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. © 2011 Elsevier B.V.

Citation
Collier, N., Pardo, D., Dalcin, L., Paszynski, M., & Calo, V. M. (2012). The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers. Computer Methods in Applied Mechanics and Engineering, 213-216, 353–361. doi:10.1016/j.cma.2011.11.002

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.

Publisher
Elsevier BV

Journal
Computer Methods in Applied Mechanics and Engineering

DOI
10.1016/j.cma.2011.11.002

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