Multiple-Precision Iterative Methods for Solving Complex Symmetric Electromagnetic Systems

Abstract

This paper deals with multiple-precision iterative methods for solving the complex symmetric linear equation derived from high-frequency electromagnetic field analysis using the edge finite element method. Double-precision iterative methods for solving this problem are slow to converge. Therefore, we implement a multiple-precision calculation, specifically, double-double (DD) precision numbers. The DD-precision complex numbers and arithmetic operations are implemented using an error-free transformation based on Knuth’s and Dekker’s algorithm. Moreover, some iterative methods with mixed precision are proposed to reduce computational cost. Using developed systems and the QD library that supports DD and quad-double arithmetics, some numerical methods are demonstrated experimentally and their performances are evaluated.