En este artículo se describe una implementación del método “Local Discontinuous Galerkin” (LDG) aplicado a problemas elípticos en 3D. Se discute la implementación de los principales operadores. En particular el uso de aproximaciones de alto orden y de mallas no estructuradas. Estructuras de datos eficientes que permiten un rápido ensamblado del sistema lineal en su formulación mixta son descritas en detalle.
Palabras clave: Métodos de elemento finito discontinuos, aproximaciones de alto orden, mallas no estructuradas, programación orientada a objetos.
Abstract
This paper describes an implementation of the Local Discontinuous Galerkin method (LDG) applied to elliptic problems in 3D. The implementation of the major operators is discussed. In particular the use of higher-order approximations and unstructured meshes. Efficient data structures that allow fast assembly of the linear system in the mixed formulation are described in detail.
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*Correspondencia a: Filánder A. Sequeira Chavarría. Escuela de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica. E-Mail: filander.sequeira@ucr.ac.cr Paul E. Castillo. Departamento de Ciencias Matem´aticas, P.O. Box 9000, Universidad de Puerto Rico, 00681 Mayagüez Puerto Rico. E-Mail: paul.castillo@upr.edu
*Escuela de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica. E-Mail: filander.sequeira@ucr.ac.cr †Departamento de Ciencias Matem´aticas, P.O. Box 9000, Universidad de Puerto Rico, 00681 Mayagüez Puerto Rico. E-Mail: paul.castillo@upr.edu
Received: 21 Feb 2011; Revised: 12 Jun 2012; Accepted: 18 Jun 2012