Fast linear equation solvers in high performance electromagnetic field analysis

Solving linear equations plays a crucial role in high performance electromagnetic field analysis. We describe forms and characteristics of a system of linear equations arising in electromagnetic field analysis with finite element method (FEM). Properties of ICCG and its parallelization are discussed in context of electromagnetic field analyses. Although current applicability of multigrid approach is rather limited in electromagnetic field analysis in comparison with ICCG, the multigrid method is important because it is quite fast when applied to very large-scale problems. We discuss the algebraic multigrid method in finite element electromagnetic field analysis.