Partitioning methods for reaction-diffusion problems

Authors:
Wolfram Heineken;Gerald Warnecke
Affiliations:
Institute for Analysis and Numerics, Otto-von-Guericke University, PSF, Magdeburg, Germany;Institute for Analysis and Numerics, Otto-von-Guericke University, PSF, Magdeburg, Germany
Venue:
Applied Numerical Mathematics
Year:
2006

Citing 8
Cited 2

BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Matrix-free W-methods using a multiple Arnoldi iteration

NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs

Applied Numerical Mathematics - Special issue on time integration
Numerical methods for ordinary differential equations in the 20th century

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Partially Implicit BDF2 Blends for Convection Dominated Flows

SIAM Journal on Numerical Analysis
Implicit-explicit time stepping with spatial discontinuous finite elements

Applied Numerical Mathematics
Combined implicit/Explicit time-integration algorithms for the numerical simulation of sheet metal forming

Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002

The analytical solution of two interesting hyperbolic problems as a test case for a finite volume method with a new grid refinement technique

Journal of Computational and Applied Mathematics
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Journal of Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the numerical solution of reaction-diffusion systems using linear finite elements on a space grid changing in time. For the integration with respect to the time variable a W-method with several variants of implicit/explicit partitioning is used. For grid adaption an algorithm featuring a flexible refinement and coarsening control is proposed. The partitioned W-methods keep the stability of implicit schemes but reduce the size of the linear systems to be solved. We combine local partitioning with partitioning between the diffusion and reaction terms, leading to a large variety of methods. The efficiency of several partitioning methods is compared in numerical tests. The calculations show an increase of efficiency if partitioned schemes are used instead of a fully implicit W-method. We include a numerical comparison of three linear solvers. Optimal truncation of the iteration process is discussed.