Wideband Directional ℋ2-Matrix Compression for the Electric Field Integral Equation with Geometry-Adaptive Cluster Trees
Abstract
We present an efficient wideband construction of directional ℋ2-matrices for the electrical field integral equation that, in contrast to existing constructions, supports not only box trees but also geometry-adaptive cluster trees. To accommodate geometry-adaptive cluster trees, we determine the number of directions from the electrical size of each cluster (instead of the level of a box tree), construct the directions using Spherical-Fibonacci points, and establish a hierarchy between the direction sets of a cluster and its children through an angular nearest-neighbor mapping. We construct the nested directional representation using the incomplete adaptive cross approximation, for which we introduce a robustified tree-mimicry pivoting strategy that prevents premature convergence for block-structured matrices arising from certain geometries and meshes. Numerical results demonstrate that the proposed approach achieves the desired accuracy, requires no more storage than the octree-based construction and substantially less when the geometry or discretization is poorly matched to octree clustering, and exhibits the expected 𝒪(Nlog N) scaling for high-frequency problems.
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BibTeX
@misc{tetzner2026wideband,
title = {{Wideband Directional $\mathcalH^2$-Matrix Compression for the Electric Field Integral Equation with Geometry-Adaptive Cluster Trees}},
author = {Joshua M. Tetzner and Simon B. Adrian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19431},
eprint = {2609.19431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19431},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Wideband Directional ℋ^2-Matrix Compression for the Electric Field Integral Equation with Geometry-Adaptive Cluster Trees
AU - Joshua M. Tetzner
AU - Simon B. Adrian
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19431
UR - https://arxiv.org/abs/2609.19431
AB - We present an efficient wideband construction of directional ℋ^2-matrices for the electrical field integral equation that, in contrast to existing constructions, supports not only box trees but also geometry-adaptive cluster trees. To accommodate geometry-adaptive cluster trees, we determine the number of directions from the electrical size of each cluster (instead of the level of a box tree), construct the directions using Spherical-Fibonacci points, and establish a hierarchy between the direction sets of a cluster and its children through an angular nearest-neighbor mapping. We construct the nested directional representation using the incomplete adaptive cross approximation, for which we introduce a robustified tree-mimicry pivoting strategy that prevents premature convergence for block-structured matrices arising from certain geometries and meshes. Numerical results demonstrate that the proposed approach achieves the desired accuracy, requires no more storage than the octree-based construction and substantially less when the geometry or discretization is poorly matched to octree clustering, and exhibits the expected 𝒪(Nlog N) scaling for high-frequency problems.
ER -