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PreprintCC BY-NC-ND 4.0arXiv

High-order L2-Galerkin schemes for the decoupled potential integral equations

  • David Scott Winterrose
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Abstract

We prove Sobolev space well-posedness of the decoupled potential integral equations. Using basic pseudo-differential techniques, discrete stability is obtained for the standard L2-pairing, and we deduce spectral convergence for high-order schemes employing discontinuous basis functions, or with additional element-wise tangential continuity imposed in the vectorial part of the system. The schemes are shown to be much better conditioned than a mature commercial EFIE/CFIE solver. In many cases appearing almost independent of wavenumber, mesh density, and the order.

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Cite

BibTeXRIS
BibTeX
@misc{winterrose2026highorder,
  title = {{High-order $L^2$-Galerkin schemes for the decoupled potential integral equations}},
  author = {David Scott Winterrose},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.10799},
  eprint = {2608.10799},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.10799},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - High-order L^2-Galerkin schemes for the decoupled potential integral equations
AU  - David Scott Winterrose
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2608.10799
UR  - https://arxiv.org/abs/2608.10799
AB  - We prove Sobolev space well-posedness of the decoupled potential integral equations. Using basic pseudo-differential techniques, discrete stability is obtained for the standard L^2-pairing, and we deduce spectral convergence for high-order schemes employing discontinuous basis functions, or with additional element-wise tangential continuity imposed in the vectorial part of the system. The schemes are shown to be much better conditioned than a mature commercial EFIE/CFIE solver. In many cases appearing almost independent of wavenumber, mesh density, and the order.
ER  -