Nonconforming Mesh Refinement for High-Order Finite Elements

Červený, Jakub; Dobrev, Veselin; Kolev, Tzanio

doi:10.1137/18m1193992

Nonconforming Mesh Refinement for High-Order Finite Elements

Journal Article · Thu Jul 25 00:00:00 EDT 2019 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/18m1193992· OSTI ID:1771021

Červený, Jakub ^[1]; Dobrev, Veselin ^[1]; ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

In this study, 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1771021

Report Number(s):: LLNL-JRNL--751849; 937932

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 4 Vol. 41; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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hr-adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio arXiv https://doi.org/10.48550/arxiv.2010.02166	text	January 2020

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Related Subjects

97 MATHEMATICS AND COMPUTING
adaptive mesh refinement
high-order finite elements
non-conforming meshes
parallel computations
unstructured grids

Nonconforming Mesh Refinement for High-Order Finite Elements

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References (22)

Cited By (1)

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