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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier
2020
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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. |
format | Online Article Text |
id | pubmed-7113627 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Elsevier |
record_format | MEDLINE/PubMed |
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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