Parallel solution of nonlinear parabolic problems on logically rectangular grids
Fecha
2007Versión
Acceso abierto / Sarbide irekia
Tipo
Contribución a congreso / Biltzarrerako ekarpena
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Gobierno de Navarra// CTP-05%2FR-8
Impacto
|
10.1007/978-3-540-68111-3_39
Resumen
This work deals with the efficient numerical solution of nonlinear
transient flow problems posed on two-dimensional porous media of
general geometry. We first consider a spatial semidiscretization of such
problems by using a cell-centered finite difference scheme on a logically
rectangular grid. The resulting nonlinear stiff initial-value problems are
then integrated in time by means of a fr ...
[++]
This work deals with the efficient numerical solution of nonlinear
transient flow problems posed on two-dimensional porous media of
general geometry. We first consider a spatial semidiscretization of such
problems by using a cell-centered finite difference scheme on a logically
rectangular grid. The resulting nonlinear stiff initial-value problems are
then integrated in time by means of a fractional step method, combined
with a decomposition of the flow domain into a set of overlapping subdomains
and a linearization procedure which involves suitable Taylor
expansions. The proposed algorithm reduces the original problem to the
solution of several linear systems per time step. Moreover, each one of
such systems can be directly decomposed into a set of uncoupled linear
subsystems which can be solved in parallel. A numerical example illustrates
the unconditionally convergent behaviour of the method in the
last section of the paper. [--]
Materias
Domain decomposition,
Fractional step method,
Linearly implicit method,
Logically rectangular grid,
Nonlinear parabolic problem,
Support-operator method
Editor
Springer
Publicado en
Wyrzykowski, R.; Dongarra, J.; Karczewski, K.; Wasniewski, J. (Eds.). Parallel Processing and Applied Mathematics: 7th International Conference, PPAM 2007: selected papers. Berlín: Springer; 2008. p.371-380 978-3-540-68105-2
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
This research is partially supported by the Spanish Ministry of Science and Education
under Research Project MTM2004-05221 and FPU Grant AP2003-2621 and by
Government of Navarre under Research Project CTP-05/R-8.