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.

### The “unknown”

“Unknown” is an unknown coefficient in the approximation of the current.

The higher complexity of the problem, the larger the number of unknowns. The number of unknowns required for a particular structure can be roughly estimated from the model size.

The minimum number of unknowns per wavelength squared is 30 for a metallic surface and 60 for a dielectric surface. At all times, a user needs to keep in mind the fact that WIPL-D uses Higher Order Basis Functions. In practice this means that a microstrip patch antenna, with approximate dimensions of half wavelength by half wavelength, can be modeled as a single mesh element.

To get a better idea about the number of unknowns required for a specific simulation scenario, visit our Benchmarks and Applications sections, where many practical modeling details are presented including the number of unknowns. To get the rough estimate about the software configuration best suited for your needs, please visit Customizing WIPL-D Suite section or contact our Sales team.

#### Beyond the Unknown Limits

Simple, brute force method of crude empowering of the computational resources is definitely an ineffective way to address a high complexity of the simulation model. Before reaching for a powerful hardware, the possibilities to cleverly reduce the problem size must be exploited.

WIPL-D has introduced a number of techniques which considerably downsize the number of unknowns and reduce the simulation time while extending the size of the problem that can be solved on a standard contemporary desktop computer or a laptop.

Special computational techniques and advanced approximation features have been developed to support the efficient operation of the kernel for the case of electrically large structures. First of all, the Outcore solver can be used to overcome the RAM limitation of the hardware. Next, the symmetry features of the structure in hand can be exploited by using Symmetry and Advanced Symmetry options to reduce the number of unknowns significantly. Lastly, Smart Reduction, Shadow Regions, Unused Entities, Transparent Radome are all specifically targeting the reduction of a number of unknowns, while Domain Decomposition Solver reduces the simulation time for a number of practically important scenarios.

For electrically moderate and large EM problems, the tremendous speed-up of WIPL-D solver is achieved by using GPU Solver or GPU Cluster Solver where one or more GPUs are used to solve problems which cannot be solved in a reasonable time relying only on the power of a CPU.

Finally, users are encouraged to use the expert help of WIPL-D technical support team offering the customers unlimited assistance to simulate their projects most efficiently using the hardware available.

#### Outcore Solver

If the installed RAM is not sufficient to store the unknowns, the out-core simulation is invoked.

Outcore solver stores the linear system matrix on the Hard Disk Drive (HDD). Blocks of the system matrix are read into the memory, calculations performed and the results saved back to the HDD, next set of blocks read in and then process continues until all of the blocks are processed. The block-by-block outcore calculation makes the size of a solvable problem independent from the RAM size, but by available HDD space. Recent tests have shown that the speed of computations with the outcore solver is 15% – 20% lower than with the standard, incore solver.

#### Smart Reduction

Smart Reduction is a feature indispensable when simulating antenna placement and RCS problems.

It automatically reduces the order of current expansion on parts of the model less significant for EM analysis by performing an adaptive reduction of current expansion order over parts of the model which are distant from the antenna or are in the shadow. Applying Smart reduction, the number of unknowns can be reduced 3-10 times, while very good accuracy of calculated radiation pattern or coupling between multiple antennas is preserved. Furthermore, some regions of the platform can be specified to lay in the shadow. Expansion orders on all patches in the shadow are reduced uniformly, in addition to the distance-to-the-antenna factor. The feature requires very little user intervention.

#### Unused Entities

A skilled user can choose to exclude from the simulation some of the model entities which insignificantly influence the output results.

Such guesses are frequently made based on user’s experience, engineering practice or intuition. By combining the Smart reduction with Unused Entities, the reduction of the number of unknowns compared to the original problem can be even more than an order of magnitude.

The antenna is represented through a far field pattern. The analysis is performed in two steps. In the first step, antenna or an antenna array is analyzed as it radiates in free space, i.e. ignoring the presence of the radome. Based on the results obtained in the first step, and using a special technique, parts of radome having insignificant influence to the accuracy are identified. These parts are excluded in the second step where the antenna is analyzed together with the remaining parts of the radome.

#### Domain Decomposition

Domain Decomposition Solver analyses electrically very large structures by subdividing the boundary problem into smaller sub-domain problems, solving the subdomain problems and combining the solutions.

Full wave solutions of Antenna Placement, including the calculation of the coupling between several antennas, monostatic and bistatic Radar Cross Section, Radomes etc. can be obtained with high numerical efficiency.

#### Parallelization

GPU Solver puts to good use the power of a GPU card to extend the performance of a single machine while GPU Cluster Solver uses the power of the cluster computations to significantly speed-up the simulation and remarkably increase the size of a solvable problem.