Comparison of Krylov-type methods for complex linear systems applied to high-voltage problems

Abstract

Krylov-subspace methods for complex-valued systems are still a present research topic in numerical mathematics. Due to the lack of theoretical results systematic numerical experiments are very important in order to find a sufficiently robust solution method. An important problem in high-voltage power plants are arc-overs on moist or contaminated insulators. A quantitative knowledge of the electric behaviour of layers of water droplets is necessary in order to understand the resulting ageing processes. Discretization of the electro-quasistatic problem leads to large sparse complex systems of linear equations. Comparisons between different Krylov-subspace methods, also in combination with residual smoothing techniques, and parameter studies are presented in this paper.