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{{Note|You can use EM.Libera either for modeling metallic wire objects and wireframe structures or for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric 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 '''[[CubeCAD]]''' with all of [[EM.Cube]]'s other computational modules.}}

=== An Overview of 3D Method Of Moments ===

EM.Libera offers two distinct 3D MoM simulation engines. The first one is a Wire MoM solver, which is based on Pocklington's integral equation. This solver can be used to simulate wireframe models of metallic structures and is particularly useful for modeling wire-type antennas and arrays. The second engine features a powerful Surface MoM solver. It can model metallic surfaces and solids as well as solid dielectric objects. The Surface MoM solver uses a surface integral equation formulation 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. For modeling dielectric regions of the physical structure , the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized, in which equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior and exterior boundary value problems.

== Constructing the Physical Structure ==

* Click the '''OK''' button of the dielectric material dialog to accept the changes and close it.

{{Note|Under dielectric material groups, you cannot draw surface or curve CAD objects.}}

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

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.

A gap source placed on one side of a polyline representing a polygonized circular loop.

=== Modeling Lumped Circuits ===

* HDMR Sweep

=== Running a Single-Frequency MoM Analysis ===

You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''.

=== Visualizing Current Distributions ===

At the end of a MoM3D simulation, [[EM.Cube|EM.CUBE]]'s Wire MoM engine generates a number of output data files that contain all the computed simulation data. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots of current distributions in the Project Workspace. Current distributions are visualized on all the wires and the magnitude and phase of the electric currents are plotted for all the PEC objects. In order to view these currents, you must first define current sensors before running the Wire MoM simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the [[MoM3D Module]] you can define only one current distribution node in the Navigation Tree, which covers all the PEC object in the Project Workspace. After a Wire MoM simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of the linear wire currents. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -π and π.

[[File:wire_pic26_tn.png|400px]] [[File:wire_pic27_tn.png|400px]]

After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once a Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -π and π. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc.

[[File:wire_pic31_tn.png]]

Unlike the FDTD method, the method of moments does not need a far field box to perform near-to-far-field transformations. But you still need to define a far field observable if you want to plot radiation patterns in EM.Libera. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output Settings section allows you to change the '''Angle Increment''' for both Theta and Phi observation angles in the degrees. These [[parameters]] indeed set the resolution of far field calculations. The default values are 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree and can be right clicked for further editing. After a 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.

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{{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.}}

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