Electrical and Computer Engineering Commons^™

H-Matrix-Based Fast Direct Finite Element Solver For Large-Scale Electromagnetic Analysis, Haixin Liu, Dan Jiao

Department of Electrical and Computer Engineering Technical Reports

In this work, we prove that the sparse matrix resulting from a finite-element-based analysis of electrodynamic problems can be represented by an H-matrix without any approximation, and the inverse of this sparse matrix has a data-sparse H-matrix approximation with error well controlled. Based on this proof, we develop an H-matrix-based direct finite-element solver of O(kNlogN) memory complexity and O(k2Nlog2N) time complexity for solving electromagnetic problems, where k is a small variable that is adaptively determined based on accuracy requirements, and N is the number of unknowns. Both inversebased and LU-based direct solutions are developed. The LU-based solution is further accelerated …