# Sophisticated Numerical Engine

In the core of WIPL-D Pro lies an extremely powerful numerical engine. It is based on the Method of Moments, Surface Integral Equations and Surface Equivalence Theorem.

Flexible geometrical modeling is based on right truncated cones and bilinear surfaces (WIPL-D quads). Right truncated cones enable precise representation not only of cylindrical wires, but also wires of variable radius and wire ends. Bilinear surfaces are the simplest quadrilaterals determined by four arbitrarily spaced points, which can be equally used for flat and curved surfaces (plates). Sophisticated segmentation techniques enable inclusion of arbitrary wire-to-plate junction and usage of electrically large quads.

Currents along wires (over plates) are approximated by single (double) polynomial type expansions, which automatically satisfy continuity of currents at arbitrary metallic and/or dielectric junctions and metallic ends (hierarchical higher order basis functions). To obtain unknown coefficients of these expansions, WIPL-D imposes a system of linear equations by applying Galerkin testing procedure to FIE (Field Integral Equation). The EFIE (Electric FIE) is used for metallic structures and PMCHW (FIE based on surface equivalence theorem) is used for dielectrics and/or magnetics.

The solution of system of linear equations is obtained using either direct method (LU decomposition) or iterative method (Conjugate Gradient). In the case of multilevel fast multipole method (MLFMM), memory requirements are reduced because of grouping of basis functions and calculation of interactions between groups instead of individual basis functions for all distant groups.

Usage of sophisticated combined numerical and analytical integration techniques in imposition of the Method of Moments makes this engine highly accurate and efficient. Requiring only 4 unknowns for wire per wavelength and 30 unknowns for metallic surface per wavelength squared (or 60 in case of dielectric), it enables that most practical calculations are finished in a minute. Combining the efficiency with variety of symmetry options, one can analyze structures of up to 10000 wavelengths squared on a PC computer. By applying special techniques such as smart reduction of expansion order and MLFMM, this limit is further extended.

## Outcore solver

Outcore (out-of-core) solver can be applied for simulation of electrically very large structures or very complex structures. When memory requirements imposed by such problems exceed the RAM capacity of the PC, usage of the PC’s hard drive during computations offers a valuable alternative, without the need of upgrading the computer hardware. If used in combination with GPU acceleration, simulations are performed much faster.

Outcore solver stores the linear system matrix, created during the simulation, on the PC’s hard drive and then reads out blocks of data, performs calculations on those blocks, saves the results and then moves on to the next block. This way, the limit in the size of solvable problems is not set by computer’s RAM, but by available hard drive space.

Recent tests have shown that the speed of computations when outcore solver is applied is some 15% to 20% slower than the standard incore solver.