Parallel solution of high frequency Helmholtz equations using high order finite difference schemes

Talk Abstract We examine the solution of high-frequency Helmholtz equations using 2nd, 4th and 6th order finite difference schemes. The examples include two problems with known analytic solutions, enabling error evaluation of the different schemes on various grids (9–18 points per wavelength). We use our block-parallel CARP-CG algorithm [Parallel Computing 36, 2010] for solving the equations. The algorithm is successful at lowering the relative residual, indicating that it is a robust and reliable parallel solver of the resulting linear systems. However, lowering the error of the solution to reasonable levels is obtained only with the higher order schemes. These results corroborate the known limitations of the low order scheme at modeling the Helmholtz equation, and they indicate that CARP-CG can also be used effectively with high order finite difference schemes. The parallel evaluation uses these two problems and a more realistic third problem.