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On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
Author(s) -
Collier N.,
Dalcin L.,
Calo V. M.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4769
Subject(s) - isogeometric analysis , solver , mathematics , discretization , partial differential equation , elliptic partial differential equation , finite element method , discontinuous galerkin method , galerkin method , convergence (economics) , mathematical optimization , mathematical analysis , physics , economics , thermodynamics , economic growth
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 C 0 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. Copyright © 2014 John Wiley & Sons, Ltd.