.Libera]]. After a 3D 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.
In EM[[Image:Info_icon.Libera, you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent png|30px]] Click here to an infinitesimally narrow gap that is placed in learn more about the path theory 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 ''[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance. EM.LiberaModel Antenna Arrays ]]'''s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:
<table><tr><td> [[Image:Info_iconwire_pic38_tn.png|40pxthumb|230px|The 3D radiation pattern of the circular loop antenna: Theta component.]] Click here to learn more about '''</td><td> [[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EMImage:wire_pic39_tn.Cube#Defining_Lumped_Elements_in_EMpng|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi component.Picasso_.26_EM]] </td><td> [[Image:wire_pic40_tn.Libera png| Defining Lumped Elementsthumb|230px|The total radiation pattern of the circular loop antenna.]]'''.</td></tr></table>
When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[Image:Info_iconEM.png|40pxLibera]] Click here for calculates the radar cross section (RCS) of a general discussion target. Three RCS quantities are computed: the θ and φ components of '''the radar cross section as well as the total radar cross section, which are dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. In addition, [[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EMEM.Cube#Linear_Passive_Devices | Linear Passive DevicesLibera]]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 θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.
=== Defining Ports === To 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 σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree.
Ports are used to order and index gap sources for S parameter calculation. They are defined in {{Note| The 3D RCS plot is always displayed at the '''Observables''' section origin of the navigation tree. By defaultspherical coordinate system, as many ports as (0,0,0), with respect to which the total number of sources are createdfar radiation zone is defined. You can define any number of ports equal to or less than Oftentimes, this might not be the total number scattering center of sources. All port impedances are 50Ω by defaultyour physical structure.}}
[[Image:Info_icon.png{{Note|40px]] Click here to learn more about Computing the '''[[Common_Excitation_Source_Types_in_EM.Cube#The_Port_Definition_Observable | Port Definition Observable]]'''3D mono-static RCS may take an enormous amount of computation time.}}
<table>
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<td> [[Image:MOM7Awire_pic51_tn.png|thumb|360px230px|Two metallic strips hosting The RCS of a gap source and metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a lumped elementmetal plate structure: σ<sub>φ</sub>.]] </td><td> [[Image:MOM7Bwire_pic53_tn.png|thumb|360px230px|The surface mesh total RCS of the two strips with a gap source and a lumped elementmetal plate structure: σ<sub>tot</sub>.]] </td>
</tr>
</table>
== Running 3D MoM Simulations Mesh Generation in EM.Libera ==
=== A Note on EM.Libera's Simulation Modes Mesh Types ===
Once you have set up your structure in [[EM.Libera]] features two simulation engines, have defined sources and observables Wire MoM and have examined the quality of the structure's meshSurface MoM, you which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are ready discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to run a 3D MoM simulationmesh density criterion. EM.Libera offers five simulation modes (click on each type Curved wires are first converted to learn multi-segment polylines and then subdivided further if necessary. At the connection points between two or more about it):wires, junction basis functions are generated to ensure current continuity.
* '''On the other hands, [[#Running a Single-Frequency MoM Analysis | Single-Frequency Analysis]]'''* '''[[Parametric_Modeling,_Sweep_%26_Optimization#Running_Frequency_Sweep_Simulations_in_EMEM.Cube | Frequency SweepLibera]]''' including uniform s Surface MoM solver requires a triangular surface mesh of surface and adaptive frequency sweeps * '''[[Parametric_Modelingsolid 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,_Sweep_%26_Optimization#Running_Parametric_Sweep_Simulations_in_EMthe mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength.Cube | Parametric Sweep]]'''* '''[[Parametric_ModelingFor meshing surfaces,_Sweep_%26_Optimization#Optimization | Optimization]]'''* '''[[Building_Reusable_Models#Running_an_HDMR_Sweep | HDMR Sweep]]'''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.
You can set the simulation mode from EM.Libera's "Simulation Run Dialog". A single-frequency analysis is a single-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 [[parametersImage:Info_icon.png|30px]] are varied and a collection of simulation data files are generatedClick here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. At the end of a sweep simulation, you can graph the simulation results in EMCube.Grid or you can animate the 3D simulation data from the navigation tree27s_Mesh_Generators | Working with Mesh Generator]]'''.
=== Running a Single-Frequency MoM Analysis === Â In a single-frequency analysis, the structure of your project workspace is meshed at the center frequency of the project and analyzed 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. Â To open the Run Simulation Dialog, click the '''Run''' [[FileImage:run_iconInfo_icon.png|30px]] button of the Click here to learn more about '''Simulate Toolbar''' or select '''Menu > Simulate > Run..[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Libera''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, the s Triangular Surface MoM solver is selected as your simulation engine. To start the simulation, click the {{key|Run}} button of this dialog. Once the 3D MoM simulation starts, a new dialog called Mesh Generator ]]'''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.
<table>
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<td> [[Image:MOM9CMesh5.png|thumb|360px400px|EM.Libera's Simulation Run Mesh Settings dialog showing Wire MoM engine as the solver.]] </td><td> [[Image:MOM9A.png|thumb|360px|EM.Libera's Simulation Run dialog showing Surface MoM engine as parameters of the solverlinear wireframe mesh generator.]] </td>
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</table>
=== Setting MoM Numerical Parameters The Linear Wireframe Mesh Generator ===  [[Image:MOM9B.png|thumb|360px|EM.Libera's Wire MoM Engine Settings dialog.]] MoM simulations involve a number 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 "Select Engine" 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. First we discuss the Wire MoM Engine Settings dialog. In the '''Solver''' section of this 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 Wire MoM solver. The BiCG solver is iterative. If BiCG is 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 Surface MoM Engine Settings dialog is bit more extensive and provides more options. In the "Integral Equation" section of the dialog, you 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 α = 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 analyze metallic wire structures very accurately with utmost computational efficiency using [[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 (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. EM.Libera]]'s Surface Wire MoM solver has been highly parallelized using MPI frameworksimulator. When you install structure contains at least one PEC line, polyline or any curve CAD object, [[EM.CubeLibera]] on your computer, 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 installer program specified mesh density. It also installs the polygonizes rounded [[WindowsCurve Objects|curve objects]] MPI package on your computer. If you into polylines with side lengths that are using a multicore CPU, taking advantage of determined by the MPI-parallelized solver can speed up your simulations significantlyspecified mesh density. In the "MPI Settings" Note that polygonizing operation is temporary and solely for he purpose of the dialogmesh generation. As for surface and solid CAD objects, you can set the "Number a wireframe mesh of CPU's Used", these objects is created which has consists of a default value large number of 4 coresinterconnected linear (wire) elements.
For both Wire MoM and Surface MoM solvers, you can instruct EM{{Note| The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool.Libera to write the contents of the MoM matrix It also discretizes surface and excitation and solutions vectors into data files with solid CAD objects temporarily using CubeCAD'''.DAT1''' file extensions. These files can be accessed from the '''Input/Output Files''' tab of the Data Manager. In both case, you 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 the total electric and magnetic field distributions including the incident field. Otherwise, only the scattered electric and magnetic field distributions are visualizeds Polymesh tool. }}
<table>
<tr>
<td> [[Image:MOM9Mesh6.png|thumb|600px200px|EMThe geometry of an expanding helix with a circular ground.Libera's Surface MoM Engine Settings dialog]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the helix with the default mesh density of 10 cells/λ<sub>0</sub>.]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 25 cells/λ<sub>0</sub>.]] </td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/λ<sub>0</sub>.]] </td>
</tr>
</table>
== Working with 3D MoM Simulation Data = Mesh of Connected Objects ===
At All the end of a 3D MoM simualtion, EM.Libera generates a number of output data files that contain all objects belonging to the computed simulation datasame PEC or dielectric group are merged together using the Boolean union operation before meshing. The primary solution of If your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and only the Wire MoM simulation engine consists surface of the linear electric currents on the wires and wireframe structuresexternal faces is meshed. The primary solution of Similarly, all the Surface MoM simulation engine consists of the electric and magnetic surface currents on objects belonging to the same PEC group are merged together and dielectric objectstheir internal edges are removed before meshing. EM.Libera currently offers the following types of observables (click on each type to learn more about it): * '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Current Distributions]]''': Electric Note that a solid and magnetic a surface current amplitude and phase on all metal and dielectric surfaces and electric current amplitude and phase on all wires * '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Near-Field Distributions]]''': Electric and magnetic field amplitude and phase on specified planes and their central axes* '''[[Data_Visualization_and_Processing#Computing_and_Graphing_Port_Characteristics | Port Characteristics]]''': S, Z and Y [[Parameters]] and Voltage Standing Wave Ratio (VSWR)* '''[[Data_Visualization_and_Processing#Far-Field_Observables | Radiation Characteristics]]''': Radiation Patterns, Directivity, Total Radiated Power, Axial Ratio, Main Beam Theta and Phi, Radiation Efficiency, Half Power Beam Width (HPBW), Maximum Side Lobe Level (SLL), First Null Level (FNL), Front-object belonging to-Back Ratio (FBR), etcthe same PEC group might not always be merged properly.* '''[[Data_Visualization_and_Processing#Computing_Radar_Cross_Section | Radar Cross Section (RCS)]]''': Bi-static and Mono-static Radar Cross Section (RCS)
If the project structure is excited by gap sources, and one When two objects belonging to two different material groups overlap or more ports have been definedintersect each other, [[EM.Libera calculates ]] has to determine how to designate the scattering (S) overlap or common volume or surface. As an example, 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 do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, [[parametersEM.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 the highest priority and reside at the top of the selected ports, all based on table. You can select an group from the port impedances specified in table and change its hierarchy using the project's "Port Definition"{{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.
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Computing_and_Graphing_Port_Characteristics | Computing and Graphing Port Characteristics]]'''.<table><tr><td> [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Rational_Interpolation_of_Port_Characteristics | Rational Interpolation of Scattering Parameters]]'''. [[Image:MOM10MOM3.png|thumb|350px300px|EM.Libera's Current Distribution Mesh Hierarchy dialog.]] </td></tr>Depending on the types of objects present in your project workspace, EM.Libera 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.  [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''.</table>
<table>
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<td> [[Image:wire_pic26_tnMOM1.png|thumb|360px|A monopole antenna connected above dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:wire_pic27_tnMOM2.png|thumb|360px|Current distribution plot The surface mesh of the monopole antenna connected above the dielectric cylinder and PEC plate.]] </td>
</tr>
</table>
[[Image:MOM11.png|thumb|350px|EM.Libera's Field Sensor dialog.]]=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===
EM.Libera allows you to visualize If the near fields at project workspace contains a specific field sensor plane of arbitrary dimensionsline object, the wireframe mesh generator is used to discretize your physical structure. Calculation From the point of near fields is a post-processing process view of this mesh generator, all PEC surface objects and may take PEC solid objects are treated as wireframe objects. If you want to model a considerable amount wire radiator connected to a metal surface, you have to make sure that the resulting wireframe mesh of time depending on the resolution that surface has a node exactly at the location where you specifywant to connect your wire. This is not guaranteed automatically. However, you can use [[EM.Cube]]'s polymesh objects to accomplish this objective.
{{Note|Keep in mind that since In [[EM.Libera uses MoM solversCube]], the calculated field value at the source point is infinite. As polymesh objects are regarded as already-meshed objects and are not re-meshed again during a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable resultssimulation.}}
[[Image:Info_icon.png|40px]] Click here You can convert any surface object or solid object to learn more about a polymesh using CubeCAD's ''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Defining a Field Sensor Observable]]'Polymesh Tool'''.
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingGlossary_of_EM.Cube%27s_CAD_Tools#Visualizing_3D_Near-Field_Maps Polymesh_Tool | Visualizing 3D Near Field MapsConverting Object to Polymesh]]'''in [[EM.Cube]]. Once an object is converted to a polymesh, you can place your wire at any of its nodes. In that case, [[EM.Libera]]'s Wire MoM engine will sense the coincident nodes between line segments and will create a junction basis function to ensure current continuity.
<table>
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<td> [[Image:wire_pic32_tnMOM4.png|thumb|360px|Electric field plot Geometry of the circular loop antennaa monopole wire connected to a PEC plate.]] </td><td> [[Image:wire_pic33_tnMOM5.png|thumb|360px|Magnetic field plot Placing the wire on the polymesh version of the circular loop antennaPEC plate.]] </td>
</tr>
</table>
[[Image:MOM12.png|thumb|380px|== Running 3D MoM Simulations in EM.Libera's Radiation Pattern dialog.]]==
You need to define a far field observable if you want to plot radiation patterns of your physical structure in === EM.Libera. After a 3D 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. 's Simulation Modes ===
Once you have set up your structure in [[Image:Info_iconEM.png|40pxLibera]] Click here , have defined sources and observables and have examined the quality of the structure's mesh, you are ready to learn more about '''run a 3D MoM simulation. [[Data_Visualization_and_Processing#Far-Field_Observables | Far Field ObservablesEM.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;" | [[Image#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:Info_icon270px;" | 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.Cube#Running_Frequency_Sweep_Simulations_in_EM.pngCube |40pxFrequency Sweep]] Click here to learn | 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 about 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 theory 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;" | [[Data_Visualization_and_ProcessingParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Using_Array_Factors_to_Model_Antenna_Arrays Performing_Optimization_in_EM.Cube | Using Array Factors to Model Antenna Arrays 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|}
You can set the simulation mode from [[Image:Info_iconEM.png|40pxLibera]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing s "Simulation Run Dialog". A single-frequency analysis is a single-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 Radiation Patterns]]'''simulation data from the navigation tree.
=== Running a Single-Frequency MoM Analysis === Â In a single-frequency analysis, the structure of your project workspace is meshed at the center frequency of the project and analyzed by one of [[Image:Info_iconEM.png|40pxLibera]] Click here '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 learn more about simulate your numerical problem. In either case, the engine type is set automatically. Â To open the Run Simulation Dialog, click the '''Run'''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation GraphsFile: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 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.
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<td> [[Image:wire_pic38_tnLibera L1 Fig13.png|thumb|230pxleft|The 3D radiation pattern of 480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the circular loop antenna: Theta componentsolver.]] </td><td/tr> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi component.]] </tdtr><td> [[Image:wire_pic40_tnMOM3D MAN10.png|thumb|230pxleft|The total radiation pattern of 480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the circular loop antennasolver.]] </td>
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[[Image:MOM13.png|thumb|380px|EM.Libera's Radar Cross Section dialog.]] === Setting MoM Numerical Parameters ===
When the physical structure is excited by MoM simulations involve a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Libera calculates the radar cross section (RCS) number of a targetnumerical parameters that normally take default values unless you change them. Three RCS quantities are computed: the θ You can access these parameters and φ components of change their values by clicking on the radar cross section as well as the total radar cross section, which are dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. In addition, EM.Libera calculates two types of RCS for each structure: '''Bi-Static RCSSettings''' and button next to the "Select Engine" dropdown list in the '''Mono-Static RCSRun Dialog'''. In bi-static RCSDepending on which MoM solver has been chosen for solving your problem, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recordedcorresponding Engine Settings dialog opens up.
To calculate RCSFirst we discuss the Wire MoM Engine Settings dialog. In the '''Solver''' section of this dialog, first you have to define an RCS observable instead can choose the type of a radiation pattern'''Linear Solver'''. At The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the end default option of a PO simulation, the thee RCS plots σ<sub>θ</sub>Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under you have to set a '''Tolerance''' for its convergence. You can also change the far field section maximum number of the navigation treeBiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''.
<table><tr><td> [[Image:Info_iconMOM9B.png|40px]] Click here to learn more about thumb|left|480px|EM.Libera'''[[Data_Visualization_and_Processing#Computing_Radar_Cross_Section | Computing Radar Cross Sections Wire MoM Engine Settings dialog.]]'''.</td></tr></table>
The Surface MoM Engine Settings dialog is bit more extensive and 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 α = 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, [[Image:Info_iconEM.png|40pxLibera]] Click here uses an acceleration technique called the Adaptive Integral Method (AIM) to learn more about '''speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. [[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS GraphsEM.Libera]]'s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the installer 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.
{{Note| The 3D RCS plot is always displayed at For both Wire MoM and Surface MoM solvers, you can instruct [[EM.Libera]] to write the origin contents of the spherical coordinate system, (0,0,0), MoM matrix and excitation and solutions vectors into data files with respect to which the far radiation zone is defined'''. Oftentimes, this might not DAT1''' file extensions. These files can be accessed from the scattering center '''Input/Output Files''' tab of the Data Manager. In both case, you have the option to uncheck the check box labeled "Superpose Incident plane Wave Fields". This option applies when your physical structureis excited by a plane wave source.}}Â {{Note|Computing When checked, the 3D mono-static RCS may take an enormous amount of computation timefield sensors plot the total electric and magnetic field distributions including the incident field. Otherwise, only the scattered electric and magnetic field distributions are visualized.}}
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<td> [[Image:wire_pic51_tnMOM9.png|thumb|230pxleft|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png640px|thumb|230px|The RCS of a metal plate structure: σ<sub>φ</sub>EM.]] </td><td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: σ<sub>tot</sub>Libera's Surface MoM Engine Settings dialog.]] </td>
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