SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Refinements in the Approximate Matrix Factorization for the time integration of advection-diffusion-reaction PDEs

S.G. Pinto, D.H. Abreu and S.P. Rodriguez

Abstract
The numerical integration of PDEs of Advection Diffusion Reaction type in several spatial variables in the MoL framework is considered. The spatial discretization is based on Finite Differences and the time integration is carried out by using splitting techniques applied to some Rosenbrock-type methods. The focus is to provide a way of making some refinements to the usual Approximate Matrix Factorization (AMF), here considered as the splitting technique to solve the large linear systems of equations. The AMF-refinements allow to recover the convergence order of the underlying method and in some cases to enlarge the linear stability regions and the Courant numbers with regard to the standard AMF-scheme. Most of these methods belong to the class of the W-methods. A few numerical experiments on some important 2D and 3D non-linear PDE problems with applications in Physics are presented. The development of some integration codes (in Fortran, Matlab, R) is in progress.

Organized by         Universidad de Valladolid     IMUVA