Multi-Level Power Series Solution for Large Surface and Volume Electric Field Integral Equation

TL;DR

This paper introduces a multilevel power series method for efficiently solving large electric field integral equations using H-Matrix, achieving fixed iteration convergence, significant time and memory savings, and maintaining O(NlogN) complexity.

Contribution

A novel multilevel power series approach for large-scale electric field integral equations that reduces computation time and memory while preserving accuracy and convergence properties.

Findings

Converges in a fixed number of iterations.

Reduces time and memory compared to traditional H-Matrix solvers.

Maintains O(NlogN) solution complexity.

Abstract

In this paper, we propose a new multilevel power series solution method for solving a large surface and volume electric field integral equation based H-Matrix. The proposed solution method converges in a fixed number of iterations and is solved at each level of the H-Matrix computation.The solution method avoids the computation of a full matrix, as it can be solved independently at each level, starting from the leaf level. Solution at each level can be used as the final solution, thus saving the matrix computation time for full H-Matrix. The paper shows that the leaf level matrix computation and solution with power series gives an accurate results as full H-Matrix iterative solver method. The method results in considerable time and memory savings compared to the H-Matrix iterative solver. Further, the proposed method retains the O(NlogN) solution complexity