The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers

Nathan Collier; David Pardo; Lisandro D. Dalcín; Maciej R. Paszyński; Victor M. Calo

doi:10.1016/j.cma.2011.11.002

The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers

Nathan Collier, David Pardo, Lisandro D. Dalcín, Maciej R. Paszyński, Victor M. Calo

Research output: Contribution to journal › Article › peer-review

109 Scopus citations

Abstract

We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.

Original language	English (US)
Pages (from-to)	353-361
Number of pages	9
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	213-216
DOIs	https://doi.org/10.1016/j.cma.2011.11.002
State	Published - Mar 2012

ASJC Scopus subject areas

General Physics and Astronomy
Mechanics of Materials
Mechanical Engineering
Computational Mechanics
Computer Science Applications

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10.1016/j.cma.2011.11.002

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title = "The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers",

abstract = "We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. {\textcopyright} 2011 Elsevier B.V.",

author = "Nathan Collier and David Pardo and Dalc{\'i}n, {Lisandro D.} and Paszy{\'n}ski, {Maciej R.} and Calo, {Victor M.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We would like to thank the anonymous reviewers for their feedback which significantly improved the quality of the paper. The second author was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511. The work of the third author has been partially supported by ANPCyT Argentina Grant PICT-1141/2007. The work of the fourth author was partially supported by Polish Ministry of Science and Higher Education Grant No. NN 519 447739.",

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doi = "10.1016/j.cma.2011.11.002",

language = "English (US)",

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AU - Paszyński, Maciej R.

AU - Calo, Victor M.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We would like to thank the anonymous reviewers for their feedback which significantly improved the quality of the paper. The second author was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511. The work of the third author has been partially supported by ANPCyT Argentina Grant PICT-1141/2007. The work of the fourth author was partially supported by Polish Ministry of Science and Higher Education Grant No. NN 519 447739.

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N2 - We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.

AB - We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.

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JO - Computer Methods in Applied Mechanics and Engineering

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ER -

The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers

Abstract

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