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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 arbitrary 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, 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 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 is 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.
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. |
