On the Parallel Solution of Large Industrial Wave Propagation Problems

The use of Fast Multipole Methods (FMM) combined with embedded Krylov solvers preconditioned by a sparse approximate inverse is investigated for the solution of large linear systems arising in industrial acoustic and electromagnetic simulations. We use a boundary element integral equation method to solve the Helmholtz and the Maxwell equations in the frequency domain. The resulting linear systems are solved by iterative solvers using FMM to accelerate the matrix-vector products. The simulation code is developed in a distributed memory environment using message passing and it has out-of-core capabilities to handle very large calculations. When the calculation involves one incident wave, one linear system has to be solved. In this situation, embedded solvers can be combined with an approximate inverse preconditioner to design extremely robust algorithms. For radar cross section calculations, several linear systems have to be solved. They involve the same coefficient matrix but different right-hand sides. In this case, we propose a block variant of the single right-hand side scheme. The efficiency, robustness and parallel scalability of our approach are illustrated on a set of large academic and industrial test problems.