Product-type Krylov subspace methods for complex symmetric matrices in the electromagnetic field problem

Abstract

To solve time-harmonic problems with complex symmetric matrices in electromagnetic field computations more robustly and efficiently, ten new product-type Krylov subspace (PT) methods are proposed. They are derived from the COCG or COCR methods and are evaluated through finite element analyses of the time-harmonic eddy current and high-frequency electromagnetic wave problems. As a result, in several test cases, iteration counts and the computational time can be substantially reduced. However, in high-frequency electromagnetic wave simulations, the convergence criteria required for the PT methods must be two to three orders of magnitude tighter than those required for the COCG method.