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[[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><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 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.

{{Note|You can use [[EM.Libera either for simulating arbitrary ]] offers two distinct 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structuresMoM simulation engines. EMThe Wire MoM solver is based on Pocklington's integral equation.Libera also serves as the frequency-domain, full-wave '''[[MoM3D Module]]''' The Surface MoM solver uses a number of surface integral equation formulations of Maxwell'''[[EMs equations.Cube]]'''In particular, a comprehensiveit uses an electric field integral equation (EFIE), integratedmagnetic field integral equation (MFIE), modular electromagnetic or combined field integral equation (CFIE) for modeling environmentPEC regions. EM.Libera shares On the visual interface, 3D parametric CAD modeler, data visualization toolsother hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions. Equivalent electric and many more utilities magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and features collectively known as '''[[CubeCAD]]''' with all of [[EM.Cube]]'s other computational modulesexterior boundary value problems.}}

{{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|40px30px]] Click here to learn more about the theory of the '''[[Getting_Started_with_EM.CUBE Basic Principles of The Method of Moments | EM.Cube Modeling Environment3D Method of Moments]]'''.

<table><tr><td>[[Image:Info_iconYagi Pattern.png|40px]] Click here to learn more about thumb|500px|3D far-field radiation pattern of the basic functionality of '''[[CubeCADexpanded Yagi-Uda antenna array with 13 directors.]]'''.</td></tr></table>

=== An Overview EM.Libera as the MoM3D Module of 3D Method Of Moments EM.Cube ===

The Method of Moments (MoM) is a rigorousYou 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]]''', numerical technique for solving open boundary a comprehensive, integrated, modular electromagnetic problemsmodeling environment. Using this technique[[EM.Libera]] shares the visual interface, you can analyze electromagnetic radiation3D parametric CAD modeler, data visualization tools, scattering and wave propagation problems with relatively short computation times many more utilities and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwell’s equations features collectively known as opposed to their differential forms used [[Building Geometrical Constructions in the finite element or finite difference time domain methodsCubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem. The given structure is immersed in the free space, and the unbounded background medium is modeled using the free-space Green's functions. The unknown physical or equivalent currents are discretized as a collection of elementary currents with small finite spatial extents. Such elementary currents are called basis functions. They obviously have a vectorial nature and must satisfy [[Maxwell's Equations|Maxwell's equations]] and the relevant boundary conditions individually. The actual currents on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents 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 structure. EM.Libera 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's Equations|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 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, 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|40px30px]] Click here to learn more about the theory of '''[[3D Method of MomentsGetting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

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.

[[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):Features at a Glance ==

Both of EM.Libera's two simulation engines, Wire MoM and Surface MoM, can handle metallic structures. You define <ul> <li> Metal wires under '''Thin Wire''' groups and surface curves in free space</li> <li> Metal surfaces 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 solids in project units. All types of free space</li> <li> Homogeneous dielectric solid and surface CAD objects can be drawn in a PEC group. Only solid free space</li> <li> Import STL CAD objects can be drawn under '''Dielectric Objects'''. files as native polymesh structures</li> <li> Export wireframe structures as STL CAD files</li></ul>

Once a new object group node has been created <ul> <li> Gap sources on the navigation treewires (for Wire MoM) and gap sources on long, it becomes the "Active" group of the project workspacenarrow, which is always listed in bold letters. When you draw a new CAD object such 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 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 collection of short dipoles</li> <li> RLC lumped elements on its name in the navigation tree wires and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create object groups, narrow strips with series-parallel combinations</li> <li> Plane wave excitation with linear and then draw new CAD objects under the active object group. However, if you start a new circular polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[EM.LiberaTerrano]] project or external files)</li> <li> Huygens sources imported from scratch, FDTD or other modules with arbitrary rotation 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.array configuration</li></ul>

[[Image:Info_icon.png|40px]] Click here <ul> <li> Polygonized mesh of curves and wireframe mesh of surfaces and solids for Wire MoM simulation</li> <li> User defined wire radius</li> <li> Connection of wires/lines to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Material Groups]]'''.wireframe surfaces and solids using polymesh objects</li> <li> Surface triangular mesh of surfaces and solids for Surface MoM simulation</li> <li> Local mesh editing of polymesh objects</li></ul>

== <ul> <li> 3D Mesh Generation ==Pocklington integral equation formulation of wire structures</li> <li> 3D electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of PEC structures</li> <li> PMCHWT formulation of homogeneous dielectric objects</li> <li> AIM acceleration of Surface MoM solver</li> <li> Uniform and fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Multi-variable and multi-goal optimization of scene</li> <li> Fully parallelized Surface MoM solver using MPI</li> <li> Both Windows and Linux versions of Wire MoM simulation engine available</li></ul>

=== A Note on EM.Libera's Mesh Types Data Generation &amp; Visualization ===

<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.Libera features two simulation enginesCube]] modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, Wire MoM side lobe levels and Surface MoMnull parameters, which require different mesh typesetc. The Wire MoM simulator handles only </li> <li> Radiation pattern of an arbitrary array configuraition of the wire objects structure</li> <li> Bi-static 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 multimono-segment polylines static radar cross section: 3D visualization and then subdivided further if necessary. At the connection points between two or more wires2D graphs</li> <li> Port characteristics: S/Y/Z parameters, junction basis functions are generated VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to ensure current continuityRF. Spice or its Device Editor</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

On == Building the other hands, Physical Structure in EM.Libera's Surface MoM solver requires a triangular surface mesh of surface and [[Solid Objects|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.==

[[Image:Info_iconAll 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.png|40px]] Click here to learn more about '''In [[Mesh_Generation_Schemes_in_EMEM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator Libera]]'''., you can create three different types of objects:

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[ImageFile:Info_iconpec_group_icon.png|40px]] Click here to learn more about | style="width:150px;" | [[Glossary of EM.LiberaCube'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 curve objects| None|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube'''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;" | [[Mesh_Generation_Schemes_in_EMFile:diel_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#The_Triangular_Surface_Mesh_Generator Dielectric Material |Dielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Triangular Surface Mesh Generator MoM solver only |-| style="width:30px;" | [[File:Virt_group_icon.png]]'''| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, 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 |}

[[Image:Info_icon.png|40px]] Click here on each category to learn more details about it in the [[Glossary of EM.LiberaCube's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Linear_Wireframe_Mesh_Generator | Linear Wireframe Mesh Generator Materials, Sources, Devices & Other Physical Object Types]]'''.

=== Mesh Both of Connected Objects ===  [[Image:MOM3.png|thumb|300px|EM.Libera]]'s Mesh Hierarchy dialogtwo simulation engines, Wire MoM and Surface MoM, can handle metallic structures.]] All the You define wires under '''Thin Wire''' groups and surface and volumetric metal objects belonging to the same under '''PEC or dielectric group are merged together using the Boolean union operation before meshingObjects'''. If your structure contains attachedIn other words, interconnected or overlapping [[Solid Objects|solid objects]]you can draw lines, their internal common faces are removed polylines and only the surface of the external faces is meshed. Similarlyother curve objects as thin wires, all the [[Surface Objects|surface objects]] belonging to the same PEC group are merged together and their internal edges are removed before meshingwhich have a radius parameters expressed in project units. Note that a All types of solid and a surface object belonging to the same PEC group might not always CAD objects can be merged properly.  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 on top of drawn in 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, EM.Libera does provide a "Material Hierarchy" table, which you Only solid CAD objects can modify. To access this table, select be drawn under '''Menu > Simulate < discretization < Mesh Hierarchy...Dielectric Objects'''. The PEC groups by default have the highest priority and reside at the top of the 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.

<td> [[Image:MOM1wire_pic1.png|thumb|360px350px|A dielectric cylinder attached to a PEC plateEM.Libera's Navigation Tree.]] </td> <td> [[Image:MOM2.png|thumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]] </td>

=== Using Polymesh Objects 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 Connect Wires the navigation tree to Wireframe Surfaces === hold your new CAD object.

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 [[Surface ObjectsImage:Info_icon.png|surface objects30px]] and PEC Click here to learn more about '''[[Solid Building Geometrical Constructions in CubeCAD#Transferring ObjectsAmong Different Groups or Modules |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.CubeMoving Objects among Different Groups]]'s polymesh objects to accomplish this objective''.

{{Note|In [[EM.Cube]], polymesh objects are regards you can import external CAD models (such as already-meshed 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 imported objects and are not re-meshed again during a simulationto [[EM.Libera]].}}

You can convert any surface object or solid object to a polymesh using [[CubeCAD]]'s '''Polymesh Tool'''.  [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Discretizing_Objects#Converting_Objects_to_Polymesh | Converting 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><tr><td> [[Image:MOM4.png|thumb|360px|Geometry of a monopole wire connected to a PEC plate.]] </td><td> [[Image:MOM5.png|thumb|360px|Placing the wire on the polymesh version of the PEC plate.]] </td></tr></table>Excitation Sources ==

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[ImageFile:MOM6Bgap_src_icon.png]]|thumb|320px|[[Glossary of EM.LiberaCube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source dialog|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]] Your 3D physical structure must be excited by some sort | [[Glossary of signal 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 that induces electric linear currents on | style="width:300px;" | Associated with an PEC or thin wireswire line or polyline, electric surface currents on metal surface and both electric magnetic surface currents on the surface works only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of dielectric objectsEM. The excitation 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 you choose depends on the observables you seek in your project|-| style="width:30px;" | [[File:plane_wave_icon. png]]| [[Glossary of EM.Libera provides the following 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 types |-| 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 exciting your physical structure (click on each type to learn more about it)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 [[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 s Materials, Sources, Devices & Other Physical Object 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 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.

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.Libera]]. 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 &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are &theta; = 180° and &phi; = 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 [[EM.Cube]] computational module.

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Defining_FiniteModeling_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'''.

<td> [[Image:wire_pic14_tn.png|thumb|600pxleft|640px|A wire gap source placed on one side of a polyline representing a polygonized circular loop.]] </td>

<td> [[Image:MOM8po_phys16_tn.png|thumb|360px|EM.Libera's Plane Wave dialog.]] </td><td> [[Image:po_phys16_tn.png|thumbleft|360px420px|Illuminating a metallic sphere with an obliquely incident plane wave source.]] </td>

In [[EM.Libera]], 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. [[EM.Libera]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Defining_Lumped_Elements_in_EM.Picasso_.26_EM.Libera Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.

[[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Linear_Passive_Devices A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''.

[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Common_Excitation_Source_Types_in_EMGlossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#The_Port_Definition_Observable Port_Definition_Observable | Port Definition Observable]]'''.

== Running 3D MoM Simulations EM.Libera's Simulation Data & Observables ==

Once you have set up your structure in At the end of a 3D MoM simulation, [[EM.Libera, have defined sources ]] 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 observables wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and have examined magnetic surface currents on the quality PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables: {| 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]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | 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 structurefrequency 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 meshSimulation 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, you are ready to run 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 MoM simulationtarget| 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.Libera offers four 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 simulationEM.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|}

* Single-Frequency Analysis* Frequency Sweep* Parametric Sweep* Click on each category to learn more details about it in the [[OptimizationGlossary of EM.Cube's Simulation Observables & Graph Types]]* HDMR Sweep.

Depending on the types of objects present in your project workspace, [[Image:Info_iconEM.png|40pxLibera]] Click here to learn more about '''[[Parametric_Modelingperforms either a Surface MoM simulation or a Wire MoM simulation. In the former case,_Sweep_%26_Optimization#Running_Parametric_Sweep_Simulations_in_EMthe electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized.Cube | Running Parametric Sweep Simulations in EM.Cube]]'''In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted.

<table><tr><td> [[Image:Info_iconwire_pic26_tn.png|40pxthumb|360px|A monopole antenna connected above a PEC plate.]] Click here to learn more about '''</td><td> [[Parametric_Modeling,_Sweep_%26_Optimization#Optimization Image:wire_pic27_tn.png| Running Optimization Simulations in EMthumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate.Cube]]'''.</td></tr></table>

[[Image:Info_icon.png{{Note|40px]] Click here to learn more about '''Keep in mind that since [[Running_HDMR_Simulations_in_EM.Cube | Running HDMR Simulations in EM.CubeLibera]]'''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.}}

In You need to define a single-frequency analysis, the structure far field observable if you want to plot radiation patterns of your project workspace is meshed at the center frequency of the project and analyzed by one of physical structure in [[EM.Libera's two MoM solvers]]. If your project contains at lease one line or curve object, the Wire After a 3D MoM solver simulation is automatically selected. Otherwisefinished, three radiation patterns plots are added to the Surface MoM solver will always be used to simulate your problemfar field entry in the Navigation Tree. In either caseThese are the far field component in Theta direction, the engine type is set automaticallyfar field component in Phi direction and the total far field.

To open the Run Simulation Dialog, click the '''Run''' [[FileImage:run_iconInfo_icon.png|30px]] button of Click here to learn more about the theory of '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays |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 Using Array Factors to Model Antenna Arrays ]]'''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.

<td> [[Image:MOM9Cwire_pic38_tn.png|thumb|360px230px|EM.Libera's Simulation Run dialog showing Wire MoM engine as The 3D radiation pattern of the solvercircular loop antenna: Theta component.]] </td><td> [[Image:MOM9Awire_pic39_tn.png|thumb|360px230px|EMThe 3D radiation pattern of the circular loop antenna: Phi component.Libera's Simulation Run dialog showing Surface MoM engine as ]] </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the solvercircular loop antenna.]] </td>

[[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 To calculate RCS, first you change themhave to define an RCS observable instead of a radiation pattern. You can access these [[parameters]] and change their values by clicking on At the '''Settings''' button next to end of a PO simulation, the thee RCS plots &quotsigma;Select Engine_{&quottheta; dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem}, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the corresponding Engine Settings dialog opens upnavigation tree.

First we discuss {{Note| The 3D RCS plot is always displayed at the Wire MoM Engine Settings dialog. In origin of the '''Solver''' section of this dialogspherical coordinate system, you can choose the type of '''Linear Solver'''. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG0,0,0)'''. The LU solver is a direct solver and is , with respect to which the default option of the Wire MoM solver. The BiCG solver far radiation zone is iterativedefined. If BiCG is selectedOftentimes, you have to set a '''Tolerance''' for its convergence. You can also change this might not be the maximum number of BiCG iterations by setting a new value for '''Max. No. scattering center of Solver Iterations / System Size'''your physical structure. }}

The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In {{Note|Computing 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 3D mono-static RCS may take 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 enormous amount 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 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.  For both Wire MoM and Surface MoM solvers, 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 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 visualizedcomputation time. }}

<td> [[Image:MOM9wire_pic51_tn.png|thumb|600px230px|EMThe RCS of a metal plate structure: &sigma;_&theta;.Libera's Surface MoM Engine Settings dialog]] </td><td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a metal plate structure: &sigma;_&phi;.]] </td><td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: &sigma;_tot.]] </td>

=== Running Frequency Sweep Simulations 3D Mesh Generation in EM.Libera ===

[[Image:wire_pic24.png|thumb|450px| === A Note on EM.Libera's Frequency Settings dialog.]]In a frequency sweep simulation, the operating frequency of the project is varied during the simulation, and the frequency response of your structure is computed at each frequency sample. EM.Libera offers two types of frequency sweep: uniform and adaptive. 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 intermediate 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. To run a 3D MoM frequency sweep, open the '''Run Simulation Dialog''' and select '''Frequency Sweep''' from the '''Simulation Mode''' dropdown list in this dialog. The '''Settings''' button located next to the simulation mode dropdown list becomes enabled. If you click this button, the Frequency Settings Dialog opens up. First you have to choose the '''Sweep Type''' with two options: '''Uniforms''' or '''Adaptive'''. The default option is a uniform sweep. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. Mesh Types ===

During a frequency sweep[[EM.Libera]] features two simulation engines, as the project's frequency changesWire MoM and Surface MoM, so does the wavelengthwhich require different mesh types. As 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 result, the mesh of density criterion. Curved wires are first converted to multi-segment polylines and then subdivided further if necessary. At the structure also changes at each frequency sampleconnection points between two or more wires, junction basis functions are generated to ensure current continuity. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:

* Fix mesh at On the highest frequencyother hands, [[EM.* Fix Libera]]'s Surface MoM solver requires a triangular surface mesh at of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the center frequencyentire structure.* ReYou 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 at each frequencydensity on "Cell Edge Length" expressed in project units.

== [[Image: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 3D MoM Simulation Data ==Mesh Generator]]'''.

At the end of a 3D MoM simualtion, 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 (click on each type to learn more about it): * '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Current Distributions]]'''Image: Electric and magnetic 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 Info_icon.png| Near-Field Distributions30px]]''': Electric and magnetic field amplitude and phase on specified planes and their central axes* Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#Computing_and_Graphing_Port_Characteristics The_Triangular_Surface_Mesh_Generator | Port Characteristics]]EM.Libera''': S, Z and Y [[Parameterss Triangular Surface Mesh Generator ]] 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-to-Back Ratio (FBR), etc.* '''[[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 or more ports have been defined, <table><tr><td> [[Image:Mesh5.png|thumb|400px|EM.Libera calculates 's Mesh Settings dialog showing the scattering (S) [[parameters]] of the selected ports, all based on the port impedances specified in the project's &quot;Port Definition&quot;linear wireframe mesh generator. ]] </td></tr></table>

You can analyze metallic wire structures very accurately with utmost computational efficiency using [[Image:Info_iconEM.png|40pxLibera]] Click here to learn more about '''s Wire MoM simulator. When you structure contains at least one PEC line, polyline or any curve CAD object, [[Data_Visualization_and_Processing#Rational_Interpolation_of_Port_Characteristics | Rational Interpolation EM.Libera]] will automatically invoke its linear wireframe mesh generator. This mesh generator subdivides straight lines and linear segments of Scattering Parameterspolyline objects into or linear elements according to the specified mesh density. It also polygonizes rounded [[Curve Objects|curve objects]]'''into polylines with side lengths that are determined by the specified mesh density. Note that polygonizing operation is temporary and solely for he purpose of mesh generation. As for surface and solid CAD objects, a wireframe mesh of these objects is created which consists of a large number of interconnected linear (wire) elements.

[[Image:MOM10.png{{Note|thumb|350px|EMThe linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool.LiberaIt also discretizes surface and solid CAD objects temporarily using CubeCAD's Current Distribution dialogPolymesh tool.]]}}

Depending on <table><tr><td> [[Image:Mesh6.png|thumb|200px|The geometry of an expanding helix with a circular ground.]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the types helix with the default mesh density of objects present in your project workspace, EM10 cells/&lambda;₀.Libera performs either ]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of the helix with a Surface MoM simulation or mesh density of 25 cells/&lambda;₀.]] </td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a Wire MoM simulationmesh density of 50 cells/&lambda;₀. In ]] </td></tr></table> === Mesh of Connected Objects ===  All the former case, objects belonging to the electric same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and magnetic surface current distributions on only the surface of PEC and dielectric objects can be visualized. In the latter caseexternal faces is meshed. Similarly, the linear electric currents on all the wires and wireframe surface objects can 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 plottedmerged properly.

When two objects belonging to two different material groups overlap or intersect each other, [[Image:Info_iconEM.png|40pxLibera]] Click here has to learn more about '''determine how to designate the 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, [[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution MapsEM.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 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.

<td> [[Image:wire_pic26_tnMOM3.png|thumb|360px300px|A monopole antenna connected above a PEC plateEM.]] </td><td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution plot of the monopole antenna connected above the PEC plateLibera's Mesh Hierarchy dialog.]] </td>

<table><tr><td> [[Image:MOM11MOM1.png|thumb|350px360px|EMA dielectric cylinder attached to a PEC plate.Libera's Field Sensor dialog]] </td><td> [[Image:MOM2.png|thumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]]</td></tr></table>

EM.Libera allows you === Using Polymesh Objects to visualize the near fields at a specific field sensor plane of arbitrary dimensions. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. Connect Wires to Wireframe Surfaces ===

{{Note|Keep in mind that since EM.Libera uses MoM solversIf the project workspace contains a line object, the calculated field value at wireframe mesh generator is used to discretize your physical structure. From the source point is infiniteof view of this mesh generator, all PEC surface objects and PEC solid objects are treated as wireframe objects. As If you want to model a wire radiator connected to a resultmetal surface, you have to make sure that the field sensors must be placed resulting wireframe mesh of the surface has a node exactly at adequate distances (at least one or few wavelengths) away from the scatterers location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[EM.Cube]]'s polymesh objects to produce acceptable resultsaccomplish this objective.}}

{{Note|In [[Image:Info_iconEM.png|40pxCube]] Click here to learn more about '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Defining , polymesh objects are regarded as already-meshed objects and are not re-meshed again during a Field Sensor Observable]]'''simulation.}}

You can convert any surface object or solid object to a polymesh using CubeCAD's '''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.

<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>

[[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 ===  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.  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.

<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>

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 &theta; You can access these parameters and &phi; components of change their values by clicking on the radar cross section as well as the total radar cross section, which are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot. In addition, EM.Libera calculates two types of RCS for each structure: '''Bi-Static RCSSettings''' and button next to the &quot;Select Engine&quot; 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 &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. 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 &theta; and &phi; 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 &sigma;_&theta;Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, &sigma;_&phi;, and &sigma;_tot 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 &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, [[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 0.05&lambda;₀. [[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.}} {{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.}}

<td> [[Image:wire_pic51_tnMOM9.png|thumb|230pxleft|The RCS of a metal plate structure: &sigma;_&theta;.]] </td><td> [[Image:wire_pic52_tn.png640px|thumb|230px|The RCS of a metal plate structure: &sigma;_&phi;EM.]] </td><td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: &sigma;_totLibera's Surface MoM Engine Settings dialog.]] </td>

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