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arXiv · 2510.09352

LR-WaveHoltz: A Low-Rank Helmholtz Solver

Andreas Granath·Daniel Appelö·Siyang Wang
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Abstract

We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave equation is discretized by high-order multiblock summation-by-parts finite differences. In two dimensions we seek to compress the solution in matrix form, and in three dimensions using tensor trains. To control rank growth we use step-truncation during time stepping and a low-rank Anderson acceleration for the WaveHoltz fixed point iteration. We have carried out extensive numerical experiments demonstrating the convergence and efficacy of the iterative scheme for free- and half-space problems in two and three dimensions with constant and piecewise constant wave speeds.

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Andreas Granath, Daniel Appelö, Siyang Wang. 2025-10-10. LR-WaveHoltz: A Low-Rank Helmholtz Solver. https://arxiv.org/abs/2510.09352

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