A combined fractional step domain decomposition method for the numerical integration of parabolic problems
Fecha
2004Versión
Acceso abierto / Sarbide irekia
Tipo
Contribución a congreso / Biltzarrerako ekarpena
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Gobierno de Navarra//134%2F2002
Impacto
|
10.1007/978-3-540-24669-5_134
Resumen
In this paper we develop parallel numerical algorithms to
solve linear time dependent coefficient parabolic problems. Such methods
are obtained by means of two consecutive discretization procedures.
Firstly, we realize a time integration of the original problem using a
Fractional Step Runge Kutta method which provides a family of elliptic
boundary value problems on certain subdomains of the ...
[++]
In this paper we develop parallel numerical algorithms to
solve linear time dependent coefficient parabolic problems. Such methods
are obtained by means of two consecutive discretization procedures.
Firstly, we realize a time integration of the original problem using a
Fractional Step Runge Kutta method which provides a family of elliptic
boundary value problems on certain subdomains of the original domain.
Next, we discretize those elliptic problems by means of standard techniques.
Using this framework, the numerical solution is obtained by solving,
at each stage, a set of uncoupled linear systems of low dimension.
Comparing these algorithms with the classical domain decomposition
methods for parabolic problems, we obtain a reduction of computational
cost because of, in this case, no Schwarz iterations are required. We give
an unconditional convergence result for the totally discrete scheme and
we include two numerical examples that show the behaviour of the proposed
method. [--]
Materias
Parabolic problemas,
Numerical integration
Editor
Springer
Publicado en
Wyrzykowski, R.; Dongarra, J.; Paprzycki, M.; Wasniewski, J. (Eds.). Parallel processing and applied mathematics: 5th international conference, PPAM 2003: revised papers. Berlín: Springer; 2004. p.1034-1041 978-3-540-21946-0
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 MCYT research project num. BFM2000-0803 and the research project resolution 134/2002 of Government of Navarra.