The EM simulation engine used in WIPL-D Pro is based on the Method of Moments (MoM), Surface Integral Equations and Surface Equivalence Theorem. Flexible modeling of an arbitrary electromagnetic 3D structure is based on WIres and PLates, the property that has been highlighted in the very name of the program code (WIPL). Right truncated cones are used to approximate the wires, and plates are used to approximate flat or curved surfaces. Plates, also called quads, are actually the bilinear surfaces determined by four points arbitrarily located in space.
An unknown current along a wire is approximated by single polynomial expansion, while a current over a plate is approximated using double polynomial expansion. Higher Order Basis Functions (HOBFs) satisfying the continuity of currents are used to approximate the currents on a mesh element. The approximation is very efficient as it requires only 4 unknown coefficients for wire per wavelength, 30 unknown coefficients for metallic surface per wavelength squared, or 60 unknown coefficients for dielectric surface per wavelength squared. In total, a large structure can be adequately modeled using approximately an order of magnitude fewer unknown coefficients compared with other MoM codes which use triangular meshing and Rao-Wilton-Glisson (RWG) basis functions.
To obtain unknown coefficients of the expansions, WIPL-D imposes a system of linear equations by applying Galerkin testing procedure. The more complex the problem, the more coefficient are required for a good approximation, and more unknown functions need to be determined. The problem comes down to inversion of a NxN matrix, which is required to solve a system with N unknown coefficients and N equations.
“Unknown” is an unknown coefficient in the approximation of the current.