Parallel High-Resolution Compact Partial FFT-Type Direct Algorithms for Subsurface Scattering Problems

This paper introduces a direct parallel partial FFT-type algorithm for the numerical solutions of the two- and three-dimensional Helmholtz equations. The governing equations are discretized by high-order compact finite difference methods. The resulting discretized system is indefinite, making the convergence of most iterative methods deteriorate as frequency increases. In this situation, the parallel direct approaches are a better alternative, especially for the systems with discontinuous and singular right-hand sides. The research focuses on the efficient parallel implementation of the proposed algorithm in shared memory environments (OpenMP). The complexity and scalability of the direct parallel method are investigated on scattering problems with realistic ranges of parameters in soil and mine-like targets.