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

TL;DR

This paper introduces a grid-based variant of a nested-sweep polarized traces method for the 2D Helmholtz equation, achieving improved computational efficiency and scalability for high-frequency wave simulations in heterogeneous media.

Contribution

It proposes a new domain decomposition approach that enhances the scalability and reduces memory usage compared to previous layered methods.

Findings

Online parallel complexity scales sub-linearly as O(N/P) with P up to O(N^{1/5})

Improved asymptotic runtime and memory footprint over previous methods

Enhanced algorithmic scalability for geophysical wave simulations

Abstract

We present a variant of the solver in Zepeda-N\'u\~nez 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 \emph{sub linearly} as $\mathcal{O} \left( \frac{N}{P} \right)$, where $N$ is the number of volume unknowns, and $P$ is the number of processors, provided that $P = \mathcal{O}(N^{1/5})$. The variant in Zepeda-N\'u\~nez and Demanet (2014) only afforded $P = \mathcal{O}(N^{1/8})$. Algorithmic scalability is a prime requirement for wave simulation in regimes of interest for geophysical imaging.