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The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis

A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only b...

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Autores principales: Drzisga, Daniel, Keith, Brendan, Wohlmuth, Barbara
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7113627/
https://www.ncbi.nlm.nih.gov/pubmed/32257835
http://dx.doi.org/10.1016/j.mex.2020.100813
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author Drzisga, Daniel
Keith, Brendan
Wohlmuth, Barbara
author_facet Drzisga, Daniel
Keith, Brendan
Wohlmuth, Barbara
author_sort Drzisga, Daniel
collection PubMed
description A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only be performed on a fraction of the elements in the computational domain. In this way, quadrature determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. We present the modifications and extensions required for a reference implementation in the open-source IGA software library GeoPDEs. The exposition is fashioned to help facilitate similar modifications in other contemporary software libraries. • The surrogate matrix methodology is implemented in GeoPDEs. • Poisson’s problem is considered. • The matrix assembly time is significantly reduced at negligible cost to solution accuracy.
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spelling pubmed-71136272020-04-03 The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis Drzisga, Daniel Keith, Brendan Wohlmuth, Barbara MethodsX Mathematics A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only be performed on a fraction of the elements in the computational domain. In this way, quadrature determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. We present the modifications and extensions required for a reference implementation in the open-source IGA software library GeoPDEs. The exposition is fashioned to help facilitate similar modifications in other contemporary software libraries. • The surrogate matrix methodology is implemented in GeoPDEs. • Poisson’s problem is considered. • The matrix assembly time is significantly reduced at negligible cost to solution accuracy. Elsevier 2020-02-20 /pmc/articles/PMC7113627/ /pubmed/32257835 http://dx.doi.org/10.1016/j.mex.2020.100813 Text en © 2020 The Author(s) http://creativecommons.org/licenses/by/4.0/ This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Mathematics
Drzisga, Daniel
Keith, Brendan
Wohlmuth, Barbara
The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
title The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
title_full The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
title_fullStr The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
title_full_unstemmed The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
title_short The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
title_sort surrogate matrix methodology: a reference implementation for low-cost assembly in isogeometric analysis
topic Mathematics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7113627/
https://www.ncbi.nlm.nih.gov/pubmed/32257835
http://dx.doi.org/10.1016/j.mex.2020.100813
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