Cheap and stable quadrature on polyhedral elements

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design Pub Date : 2025-07-20 DOI:10.1016/j.finel.2025.104409

Alvise Sommariva, Marco Vianello

引用次数: 0

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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在多面体上进行便宜稳定的正交

基于边界框超插值和发散定理的切比雪夫矩计算，讨论了多面体元上多项式数值积分的一种廉价的无四面体方法。没有条件问题出现，因为不需要矩阵分解或反转。所得到的正交公式在理论上是稳定的，即使存在一些负权值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Elements in Analysis and Design 工程技术-力学

CiteScore

4.80

自引率

3.20%

发文量

审稿时长

27 days

期刊介绍： The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.