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arXiv · 2511.20529

SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus

Daniel Bach·Andrés M. Rueda-Ramírez·Eric Sonnendrücker·David C. Del Rey Fernández·Gregor J. Gassner
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Abstract

We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of freedom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties.

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Daniel Bach, Andrés M. Rueda-Ramírez, Eric Sonnendrücker, David C. Del Rey Fernández, Gregor J. Gassner. 2026-09-12. SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus. https://arxiv.org/abs/2511.20529

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