Computational Complexity of Hierarchically Adapted Meshes
We show that for meshes hierarchically adapted towards singularities there exists an order of variable elimination for direct solvers that will result in time complexity not worse than [Formula: see text], where N is the number of nodes and q is the dimensionality of the singularity. In particular,...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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2020
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7304036/ http://dx.doi.org/10.1007/978-3-030-50420-5_17 |
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author | Skotniczny, Marcin |
author_facet | Skotniczny, Marcin |
author_sort | Skotniczny, Marcin |
collection | PubMed |
description | We show that for meshes hierarchically adapted towards singularities there exists an order of variable elimination for direct solvers that will result in time complexity not worse than [Formula: see text], where N is the number of nodes and q is the dimensionality of the singularity. In particular, we show that this formula does not change depending on the spatial dimensionality of the mesh. We also show the relationship between the time complexity and the Kolmogorov dimension of the singularity. |
format | Online Article Text |
id | pubmed-7304036 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
spelling | pubmed-73040362020-06-19 Computational Complexity of Hierarchically Adapted Meshes Skotniczny, Marcin Computational Science – ICCS 2020 Article We show that for meshes hierarchically adapted towards singularities there exists an order of variable elimination for direct solvers that will result in time complexity not worse than [Formula: see text], where N is the number of nodes and q is the dimensionality of the singularity. In particular, we show that this formula does not change depending on the spatial dimensionality of the mesh. We also show the relationship between the time complexity and the Kolmogorov dimension of the singularity. 2020-05-22 /pmc/articles/PMC7304036/ http://dx.doi.org/10.1007/978-3-030-50420-5_17 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Skotniczny, Marcin Computational Complexity of Hierarchically Adapted Meshes |
title | Computational Complexity of Hierarchically Adapted Meshes |
title_full | Computational Complexity of Hierarchically Adapted Meshes |
title_fullStr | Computational Complexity of Hierarchically Adapted Meshes |
title_full_unstemmed | Computational Complexity of Hierarchically Adapted Meshes |
title_short | Computational Complexity of Hierarchically Adapted Meshes |
title_sort | computational complexity of hierarchically adapted meshes |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7304036/ http://dx.doi.org/10.1007/978-3-030-50420-5_17 |
work_keys_str_mv | AT skotnicznymarcin computationalcomplexityofhierarchicallyadaptedmeshes |