A direct finite-element-based solver of significantly reduced complexity for solving large-scale electromagnetic problems

Abstract

Based on the observation that the sparse matrix resulting from a finite-element-based analysis can be represented by an H matrix without any approximation, and the inverse of this sparse matrix has a data-sparse H-matrix representation, in this work, we developed a direct finite-element-based solver of O(NlogN) memory complexity and O(Nlog <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N) time complexity. Numerical results have demonstrated the accuracy and complexity of the proposed solver in both large-scale electrostatic and electrodynamic applications. A comparison with state-of-the-art sparse matrix solvers has shown the advantages of the proposed solver. In addition, the proposed numerical scheme is applicable to arbitrary three-dimensional structures.