Application of a Sparsity Pattern and Region Clustering for Near Field Sparse Approximate Inverse Preconditioners in Method of Moments Simulations

Carlos Delgado,Felipe Cátedra,Javier Moreno

doi:10.1155/2017/9845050

Carlos Delgado, Felipe Cátedra + Show 1 more

Open Access

https://doi.org/10.1155/2017/9845050

Copy DOI

Abstract

This document presents a technique for the generation of Sparse Inverse Preconditioners based on the near field coupling matrices of Method of Moments simulations where the geometry has been partitioned in terms of regions. A distance parameter is used to determine the sparsity pattern of the preconditioner. The rows of the preconditioner are computed in groups at a time, according to the number of unknowns contained in each region of the geometry. Two filtering thresholds allow considering only the coupling terms with a significant weight for a faster generation of the preconditioner and storing only the most significant preconditioner coefficients in order to decrease the memory required. The generation of the preconditioner involves the computation of as many independent linear least square problems as the number of regions in which the geometry is partitioned, resulting in very good scalability properties regarding its parallelization.

Highlights

Many of the modern approaches for electromagnetic analysis based on the Method of Moments (MoM) [1] rely on the idea of only storing the near field coupling terms of the impedance matrix, which typically extends about onequarter of the wavelength under analysis
In all the cases we have applied the Method of Moments combined with the Multilevel Fast Multipole Algorithm using 0.25 λ as the region size unless otherwise indicated
The Generalized Minimal Residual (GMRES) iterative solver [21] with a restart parameter of 300 has been used for all the simulations presented

Summary

Introduction

Many of the modern approaches for electromagnetic analysis based on the Method of Moments (MoM) [1] rely on the idea of only storing the near field coupling terms of the impedance matrix, which typically extends about onequarter of the wavelength under analysis. A method for the generation of a preconditioner for problems involving multiple scatterers, based on splitting the system matrix according to the types of material of the subdomains as well as currents on different parts, is shown in [8] Another group of preconditioners that are commonly used in the context mentioned above rely on the numerical manipulation of the system matrix rather than on physical properties of the problem under analysis. The preconditioners based on the ILU and SAI approaches are often generated considering only the near field part of the coupling matrix, which includes the strongest interactions between basis and testing functions This allows a fast generation and reasonably reduced size, the performance of such preconditioners may be lacking in the analysis of problems in which there are strong interactions between parts of the geometry that are physically distant, like the interaction between the feed of a reflector antenna and the main reflector or between parts of certain cavities.

Description of the Approach

Numerical Results

Figure 1

Conclusion