期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 41, 期 4, 页码 C367-C392出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1193992
关键词
adaptive mesh refinement; nonconforming meshes; high-order finite elements; anisotropic refinement; parallel computations; unstructured grids
资金
- U.S. Department of Energy [DE-AC52-07NA27344 (LLNL-JRNL-751849)]
- Ministry of Education, Youth and Sports of the Czech Republic under the RICE New Technologies and Concepts for Smart Industrial Systems project [LO1607]
We propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.
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