Parallel discontinuous Galerkin surface integral equation method for solving large and complex PEC scattering problems

Abstract

We present flexible and efficient solutions of large-scale scattering problems involving three-dimensional conductors with arbitrary shapes using the parallel discontinuous Galerkin (DG) surface integral equation (SIE) method. The use of DG domain decomposition framework allows conformal as well as nonconformal surface discretizations of the targets thus brings significant flexibility in the meshing. The coefficient of the interior penalty term of the conventional DG is specially set to avoid extra treatment on the contour boundary to further improve its flexibility. To reduce the number of iterations required for the solutions, two types of preconditioners are applied by using the near-field matrix of the whole region. The well-scaling ternary parallelization approach of the multilevel fast multipole algorithm (MLFMA) is employed for solving problems involving over billions of unknowns. Numerical results are included to validate the accuracy and demonstrate the versatility of the proposed method. In addition, we present the effectiveness of our algorithm by solving a complicated aircraft mode with inlets involving 624 million unknowns.