A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

Abstract

We present a variant of the solver in Zepeda-Núñez and Demanet (2014), for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media. By changing the domain decomposition from a layered to a grid-like partition, this variant yields improved asymptotic online and offline runtimes and a lower memory footprint. The solver has online parallel complexity that scales sublinearly as θ(N/P), where N is the number of volume unknowns, and P is the number of processors, provided that P = θ(N[superscript 1/5]). The variant in Zepeda-Núñez and Demanet (2014) only afforded P = θ(N[superscript 1/5]). Algorithmic scalability is a prime requirement for wave simulation in regimes of interest for geophysical imaging. Keywords: frequency-domain, finite difference, modeling, wave equation, numerical