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Journal of Scientific Computing
Published in: Journal of Scientific Computing 2/2019

22-08-2018

Mesh Smoothing for the Spectral Element Method

Authors: Ketan Mittal, Paul Fischer

Published in: Journal of Scientific Computing | Issue 2/2019

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Abstract

Laplacian- and optimization-based mesh-improvement methods are developed for high-order finite- and spectral-element based on 2D quadrilateral and 3D hexahedral meshes in general domains. A robust high-order interpolation library is used during the mesh smoothing process to improve the quality of the surface mesh while retaining the integrity of the original surface approximation. Boundary layer resolution in the original mesh is preserved through various controls in the smoothing process, including weighted interpolation between the optimized and original mesh. All mesh motion and gradient evaluations are performed on an element-by-element basis to ensure that all elements in a large mesh can be smoothed in parallel with minimum communication between different processors. Mesh quality improvements are shown to reduce the condition number of the preconditioned linear systems governing the numerical solution of the discretized partial differential equations, with corresponding reductions in iteration counts. The mesh smoother is tested on various meshes and is found to significantly improve the computational efficiency of calculations.
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Footnotes
1
The actual vertex count can vary from \((N-1)^3\) to \((N+1)^3\) per element, depending on boundary conditions and domain connectivity. Throughout the text, we will use the simpler expression of \(N^3\) unless otherwise noted.
 
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Metadata
Title
Mesh Smoothing for the Spectral Element Method
Authors
Ketan Mittal
Paul Fischer
Publication date
22-08-2018
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0812-9

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