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Energy-Minimizing, Symmetric Discretizations for Anisotropic Meshes and Energy Functional Extrapolation

Kühn, Martin Joachim and Kruse, Carola and Rüde, Ulrich (2021) Energy-Minimizing, Symmetric Discretizations for Anisotropic Meshes and Energy Functional Extrapolation. Siam Journal on Scientific Computing, 43 (4), A2448-A2473. SIAM - Society for Industrial and Applied Mathematics. doi: 10.1137/21M1397520. ISSN 1064-8275.

[img] PDF - Postprint version (accepted manuscript)

Official URL: https://epubs.siam.org/doi/abs/10.1137/21M1397520


Self-adjoint differential operators often arise from variational calculus on energy functionals. In this case, a direct discretization of the energy functional induces a discretization of the differential operator. Following this approach, the discrete equations are naturally symmetric if the energy functional was self-adjoint, a property that may be lost when using standard difference formulas on nonuniform meshes or when the differential operator has varying coefficients. Low order finite difference or finite element systems can be derived by this approach in a systematic way and on logically structured meshes they become compact difference formulas. Extrapolation formulas used on the discrete energy can then lead to higher oder approximations of the differential operator. A rigorous analysis is presented for extrapolation used in combination with nonstandard integration rules for finite elements. Extrapolation can likewise be applied on matrix-free finite difference stencils. In our applications, both schemes show up to quartic order of convergence.

Item URL in elib:https://elib.dlr.de/143792/
Document Type:Article
Title:Energy-Minimizing, Symmetric Discretizations for Anisotropic Meshes and Energy Functional Extrapolation
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Kühn, Martin JoachimUNSPECIFIEDhttps://orcid.org/0000-0002-0906-6984
Kruse, CarolaParallel Algorithms Team, CERFACS (Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique), 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, Francehttps://orcid.org/0000-0002-4142-7356
Rüde, UlrichLehrstuhl für Informatik 10 (Systemsimulation), Universität Erlangen-Nürnberg, Nürnberghttps://orcid.org/0000-0001-8796-8599
Journal or Publication Title:Siam Journal on Scientific Computing
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:A2448-A2473
Publisher:SIAM - Society for Industrial and Applied Mathematics
Keywords:partial differential equation, energy functional, symmetry, anisotropy, extrapolation, finite differences, finite elements
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Tasks SISTEC
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology
Institute for Software Technology > High-Performance Computing
Deposited By: Kühn, Dr. Martin Joachim
Deposited On:09 Sep 2021 11:36
Last Modified:09 Sep 2021 11:36

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