Artículo
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
Fecha de publicación:
11/2014
Editorial:
John Wiley & Sons Ltd
Revista:
International Journal for Numerical Methods in Engineering
ISSN:
0029-5981
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Resumen
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.
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Articulos(CIMEC)
Articulos de CENTRO DE INVESTIGACION DE METODOS COMPUTACIONALES
Articulos de CENTRO DE INVESTIGACION DE METODOS COMPUTACIONALES
Citación
Collier, N.; Dalcin, Lisandro Daniel; Calo, V.M.; On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers; John Wiley & Sons Ltd; International Journal for Numerical Methods in Engineering; 100; 8; 11-2014; 620-632
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