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EM.Libera

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/* An EM.Libera Primer */
=== EM.Libera in a Nutshell ===
EM.Libera is a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space metallic structures made up of metal and dielectric structuresregions or a combination of them. It features two full-wave Method of Moments (MoM) separate simulation engines, one based on a Wire Surface MoM formulation solver and the other based on a Surface Wire MoM formulation. In generalsolver, the surface that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver is used to simulate your physical structure, which can be made utilizes a surface integration equation formulation of metallic the metal and dielectric objects of arbitrary shapes as well as composite structures that contain conjoined metal and dielectric regions. If in your project workspace contains at least one line or curve object, EMphysical structure.Libera then invokes its The Wire MoM solver. In that case, can only handle metallic wireframe structures can be modeled, and all . EM.Libera selects the surface and solid PEC simulation engine automatically based on the types of objects are meshed as wireframescontained in your project workspace.
{{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 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 '''[[CubeCAD]]''' with all of [[EM.Cube]]'s other computational modules.}}
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.CUBE | EM.Cube Modeling Environment]]'''.
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 Maxwell’s equations as opposed to their differential forms used in the finite element or finite difference time domain methods.
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 spaceand the unbounded background medium is modeled using the free-space Green's functions. The unknown currents physical or fields equivalent currents are discretized as a collection of elementary currents or fields with small finite spatial extents. Such elementary currents or fields 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 or fields on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields 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 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 number of surface integral equation formulation 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. For modeling dielectric regions of On the physical structure other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized, in which equivalent for modeling dielectric regions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the 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|40px]] Click here to learn more about the theory of '''[[3D Method of Moments]]'''.
 
=== Advantages & Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===
 
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 choose 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 structure with high geometrical fidelity.
 
 
In general, the surface MoM solver is used to simulate your physical structure, which can be made of metallic and dielectric objects of arbitrary shapes as well as composite structures that contain conjoined metal and dielectric regions. If your project workspace contains at least one line or curve object, EM.Libera then invokes its Wire MoM solver. In that case, only metallic structures can be modeled, and all the surface and solid PEC objects are meshed as wireframes.
This solver can be used to simulate wireframe models of metallic structures and is particularly useful for modeling wire-type antennas and arrays.
== Constructing the Physical Structure ==
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