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.
Categories: math.NA