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Decoupling simulation accuracy from mesh quality

Authors:

Teseo Schneider,

Jérémie Dumas,

Daniele Panozzo,

Denis ZorinAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 37, Issue 6

Article No.: 280, Pages 1 - 14

https://doi.org/10.1145/3272127.3275067

Published: 04 December 2018 Publication History

Abstract

For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved.

We propose to use p-refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs.

Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance.

Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary constraints or limitations of current meshing methods. By tackling mesh generation and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms.

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This repository contains the scripts to regenerate the figures in the paper "Decoupling Simulation Accuracy from Mesh Quality" published in ACM Trans. on Graphics, Vol. 37(6), 2018.

The code is also available on GitHub: https://github.com/polyfem/Decoupling-Simulation-Accuracy-from-Mesh-Quality

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Index Terms

Decoupling simulation accuracy from mesh quality
1. Computing methodologies
  1. Modeling and simulation

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 37, Issue 6

December 2018

1401 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3272127

Editor:
Takeo Igarashi
The University of Tokyo, Japan

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Copyright © 2018 ACM.

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Published: 04 December 2018

Published in TOG Volume 37, Issue 6

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