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A Memory-Efficient Finite Volume Method for Advection-Diffusion-Reaction Systems with Non-Smooth Sources

Schäfer, Jonas; Huang, Xuan; Birken, Philipp LU ; Gobbert, Matthias K. and Andreas, Meister (2015) In Numerical Methods for Partial Differential Equations 31(1). p.143-167
Abstract
We present a parallel matrix-free implicit nite volume scheme for the solution of unsteady three-dimensional advection-diusion-reaction equations with smooth and Dirac-Delta source terms. The scheme is formally second order in space and a Newton-Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix-vector product required is hardcoded without any approximations, obtaining a matrix-free method that needs little storage and is well suited for parallel implementation. We describe the matrix-free implementation of the method in detail and give numerical evidence of its second order convergence in the presence of smooth source terms. For non-smooth source terms the convergence order drops to... (More)
We present a parallel matrix-free implicit nite volume scheme for the solution of unsteady three-dimensional advection-diusion-reaction equations with smooth and Dirac-Delta source terms. The scheme is formally second order in space and a Newton-Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix-vector product required is hardcoded without any approximations, obtaining a matrix-free method that needs little storage and is well suited for parallel implementation. We describe the matrix-free implementation of the method in detail and give numerical evidence of its second order convergence in the presence of smooth source terms. For non-smooth source terms the convergence order drops to one half. Furthermore, we demonstrate the method's applicability for the long time simulation of calcium ow in heart cells and show its parallel scaling. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Finite volume method, Dirac delta distribution, Matrix-free Newton-Krylov method, Calcium waves, Parallel computing
in
Numerical Methods for Partial Differential Equations
volume
31
issue
1
pages
143 - 167
publisher
John Wiley & Sons
external identifiers
  • scopus:84914181257
ISSN
1098-2426
DOI
10.1002/num.21897
language
English
LU publication?
yes
id
f2cd232f-3e7a-4afc-a520-8e4f66891de7 (old id 4457914)
alternative location
http://onlinelibrary.wiley.com/doi/10.1002/num.21897/full
date added to LUP
2014-07-02 17:29:57
date last changed
2017-02-16 12:55:19
@article{f2cd232f-3e7a-4afc-a520-8e4f66891de7,
  abstract     = {We present a parallel matrix-free implicit nite volume scheme for the solution of unsteady three-dimensional advection-diusion-reaction equations with smooth and Dirac-Delta source terms. The scheme is formally second order in space and a Newton-Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix-vector product required is hardcoded without any approximations, obtaining a matrix-free method that needs little storage and is well suited for parallel implementation. We describe the matrix-free implementation of the method in detail and give numerical evidence of its second order convergence in the presence of smooth source terms. For non-smooth source terms the convergence order drops to one half. Furthermore, we demonstrate the method's applicability for the long time simulation of calcium ow in heart cells and show its parallel scaling.},
  author       = {Schäfer, Jonas and Huang, Xuan and Birken, Philipp and Gobbert, Matthias K. and Andreas, Meister},
  issn         = {1098-2426},
  keyword      = {Finite volume method,Dirac delta distribution,Matrix-free Newton-Krylov method,Calcium waves,Parallel computing},
  language     = {eng},
  number       = {1},
  pages        = {143--167},
  publisher    = {John Wiley & Sons},
  series       = {Numerical Methods for Partial Differential Equations},
  title        = {A Memory-Efficient Finite Volume Method for Advection-Diffusion-Reaction Systems with Non-Smooth Sources},
  url          = {http://dx.doi.org/10.1002/num.21897},
  volume       = {31},
  year         = {2015},
}