The Method of Moments (MoM) is a rigorous, full-wave numerical technique for solving open boundary electromagnetic problems. Using this technique, you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwellâs equations as opposed to their differential forms that are used in the finite element or finite difference time domain methods.
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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 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.
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[[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. 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.
In [[EM.Picasso]], the background structure is a planar layered substrate that consists of one or more laterally infinite material layers always stacked along the Z-axis. In other words, the dimensions of the layers are infinite along the X and Y axes. Your substrate can be a dielectric half-space, or a single conductor-backed dielectric layer (as in microstrip components or patch antennas), or simply the unbounded free space, or any arbitrary multilayer stack-up configuration. In the special case of a free space substrate, [[EM.Picasso]] behaves similar to [[EM.Libera]]'s Surface MoM simulator. Metallic traces are placed at the boundaries between the substrate or superstrate layers. These are modeled by perfect electric conductor (PEC) traces or conductive sheet traces of finite thickness and finite conductivity. Some layers might be separated by infinite perfectly conducting ground planes. The two sides of a ground plane can be electromagnetically coupled through one or more slots (apertures). Such slots are modeled by magnetic surface currents. Furthermore, the metallic traces can be interconnected or connected to ground planes using embedded objects. Such objects can be used to model circuit vias, plated-through holes or dielectric inserts. These are modeled as volume polarization currents.