A short note on a pipelined polarized-trace algorithm for 3D Helmholtz

Abstract

We present a fast solver for the 3D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media. The solver is based on the method of polarized traces, coupled with distributed linear algebra libraries and pipelining to obtain a solver with online runtime $\mathcal{O}(\max(1,R/n)N \log N)$ where $N = n^3$ is the total number of degrees of freedom and R is the number of right-hand sides.