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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Autor principal: Skotniczny, Marcin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
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.
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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

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