Authors: Wenwen Chai, and Dan Jiao
Abstract: In this paper, we will develop a fast direct integral equation solver for large-scale electrodynamic analysis. In this solver, we significantly reduce the cost of an H-matrix-based computation of electrodynamic problems with prescribed accuracy satisfied, by constructing an efficient matrix algebra-based method that minimizes the rank of each admissible block based on accuracy; and by developing a new frequency-dependent Hpartition that minimizes the number of admissible blocks at each tree level for each frequency point. We will then develop a fast H-matrix-based LU factorization for directly solving the dense system matrix resulting from an integral-equation-based analysis of large-scale electrodynamic problems. The proposed direct solver successfully solves dense matrices that involve more than 1 million unknowns associated with electrodynamic problems of 96 wavelengths in fast CPU time (less than 20 hours in LU factorization, 85 seconds in LU solution), modest memory consumption, and with the prescribed accuracy satisfied on a single CPU running at 3 GHz. As an algebraic method, the underlying fast techniques are kernel independent.
Index Terms: Integral-equation based methods, electrodynamic analysis, direct solution, H matrix, large-scale analysis
View PDFA Fast H-Matrix Based Direct Integral Equation Solver with Optimized H-Partition and Minimized Rank for Large-Scale Electrodynamic Analysis