Efficient iterative solvers for time-harmonic Maxwell equations using domain decomposition and algebraic multigrid

Paper presents a set of parallel iterative solvers and preconditioners for the efficient solution of systems of linear equations arising in the high order finite-element approximations of boundary value problems for 3-D time-harmonic Maxwell equations on unstructured tetrahedral grids. Balancing geometric domain decomposition techniques combined with algebraic multigrid approach and coarse-grid correction using hierarchic basis functions are exploited to achieve high performance of the solvers and small memory load on the supercomputers with shared and distributed memory. Testing results for model and real-life problems show the efficiency and scalability of the presented algorithms.

► Efficient distributed iterative solvers for time-harmonic Maxwell equations are presented. ► Numerical results include the solution of the system with 2 × 108 unknows in 15 min on 64 nodes cluster. ► The solver is faster than MUMPs by more than an order of magnitude and can solve problems 20 times larger.