Changes

[[Image:Splash-mom.jpg|right|800px720px]]

<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>

[[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]]'''

[[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 of '''[[Building Geometrical Constructions in CubeCAD Getting_Started_with_EM.Cube | CubeCADEM.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 [[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. <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>

[[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):

* '''{| 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;" | [[Defining_Materials_in_EMGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect_Electric_Conductors_.26_Metal_Traces Perfect Electric Conductor (PEC) | Perfect Electric Conductor (PEC) Objects]]'''* '''| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects| None|-| style="width:30px;" | [[Defining_Materials_in_EMFile:thin_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Thin_Wires Thin Wire | Thin WiresWire]]'''* '''| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only |-| style="width:30px;" | [[Defining_Materials_in_EMFile:diel_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Defining_Dielectric_Materials Dielectric Material | Dielectric ObjectsMaterial]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface 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 |}

Both Click on each category to learn more details about it in the [[Glossary of EM.LiberaCube's two simulation enginesMaterials, Wire MoM and Surface MoMSources, 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 objectsDevices & Other Physical Object Types]] 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 Both of '''[[Defining Materials in EM.CubeLibera]]'''. Once a new object group node has been created on the navigation trees two simulation engines, it becomes the "Active" group of the project workspaceWire MoM and Surface MoM, which is always listed in bold letterscan handle metallic structures. When you draw a new CAD object such as a Box or a Sphere, it is inserted You define wires 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 '''ActivateThin Wire''' item of the contextual menu. It is recommended that you first create object groups, and then draw new CAD surface and volumetric metal 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|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Object Group]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving PEC Objects among Material Groups]]'''. {{Note|In [[EM.Cube]]other words, you can import external CAD models (such as STEPdraw lines, IGES, STL models, etc.) only to [[CubeCAD]]. From [[CubeCAD]], you can then move the imported objects to EM.Libera.}} == 3D Mesh Generation == === A Note on EM.Libera's Mesh Types === EM.Libera features two simulation engines, Wire MoM polylines and Surface MoM, which require different mesh types. The Wire MoM simulator handles only wire other curve 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 thin wires, junction basis functions are generated to ensure current continuity.  On the other hands, EM.Libera's Surface MoM solver requires which have 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" radius parameters expressed in project units. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator ]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about EM.Libera's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator ]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about EM.Libera's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Linear_Wireframe_Mesh_Generator | Linear Wireframe Mesh Generator ]]'''. === Mesh All types of Connected Objects ===  [[Image:MOM3.png|thumb|300px|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 Objects|solid objects]], their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the [[Surface Objects|surface CAD objects]] belonging to the same can be drawn in a PEC group are merged together and their internal edges are removed before meshing. Note that a Only solid and a surface object belonging to the same PEC group might not always be merged properly.  When two CAD 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 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 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 objects and are not re-meshed again during a simulationSTEP, IGES, STL models, etc.}}  You can convert any surface object or solid object ) only to a polymesh using [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]'s '''Polymesh Tool'''.  From [[Image:Info_icon.pngBuilding_Geometrical_Constructions_in_CubeCAD |40pxCubeCAD]] 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 then move the coincident nodes between line segments and will create a junction basis function imported objects to ensure current continuity.  <table><tr><td> [[Image:MOM4.png|thumb|360px|Geometry of a monopole wire connected to a PEC plateEM.Libera]] </td><td> [[Image:MOM5.png|thumb|360px|Placing the wire on the polymesh version of the PEC plate.]] </td></tr></table>}}

== EM.Libera's Excitation Sources ==

[[Image:MOM6B.png|thumb|320px|EM.Libera's Strip Gap Source dialog.]] Your 3D 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:

| '''style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]'''

| '''style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]'''

| '''style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]'''

| '''style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]'''

| '''style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]'''| style="width:300px;" | Used for modeling equivalent sourced sources imported from other [[EM.Cube]] modules

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types]].

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 ==

=== EM.Libera's Simulation Modes === Once you have set up your structure in EM.Libera, have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a 3D MoM simulation. EM.Libera offers five simulation modes (click on each type to learn more about it): * '''[[#Running a Single-Frequency MoM Analysis | Single-Frequency Analysis]]'''* '''[[Parametric_Modeling,_Sweep_%26_Optimization#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]''' including uniform and adaptive frequency sweeps * '''[[Parametric_Modeling,_Sweep_%26_Optimization#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]'''* '''[[Parametric_Modeling,_Sweep_%26_Optimization#Optimization | Optimization]]'''* '''[[Building_Reusable_Models#Running_an_HDMR_Sweep | HDMR Sweep]]''' 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 [[parameters]] are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree. === 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 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.  To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, the Surface MoM solver is selected as your simulation engine. To start the simulation, click the {{key|Run}} button of this dialog. Once the 3D 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.  <table><tr><td> [[Image:MOM9C.png|thumb|360px|EM.Libera's Simulation Run 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 the solver.]] </td></tr></table> === Setting MoM Numerical Parameters ===  [[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 &quot;Select Engine&quot; dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up. 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 can choose among the three PEC formulations: EFIE, MFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is &alpha; = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional [[parameters]]: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, EM.Libera uses an acceleration technique called the Adaptive Integral Method (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05&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 visualized.  <table><tr><td> [[Image:MOM9.png|thumb|600px|EM.Libera's Surface MoM Engine Settings dialog.]] </td></tr></table> == Working with 3D MoM Simulation Data == 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:

| style="width:150px30px;" | '''[[Glossary of EMFile:currdistr_icon.Cube's Simulation Observables#Current Distributionpng]]| 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 linera linear current distribution on wires

| style="width:150px30px;" | '''[[Glossary of EMFile:fieldsensor_icon.Cube's Simulation Observables#Near-Field Sensor 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 E- electric and H-magnetic field components on a planar cross section of specified plane in the computational frequency domain in both time and frequency domains

| style="width:150px30px;" | '''[[Glossary of EMFile:farfield_icon.Cube's Simulation Observables#Far-Field Radiation Pattern png]]| style="width:150px;" |Far-Field Radiation Characteristics]]'''| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]'''

| style="width:150px30px;" | '''[[Glossary of EMFile:rcs_icon.Cube's Simulation Observables#Radar Cross Section (RCS) 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:150px30px;" | '''[[Glossary of EMFile:port_icon.Cube's Simulation Observables#Port Definition png]]| style="width:150px;" |Port Characteristics]]'''| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#Port Definition |Port Definition]]'''

| style="width:150px30px;" | '''[[Glossary of EMFile:huyg_surf_icon.Cube's Simulation Observables#Huygens Surface |Huygens Surfacepng]]'''| 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]]'''

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables& Graph Types]].

If Depending on the types of objects present in your project structure is excited by gap sources, and one or more ports have been definedworkspace, [[EM.Libera calculates the scattering (S) [[parameters]] of performs either a Surface MoM simulation or a Wire MoM simulation. In the selected portsformer case, all based the electric and magnetic surface current distributions on the port impedances specified in surface of PEC and dielectric objects can be visualized. In the project's &quot;Port Definition&quot;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> [[Data_Visualization_and_Processing#Computing_and_Graphing_Port_Characteristics Image:wire_pic27_tn.png| Computing and Graphing Port Characteristicsthumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate.]]'''.</td></tr></table>

{{Note|Keep in mind that since [[Image:Info_iconEM.png|40pxLibera]] Click here 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 learn more about '''[[Data_Visualization_and_Processing#Rational_Interpolation_of_Port_Characteristics | Rational Interpolation of Scattering Parameters]]'''produce acceptable results.}}

<table><tr><td> [[Image:MOM10wire_pic32_tn.png|thumb|350px360px|EMElectric field plot of the circular loop antenna.Libera's Current Distribution dialog]] </td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]]</td></tr></table>

Depending on the types You need to define a far field observable if you want to plot radiation patterns of objects present your physical structure in your project workspace, [[EM.Libera performs either ]]. After a Surface 3D MoM simulation or a Wire MoM simulation. In the former caseis finished, three radiation patterns plots are added to the electric and magnetic surface current distributions on far field entry in the surface of PEC and dielectric objects can be visualizedNavigation Tree. In These are the latter casefar field component in Theta direction, the linear electric currents on all the wires far field component in Phi direction and wireframe objects can be plottedthe total far field.

[[Image:Info_icon.png|40px30px]] Click here to learn more about the theory of '''[[Data_Visualization_and_ProcessingDefining_Project_Observables_%26_Visualizing_Output_Data#Visualizing_3D_Current_Distribution_Maps Using_Array_Factor_to_Model_Antenna_Arrays | Visualizing 3D Current Distribution MapsUsing Array Factors to Model Antenna Arrays ]]'''.

<td> [[Image:wire_pic26_tnwire_pic38_tn.png|thumb|360px230px|A monopole The 3D radiation pattern of the circular loop antenna connected above a PEC plate: Theta component.]] </td><td> [[Image:wire_pic27_tnwire_pic39_tn.png|thumb|360px230px|Current distribution plot The 3D radiation pattern of the monopole circular loop antenna connected above : Phi component.]] </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the PEC platecircular loop antenna.]] </td>

When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[ImageEM.Libera]] calculates the radar cross section (RCS) of a target. Three RCS quantities are computed:MOM11the &theta; and &phi; components of the radar cross section as well as the total radar cross section, which are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot.png|thumb|350px|In addition, [[EM.Libera]] calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''s Field Sensor dialog.In bi-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 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 recorded.

EM.Libera allows To calculate RCS, first you have to visualize the near fields at define an RCS observable instead of a specific field sensor plane of arbitrary dimensionsradiation pattern. Calculation At the end of near fields is a post-processing process PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and may take a considerable amount &sigma;_tot are added under the far field section of time depending on the resolution that you specifynavigation tree.

{{Note|Keep in mind that since EM.Libera uses MoM solvers, the calculated field value The 3D RCS plot is always displayed at the source point origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is infinitedefined. As a resultOftentimes, the field sensors must this might not be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable resultsscattering center of your physical structure.}}

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable {{Note| Defining a Field Sensor Observable]]'''Computing the 3D mono-static RCS may take an enormous amount of computation time.}}

<table><tr><td> [[Image:wire_pic51_tn.png|thumb|230px|The RCS of a metal plate structure: &sigma;_&theta;.]] </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></tr></table> == 3D Mesh Generation in EM.Libera == === A Note on EM.Libera's Mesh Types === [[EM.Libera]] features two simulation engines, Wire MoM and Surface MoM, which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to a mesh density criterion. Curved wires are first converted to multi-segment polylines and then subdivided further if necessary. At the connection points between two or more wires, junction basis functions are generated to ensure current continuity.  On the other hands, [[EM.Libera]]'s Surface MoM solver requires a triangular surface mesh of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units. [[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#Visualizing_3D_Near-Field_Maps Working_with_EM.Cube.27s_Mesh_Generators | Visualizing 3D Near Field MapsWorking with Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Libera's Triangular Surface Mesh Generator ]]'''.

<td> [[Image:wire_pic32_tnMesh5.png|thumb|360px400px|Electric field plot of EM.Libera's Mesh Settings dialog showing the circular loop antenna.]] </td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot parameters of the circular loop antennalinear wireframe mesh generator.]] </td>

You need to define a far field observable if can analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Libera]]'s Wire MoM simulator. When you want to plot radiation patterns of your physical structure in contains at least one PEC line, polyline or any curve CAD object, [[EM.Libera]] will automatically invoke its linear wireframe mesh generator. After a 3D MoM simulation is finished, three radiation patterns plots are added This mesh generator subdivides straight lines and linear segments of polyline objects into or linear elements according to the far field entry in the Navigation Treespecified mesh density. These It also polygonizes rounded [[Curve Objects|curve objects]] into polylines with side lengths that are determined by the far field component in Theta direction, the far field component in Phi direction specified mesh density. Note that polygonizing operation is temporary and the total far fieldsolely 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:Info_icon.png{{Note|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Far-Field_Observables | Far Field Observables]]'The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. It also discretizes surface and solid CAD objects temporarily using CubeCAD's Polymesh tool.}}

<table><tr><td> [[Image:Info_iconMesh6.png|40pxthumb|200px|The geometry of an expanding helix with a circular ground.]] Click here to learn more about </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the theory helix with the default mesh density of '''10 cells/&lambda;₀.]] </td><td> [[Data_Visualization_and_Processing#Using_Array_Factors_to_Model_Antenna_Arrays Image:Mesh8.png| Using Array Factors to Model Antenna Arrays thumb|200px|Wireframe mesh of the helix with a mesh density of 25 cells/&lambda;₀.]]'''</td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/&lambda;₀.]] </td></tr></table>

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 objects, their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the 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.  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#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation GraphsEM.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_pic38_tnMOM3.png|thumb|230px300px|The 3D radiation pattern of the circular loop antenna: Theta componentEM.]] </td><td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi componentLibera's Mesh Hierarchy dialog.]] </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the circular loop antenna.]] </td>

<table><tr><td> [[Image:MOM13MOM1.png|thumb|380px360px|EMA dielectric cylinder attached to a PEC plate.Libera's Radar Cross Section dialog]] </td><td> [[Image:MOM2.png|thumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]] </td></tr></table>

To calculate RCSIf the project workspace contains a line object, first you have the wireframe mesh generator is used to define an RCS observable instead of a radiation patterndiscretize your physical structure. At From the end point of a PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;view of this mesh generator, all PEC surface objects and &sigma;_tot PEC solid objects are added under treated as wireframe objects. If you want to model a wire radiator connected to a metal surface, you have to make sure that the far field section resulting wireframe mesh of the navigation treesurface has a node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[EM.Cube]]'s polymesh objects to accomplish this objective.

{{Note|In [[Image:Info_iconEM.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Computing_Radar_Cross_Section | Computing Radar Cross SectionCube]]''', polymesh objects are regarded as already-meshed objects and are not re-meshed again during a simulation.}}

[[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#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]Polymesh Tool'''.

{{Note[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool | The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect Converting Object to which the far radiation zone is definedPolymesh]]''' in [[EM. Oftentimes, this might not be the scattering center of your physical structureCube]].}}

{{Note|Computing the 3D mono-static RCS may take Once an enormous amount object is converted to a polymesh, you can place your wire at any of computation timeits 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_pic51_tnMOM4.png|thumb|230px360px|The RCS Geometry of a metal plate structure: &sigma;_&theta;.]] </td><td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of monopole wire connected to a metal PEC plate structure: &sigma;_&phi;.]] </td><td> [[Image:wire_pic53_tnMOM5.png|thumb|230px360px|The total RCS Placing the wire on the polymesh version of a metal the PEC plate structure: &sigma;_tot.]] </td>

== Running 3D MoM Simulations in EM.Libera == === EM.Libera's Simulation Modes === Once you have set up your structure in [[EM.Libera]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a 3D MoM simulation. [[EM.Libera]] offers five simulation modes: {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:270px;" | 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.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|} 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 parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree. === 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 [[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.  To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, the Surface MoM solver is selected as your simulation engine. To start the simulation, click the {{key|Run}} button of this dialog. Once the 3D 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.  <ptable><tr><td> [[Image:Libera L1 Fig13.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] </td></tr><tr><td> [[Image:MOM3D MAN10.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]] </td></tr></table> === Setting MoM Numerical Parameters ===  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 &nbspquot;Select Engine&quot; dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up. 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'''.  <table><tr><td> [[Image:MOM9B.png|thumb|left|480px|EM.Libera's Wire MoM Engine Settings dialog.]] </ptd></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, [[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 0.05&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 visualized.  <table><tr><td> [[Image:MOM9.png|thumb|left|640px|EM.Libera's Surface MoM Engine Settings dialog.]] </td></tr></table> <br /> <hr> [[Image:Top_icon.png|48px30px]] '''[[EM.Libera#Product_Overview | Back to the Top of the Page]]'''

[[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]]'''