A Memory-Efficient Finite Volume Method for Advection-Diffusion-Reaction Systems with Non-Smooth Sources
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4457914
- author
- Schäfer, Jonas ; Huang, Xuan ; Birken, Philipp LU ; Gobbert, Matthias K. and Andreas, Meister
- organization
- publishing date
- 2015
- 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 Inc.
- external identifiers
-
- scopus:84914181257
- ISSN
- 1098-2426
- DOI
- 10.1002/num.21897
- language
- English
- LU publication?
- yes
- additional info
- First published online (Early View) 20th of June 2014 on Wiley Online Library. The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- 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
- 2016-04-01 10:14:28
- date last changed
- 2022-03-12 03:34:31
@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}},
keywords = {{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 Inc.}},
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}},
doi = {{10.1002/num.21897}},
volume = {{31}},
year = {{2015}},
}