Work

Uniform H-Matrix Compression with Applications to Boundary Integral Equations

Year: 2025

Type: article

Abstract: . Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the [Formula: see text]-matrix format, this sparsity is exploited to achieve [Formula: see text] complexity for storage and multiplication by a vector. This is achieved purely algebraically, based on low-rank approximations of subblocks, and hence the format is also applicable to a wider range of problems. The [Formula: see text]-matrix format improves the complexity to [Formula: see text] by introducing a recursive structure onto subblocks on multiple levels. However, in many cases this comes with a large proportionality constant, making the [Formula: see text]-matrix format advantageous mostly for large problems. In this paper we investigate the usefulness of a matrix format that lies in between these two: uniform [Formula: see text]-matrices. An algebraic compression algorithm is introduced to transform a regular [Formula: see text]-matrix into a uniform [Formula: see text]-matrix, which maintains the asymptotic complexity. Using examples of the boundary element method formulation of the Helmholtz equation, we show that this scheme lowers the storage requirement and execution time of the matrix-vector product without significantly impacting the construction time. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://gitlab.kuleuven.be/numa/software/beachpack/-/tree/kb-exp-paper-uhmatrix?ref_type=tags and in the supplementary materials ( beachpack-kb-exp-paper-uhmatrix-v2.zip [210MB]). [Formula: see text]

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/24m1665209

Authors: Kobe Bruyninckx, Daan Huybrechs, Karl Meerbergen

Institution: KU Leuven

Language: English

Topic: Electromagnetic Scattering and Analysis

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, Vlaamse regering

Award: Structured low-rank representations for frequency-dependent wave scattering simulations using boundary element methods