Hierarchical low-rank compression exploiting symmetric boundary integral equations in transmission scattering
Abstract
We propose an approach using matrix symmetry to accelerate hierarchical low-rank compression for wave transmission scattering. For Helmholtz transmission problems, we introduce a symmetric Müller-like boundary integral equation formulation. Although not of the second kind, this formulation creates no difficulties for direct solvers. A one-point corrected quadrature in a Nyström discretization preserves the complex symmetry of the discretized system. This formulation is integrated into a variant of a hierarchical semiseparable direct solver. Within this framework, the computational workload of the low-rank approximation in the proxy method is halved by exploiting the symmetric relationship between the left and right coefficients. Furthermore, we extend this symmetry-exploiting approach to elastic transmission problems by using a symmetric Galerkin boundary element method. Numerical experiments on a multi-node computing cluster demonstrate that the symmetric Müller-like formulation for Helmholtz scattering achieves on average a 1.41-fold speedup compared to the non-symmetric baseline while maintaining third-order convergence. Furthermore, the symmetry-aware solver for elastic scattering is more than 1.5 times faster.
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BibTeX
@misc{matsumoto2026hierarchical,
title = {{Hierarchical low-rank compression exploiting symmetric boundary integral equations in transmission scattering}},
author = {Yasuhiro Matsumoto and Taizo Maruyama and Qianxiang Ma and Rio Yokota},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33216},
eprint = {2609.33216},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33216},
}
RIS
TY - UNPB
TI - Hierarchical low-rank compression exploiting symmetric boundary integral equations in transmission scattering
AU - Yasuhiro Matsumoto
AU - Taizo Maruyama
AU - Qianxiang Ma
AU - Rio Yokota
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33216
UR - https://arxiv.org/abs/2609.33216
AB - We propose an approach using matrix symmetry to accelerate hierarchical low-rank compression for wave transmission scattering. For Helmholtz transmission problems, we introduce a symmetric Müller-like boundary integral equation formulation. Although not of the second kind, this formulation creates no difficulties for direct solvers. A one-point corrected quadrature in a Nyström discretization preserves the complex symmetry of the discretized system. This formulation is integrated into a variant of a hierarchical semiseparable direct solver. Within this framework, the computational workload of the low-rank approximation in the proxy method is halved by exploiting the symmetric relationship between the left and right coefficients. Furthermore, we extend this symmetry-exploiting approach to elastic transmission problems by using a symmetric Galerkin boundary element method. Numerical experiments on a multi-node computing cluster demonstrate that the symmetric Müller-like formulation for Helmholtz scattering achieves on average a 1.41-fold speedup compared to the non-symmetric baseline while maintaining third-order convergence. Furthermore, the symmetry-aware solver for elastic scattering is more than 1.5 times faster.
ER -