Mesh Smoothing for the Spectral Element Method

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.