Parallel iterative solution for the Helmholtz equation with exact non-reflecting boundary conditions

Efficient and scalable parallel solution methods are presented for the Helmholtz equation with global non-reflecting DtN boundary conditions. The symmetric outer-product structure of the DtN operator is exploited to significantly reduce inter-processor communication required by the non-locality of the DtN to one collective communication per iteration with a vector size equal to the number of harmonics included in the DtN series expansion, independent of the grain size. Numerical studies show that in the context of iterative equation solvers, and for the same accuracy, the global DtN applied to a tightly fitting spheroidal boundary and implemented as a low-rank update with the multiplicative split is more cost-effective (both in wall-clock times and memory) compared to local approximate boundary conditions.