On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

Nathan Collier, Lisandro Dalcin, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.
Original languageEnglish (US)
Pages (from-to)620-632
Number of pages13
JournalInternational Journal for Numerical Methods in Engineering
Volume100
Issue number8
DOIs
StatePublished - Sep 17 2014

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)
  • Numerical Analysis

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