Half-closed discontinuous Galerkin discretisations

Pan, Y.; Persson, P. -O.

doi:10.1016/j.jcp.2025.113731

Half-closed discontinuous Galerkin discretisations

Journal Article · Fri Jan 10 00:00:00 EST 2025 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2025.113731· OSTI ID:2565910

Pan, Y. ^[1]; Persson, P. -O. ^[1]

University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Here we introduce the concept of half-closed nodes for nodal discontinuous Galerkin (DG) discretisations. Unlike more commonly used closed nodes in DG, where on every element nodes are placed on all of its boundaries, half-closed nodes only require nodes to be placed on a subset of the element's boundaries. The effect of using different nodes on DG operator sparsity is studied and we find in particular for there to be no difference in the sparsity pattern of the Laplace operator whether closed or half-closed nodes are used. On quadrilateral/hexahedral elements we use the Gauss-Radau points as the half-closed nodes of choice, which we demonstrate is able to speed up DG operator assembly in addition to leverage previously known superconvergence results. We also discuss in this work some linear solver techniques commonly used for Finite Element or discontinuous Galerkin methods such as static condensation and block-based methods, and how they can be applied to half-closed DG discretisations.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 2565910

Alternate ID(s):: OSTI ID: 2498418

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 524; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Half-closed discontinuous Galerkin discretisations

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