Performance of Preconditioned Linear Solvers Based on Minimum Residual for Complex Symmetric Linear Systems

Abstract

Fast computation of linear systems is essential for reducing the elapsed time when using finite element analysis. The incomplete Cholesky conjugate orthogonal conjugate gradient method is widely used as a linear solver for complex symmetric systems derived from the edge-based FEM in the frequency domain. On the other hand, the performance of the preconditioned minimized residual method based on the three-term recurrence (MRTR) formula of the conjugate gradient-type method has been demonstrated on various symmetric sparse linear systems obtained from edge-based FEM formulated in the magnetostatic and time domain. This paper shows for the first time the performance of the preconditioned conjugate orthogonal MRTR method applied to complex symmetric linear systems.