Block variants of the COCG and COCR methods for solving complex symmetric linear systems with multiple right-hand sides

TL;DR

This paper introduces new block variants of the COCG and COCR methods that leverage complex symmetry to efficiently solve large complex symmetric linear systems with multiple right-hand sides, demonstrating improved convergence in electromagnetic simulations.

Contribution

The paper presents novel block algorithms for COCG and COCR that exploit complex symmetry, enhancing efficiency for systems with multiple right-hand sides.

Findings

Favorable convergence properties demonstrated in numerical experiments.

Effective in solving electromagnetic simulation problems.

Leverages complex symmetry for computational efficiency.

Abstract

In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symmetric linear systems with multiple right hand sides. The proposed Block iterative solvers can fully exploit the complex symmetry property of coefficient matrix of the linear system. We report on extensive numerical experiments to show the favourable convergence properties of our newly developed Block algorithms for solving realistic electromagnetic simulations.