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

• Autores: Collier, N.; Dalcin, Lisandro Daniel; Calo, V.M.
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Asymptotic Analysis; Collocation; Computational Efficiency; Finite Elements; Isogeometric
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Collier, N.. King Abdullah University Of Science And Technology; Arabia Saudita
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
Fil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia Saudita