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Generation of Hierarchical Tetrahedral Meshes with High-Order Projections for Efficient Multigrid Solvers

Lu, Cao, Xinglin Zhao, Navamita Ray, Xiangmin Jiao

23rd International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-15 2014

IMR
PROCEEDINGS

23rd International Meshing Roundtable
London, UK
October 12-15,2014

Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA.
Mathematics and Computer Science, Argonne National Laboratory, Argonne, IL 60439, USA
Email: jiao@ams.sunysb.edu

Abstract
We investigate the problem of generating hierarchical unstructured meshes through uniform mesh refinement for efficient solution of PDEs using finite element methods and multigrid solvers. To ensure high accuracy along curved boundaries, we utilize high- order surface reconstruction and projection, without requiring a CAD model. The resulting mesh is then used with a Hybrid Geometric+Algebraic (HyGA) multigrid method. We describe the data structure and software requirements, and present numerical results to demonstrate the accuracy and efficiency of multigrid finite-element solver with the proposed techniques.

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