Discretization and parallel iterative schemes for advection-diffusion-reaction problems

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

3 Downloads (Pure)

Uittreksel

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 27-point 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.

Originele taal-2Engels
TitelNumerical Mathematics and Advanced Applications ENUMATH 2015
RedacteurenB. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, Ö. Uğur
Plaats van productieDordrecht
UitgeverijSpringer
Pagina's275-283
Aantal pagina's9
ISBN van elektronische versie978-3-319-39929-4
ISBN van geprinte versie978-3-319-39927-0
DOI's
StatusGepubliceerd - 2016
Evenement2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015) - Middle East Technical University, Ankara, Turkije
Duur: 14 sep 201518 sep 2015

Publicatie series

NaamLecture Notes in Computational Science and Engineering
Volume112
ISSN van geprinte versie14397358

Congres

Congres2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015)
Verkorte titelENUMATH 2015
LandTurkije
StadAnkara
Periode14/09/1518/09/15

Vingerafdruk

Advection-diffusion
Advection
Iterative Scheme
Discretization
Fluxes
Linear systems
Source Terms
Conservation Laws
Conservation
Linear Systems
Preconditioning Techniques
Iterative Solvers
Sparse Linear Systems
Finite volume method
Iterative Solution
Finite Volume Method
Preconditioner
Superposition
Continuum
Physics

Citeer dit

Sivas, A. A., Manguoğlu, M., ten Thije Boonkkamp, J. H. M., & Anthonissen, M. J. H. (2016). Discretization and parallel iterative schemes for advection-diffusion-reaction problems. In B. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, & Ö. Uğur (editors), Numerical Mathematics and Advanced Applications ENUMATH 2015 (blz. 275-283). (Lecture Notes in Computational Science and Engineering; Vol. 112). Dordrecht: Springer. https://doi.org/10.1007/978-3-319-39929-4_27
Sivas, A.A. ; Manguoğlu, M. ; ten Thije Boonkkamp, J.H.M. ; Anthonissen, M.J.H. / Discretization and parallel iterative schemes for advection-diffusion-reaction problems. Numerical Mathematics and Advanced Applications ENUMATH 2015. redacteur / B. Karasözen ; M. Manguoğlu ; M. Tezer-Sezgin ; S. Göktepe ; Ö. Uğur . Dordrecht : Springer, 2016. blz. 275-283 (Lecture Notes in Computational Science and Engineering).
@inproceedings{291b238810194800827a7c77e03e8bc9,
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 27-point 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.",
author = "A.A. Sivas and M. Manguoğlu and {ten Thije Boonkkamp}, J.H.M. and M.J.H. Anthonissen",
year = "2016",
doi = "10.1007/978-3-319-39929-4_27",
language = "English",
isbn = "978-3-319-39927-0",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
pages = "275--283",
editor = "B. Karas{\"o}zen and M. Manguoğlu and M. Tezer-Sezgin and S. G{\"o}ktepe and {Uğur }, {\"O}.",
booktitle = "Numerical Mathematics and Advanced Applications ENUMATH 2015",
address = "Germany",

}

Sivas, AA, Manguoğlu, M, ten Thije Boonkkamp, JHM & Anthonissen, MJH 2016, Discretization and parallel iterative schemes for advection-diffusion-reaction problems. in B Karasözen, M Manguoğlu, M Tezer-Sezgin, S Göktepe & Ö Uğur (redactie), Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol. 112, Springer, Dordrecht, blz. 275-283, 2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015), Ankara, Turkije, 14/09/15. https://doi.org/10.1007/978-3-319-39929-4_27

Discretization and parallel iterative schemes for advection-diffusion-reaction problems. / Sivas, A.A.; Manguoğlu, M.; ten Thije Boonkkamp, J.H.M.; Anthonissen, M.J.H.

Numerical Mathematics and Advanced Applications ENUMATH 2015. redactie / B. Karasözen; M. Manguoğlu; M. Tezer-Sezgin; S. Göktepe; Ö. Uğur . Dordrecht : Springer, 2016. blz. 275-283 (Lecture Notes in Computational Science and Engineering; Vol. 112).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

TY - GEN

T1 - Discretization and parallel iterative schemes for advection-diffusion-reaction problems

AU - Sivas, A.A.

AU - Manguoğlu, M.

AU - ten Thije Boonkkamp, J.H.M.

AU - Anthonissen, M.J.H.

PY - 2016

Y1 - 2016

N2 - 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 27-point 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.

AB - 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 27-point 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.

UR - http://www.scopus.com/inward/record.url?scp=84998546855&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-39929-4_27

DO - 10.1007/978-3-319-39929-4_27

M3 - Conference contribution

AN - SCOPUS:84998546855

SN - 978-3-319-39927-0

T3 - Lecture Notes in Computational Science and Engineering

SP - 275

EP - 283

BT - Numerical Mathematics and Advanced Applications ENUMATH 2015

A2 - Karasözen, B.

A2 - Manguoğlu, M.

A2 - Tezer-Sezgin, M.

A2 - Göktepe, S.

A2 - Uğur , Ö.

PB - Springer

CY - Dordrecht

ER -

Sivas AA, Manguoğlu M, ten Thije Boonkkamp JHM, Anthonissen MJH. Discretization and parallel iterative schemes for advection-diffusion-reaction problems. In Karasözen B, Manguoğlu M, Tezer-Sezgin M, Göktepe S, Uğur Ö, redacteurs, Numerical Mathematics and Advanced Applications ENUMATH 2015. Dordrecht: Springer. 2016. blz. 275-283. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-39929-4_27