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arXiv · 2502.03446

Cheap and stable quadrature on polyhedral elements

Alvise Sommariva·Marco Vianello
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Abstract

We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment computation via the divergence theorem. No conditioning issues arise, since no matrix factorization or inversion is needed. The resulting quadrature formula is theoretically stable even in the presence of some negative weights.

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Alvise Sommariva, Marco Vianello. 2025-02-05. Cheap and stable quadrature on polyhedral elements. https://arxiv.org/abs/2502.03446

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