Paper Info
Title
Discretization and Parallel Iterative Schemes for Advection-Diffusion-Reaction Problems.
Abstract
Conservation laws of advection-diffusion-reaction (ADR) type are ubiquitous in continuum physics. In this paper we outline discretization of these problems and iterative schemes for the resulting linear system. For discretization we use the finite volume method in combination with the complete flux scheme. The numerical flux is the superposition of a homogeneous flux, corresponding to the advection-diffusion operator, and the inhomogeneous flux, taking into account the effect of the source term (ten Thije Boonkkamp and Anthonissen, J Sci Comput 46(1): 47-70, 2011). For a three-dimensional conservation law this results in a 27point coupling for the unknown as well as the source term. Direct solution of the sparse linear systems that arise in 3D ADR problems is not feasible due to fill-in. Iterative solution of such linear systems remains to be the only efficient alternative which requires less memory and shorter time to solution compared to direct solvers. Iterative solvers require a preconditioner to reduce the number of iterations. We present results using several different preconditioning techniques and study their effectiveness.
Year
DOI
Venue
2015
10.1007/978-3-319-39929-4_27
Lecture Notes in Computational Science and Engineering
Field
DocType
Volume
Applied mathematics,Discretization,Superposition principle,Mathematical optimization,Linear system,Preconditioner,Computer science,Flux,Operator (computer programming),Finite volume method,Conservation law,Distributed computing
Conference
112
ISSN
Citations 
PageRank 
1439-7358
0
0.34
References 
Authors
0
4
Name
Order
Citations
PageRank
Abdullah Ali Sivas100.34
Murat Manguoglu2759.28
J. H. Thije Boonkkamp3237.77
M. J. H. Anthonissen4103.12