Quasi-Helmholtz Calderón Multiplicative Preconditioning for Higher-Order Global Multi-Trace Integral Equations
Abstract
The paper presents a higher-order global multi-trace integral equation for time-harmonic electromagnetic scattering by composite objects. The higher-order multi-trace formulation is preconditioned with a Calderón multiplicative preconditioner using higher-order quasi-Helmholtz projectors. The higher-order quasi-Helmholtz projectors separate the solenoidal and non-solenoidal components of the basis functions. Separate access to the Helmholtz components circumvents the explicit inversion of an ill-conditioned mixed Gram matrix. This enables the application of Calderón multiplicative preconditioning without refining the mesh and resorting to dual basis functions. Furthermore, it enables low-frequency stabilization, as the solenoidal and non-solenoidal components can be rescaled individually. The higher-order quasi-Helmholtz projectors are computed iteratively, enabling iterative solvers to efficiently solve the preconditioned matrix system, yielding accurate solutions in a few dozen iterations. Numerical experiments are conducted for composite dielectric bodies, confirming the effectiveness of the proposed preconditioner for the global multi-trace formulation discretized with higher-order basis functions for dense meshes and at very low frequencies
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BibTeX
@misc{munger2026quasihelmholtz,
title = {{Quasi-Helmholtz Calderón Multiplicative Preconditioning for Higher-Order Global Multi-Trace Integral Equations}},
author = {Cedric Münger and Alessandro Zuccotti and Van Chien Le and Kristof Cools},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17252},
eprint = {2609.17252},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17252},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasi-Helmholtz Calderón Multiplicative Preconditioning for Higher-Order Global Multi-Trace Integral Equations
AU - Cedric Münger
AU - Alessandro Zuccotti
AU - Van Chien Le
AU - Kristof Cools
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17252
UR - https://arxiv.org/abs/2609.17252
AB - The paper presents a higher-order global multi-trace integral equation for time-harmonic electromagnetic scattering by composite objects. The higher-order multi-trace formulation is preconditioned with a Calderón multiplicative preconditioner using higher-order quasi-Helmholtz projectors. The higher-order quasi-Helmholtz projectors separate the solenoidal and non-solenoidal components of the basis functions. Separate access to the Helmholtz components circumvents the explicit inversion of an ill-conditioned mixed Gram matrix. This enables the application of Calderón multiplicative preconditioning without refining the mesh and resorting to dual basis functions. Furthermore, it enables low-frequency stabilization, as the solenoidal and non-solenoidal components can be rescaled individually. The higher-order quasi-Helmholtz projectors are computed iteratively, enabling iterative solvers to efficiently solve the preconditioned matrix system, yielding accurate solutions in a few dozen iterations. Numerical experiments are conducted for composite dielectric bodies, confirming the effectiveness of the proposed preconditioner for the global multi-trace formulation discretized with higher-order basis functions for dense meshes and at very low frequencies
ER -