TY - GEN
T1 - Decoupling simulation accuracy from mesh quality
AU - Schneider, Teseo
AU - Hu, Yixin
AU - Dumas, Jérémie
AU - Gao, Xifeng
AU - Panozzo, Daniele
AU - Zorin, Denis
N1 - Publisher Copyright:
© 2018 Association for Computing Machinery.
PY - 2018/12/4
Y1 - 2018/12/4
N2 - 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.
AB - 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.
KW - Error Estimates
KW - Finite Elements
KW - Mesh Quality
KW - P-Refinement
UR - http://www.scopus.com/inward/record.url?scp=85066076064&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85066076064&partnerID=8YFLogxK
U2 - 10.1145/3272127.3275067
DO - 10.1145/3272127.3275067
M3 - Conference contribution
AN - SCOPUS:85066076064
T3 - SIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018
BT - SIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018
PB - Association for Computing Machinery, Inc
T2 - SIGGRAPH Asia 2018 Technical Papers - International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH Asia 2018
Y2 - 4 December 2018 through 7 December 2018
ER -