Efficient Wave Propagation in Discontinuous Media and Complex Geometry for Many-core Architectures

Abstract: We present an accelerated numerical solver for the scalar wave equation using one and two GPUs. We consider complex geometry and study accuracy when performing the computation in both single and double precision. The method uses a high-order accurate approximation of the derivatives using summation-by-parts operators.  The boundary conditions are imposed using the simultaneous approximation term technique for Dirichlet type boundary conditions. We develop a novel implementation of the discretization and perform experiments in one dimension with a discontinuity and in two dimensions for a simple embedded geometry. Numerical experiments show that the rate of convergence is as expected using double precision but levels-out for single precision. The performance of the solver when implemented using the GPU shows that runtime is significantly decreased using one graphics card. We then describe a strategy for further increasing performance using two graphics cards.