Isogeometric multi-patch preconditioner for time-dependent electromagnetic problems
Abstract
We build upon recent developments in high-order spline-based geometric methods for the three-dimensional initial boundary value problem of Maxwell's equations. Previous schemes were limited to single-patch geometries. To address the computational challenges associated with inverting mass matrices in multi-patch settings, we extend existing techniques for 0-forms mass and stiffness matrices to 1-forms mass matrices. Our approach leverages the tensor-product structure of spline spaces to construct a spectrally equivalent preconditioner for the 1-forms mass matrices. Specifically, we design an efficient preconditioner for single-patch domains that is robust with respect to both mesh size and spline degree. In the multi-patch case, this methodology is extended by integrating the single-patch preconditioner with an additive Schwarz approach, ensuring robustness and scalability with respect to the number of patches. We analyze the computational complexity of the proposed preconditioner and validate its robustness and efficiency through comprehensive numerical experiments.
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BibTeX
@misc{kapidani2026isogeometric,
title = {{Isogeometric multi-patch preconditioner for time-dependent electromagnetic problems}},
author = {Bernard Kapidani and Gabriele Loli and Giancarlo Sangalli and Mattia Tani and Rafael Vázquez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35636},
eprint = {2609.35636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35636},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Isogeometric multi-patch preconditioner for time-dependent electromagnetic problems
AU - Bernard Kapidani
AU - Gabriele Loli
AU - Giancarlo Sangalli
AU - Mattia Tani
AU - Rafael Vázquez
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35636
UR - https://arxiv.org/abs/2609.35636
AB - We build upon recent developments in high-order spline-based geometric methods for the three-dimensional initial boundary value problem of Maxwell's equations. Previous schemes were limited to single-patch geometries. To address the computational challenges associated with inverting mass matrices in multi-patch settings, we extend existing techniques for 0-forms mass and stiffness matrices to 1-forms mass matrices. Our approach leverages the tensor-product structure of spline spaces to construct a spectrally equivalent preconditioner for the 1-forms mass matrices. Specifically, we design an efficient preconditioner for single-patch domains that is robust with respect to both mesh size and spline degree. In the multi-patch case, this methodology is extended by integrating the single-patch preconditioner with an additive Schwarz approach, ensuring robustness and scalability with respect to the number of patches. We analyze the computational complexity of the proposed preconditioner and validate its robustness and efficiency through comprehensive numerical experiments.
ER -