A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem

Marcin Łoś; Sergio Rojas; Maciej Paszyński; Ignacio Muga; Victor M. Calo

doi:10.1007/978-3-030-50417-5_15

A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem

Marcin Łoś, Sergio Rojas, Maciej Paszyński, Ignacio Muga, Victor M. Calo

INSTITUTE OF MATHEMATICS

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

We investigate a residual minimization (RM) based stabilized isogeometric finite element method (IGA) for the Stokes problem. Starting from an inf-sup stable discontinuous Galerkin (DG) formulation, the method seeks for an approximation in a highly continuous trial space that minimizes the residual measured in a dual norm of the discontinuous test space. We consider two-dimensional Stokes problems with manufactured solutions and the cavity flow problem. We explore the results obtained by considering highly continuous isogeometric trial spaces, and discontinuous test spaces. We compare by the Pareto front the resulting numerical accuracy and the computational cost, expressed by the number of floating-point operations performed by the direct solver algorithm.

Original language	English
Title of host publication	Computational Science – ICCS 2020 - 20th International Conference, Proceedings
Editors	Valeria V. Krzhizhanovskaya, Gábor Závodszky, Michael H. Lees, Peter M.A. Sloot, Peter M.A. Sloot, Peter M.A. Sloot, Jack J. Dongarra, Sérgio Brissos, João Teixeira
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	197-211
Number of pages	15
ISBN (Print)	9783030504168
DOIs	https://doi.org/10.1007/978-3-030-50417-5_15
State	Published - 2020
Event	20th International Conference on Computational Science, ICCS 2020 - Amsterdam, Netherlands Duration: 3 Jun 2020 → 5 Jun 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12138 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th International Conference on Computational Science, ICCS 2020
Country/Territory	Netherlands
City	Amsterdam
Period	3/06/20 → 5/06/20

Keywords

Computational cost
Direct solvers
Discontinuous Galerkin
Isogeometric analysis
Residual minimization
Stokes problem

Access to Document

10.1007/978-3-030-50417-5_15

Cite this

Łoś, M., Rojas, S., Paszyński, M., Muga, I., & Calo, V. M. (2020). A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem. In V. V. Krzhizhanovskaya, G. Závodszky, M. H. Lees, P. M. A. Sloot, P. M. A. Sloot, P. M. A. Sloot, J. J. Dongarra, S. Brissos, & J. Teixeira (Eds.), Computational Science – ICCS 2020 - 20th International Conference, Proceedings (pp. 197-211). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12138 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-50417-5_15

Łoś, Marcin ; Rojas, Sergio ; Paszyński, Maciej et al. / A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem. Computational Science – ICCS 2020 - 20th International Conference, Proceedings. editor / Valeria V. Krzhizhanovskaya ; Gábor Závodszky ; Michael H. Lees ; Peter M.A. Sloot ; Peter M.A. Sloot ; Peter M.A. Sloot ; Jack J. Dongarra ; Sérgio Brissos ; João Teixeira. Springer Science and Business Media Deutschland GmbH, 2020. pp. 197-211 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem",

abstract = "We investigate a residual minimization (RM) based stabilized isogeometric finite element method (IGA) for the Stokes problem. Starting from an inf-sup stable discontinuous Galerkin (DG) formulation, the method seeks for an approximation in a highly continuous trial space that minimizes the residual measured in a dual norm of the discontinuous test space. We consider two-dimensional Stokes problems with manufactured solutions and the cavity flow problem. We explore the results obtained by considering highly continuous isogeometric trial spaces, and discontinuous test spaces. We compare by the Pareto front the resulting numerical accuracy and the computational cost, expressed by the number of floating-point operations performed by the direct solver algorithm.",

keywords = "Computational cost, Direct solvers, Discontinuous Galerkin, Isogeometric analysis, Residual minimization, Stokes problem",

author = "Marcin {\L}o{\'s} and Sergio Rojas and Maciej Paszy{\'n}ski and Ignacio Muga and Calo, {Victor M.}",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 20th International Conference on Computational Science, ICCS 2020 ; Conference date: 03-06-2020 Through 05-06-2020",

year = "2020",

doi = "10.1007/978-3-030-50417-5_15",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "197--211",

editor = "Krzhizhanovskaya, {Valeria V.} and G{\'a}bor Z{\'a}vodszky and Lees, {Michael H.} and Sloot, {Peter M.A.} and Sloot, {Peter M.A.} and Sloot, {Peter M.A.} and Dongarra, {Jack J.} and S{\'e}rgio Brissos and Jo{\~a}o Teixeira",

booktitle = "Computational Science – ICCS 2020 - 20th International Conference, Proceedings",

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Łoś, M, Rojas, S, Paszyński, M, Muga, I & Calo, VM 2020, A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem. in VV Krzhizhanovskaya, G Závodszky, MH Lees, PMA Sloot, PMA Sloot, PMA Sloot, JJ Dongarra, S Brissos & J Teixeira (eds), Computational Science – ICCS 2020 - 20th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12138 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 197-211, 20th International Conference on Computational Science, ICCS 2020, Amsterdam, Netherlands, 3/06/20. https://doi.org/10.1007/978-3-030-50417-5_15

A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem. / Łoś, Marcin; Rojas, Sergio; Paszyński, Maciej et al.
Computational Science – ICCS 2020 - 20th International Conference, Proceedings. ed. / Valeria V. Krzhizhanovskaya; Gábor Závodszky; Michael H. Lees; Peter M.A. Sloot; Peter M.A. Sloot; Peter M.A. Sloot; Jack J. Dongarra; Sérgio Brissos; João Teixeira. Springer Science and Business Media Deutschland GmbH, 2020. p. 197-211 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12138 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem

AU - Łoś, Marcin

AU - Rojas, Sergio

AU - Paszyński, Maciej

AU - Muga, Ignacio

AU - Calo, Victor M.

PY - 2020

Y1 - 2020

N2 - We investigate a residual minimization (RM) based stabilized isogeometric finite element method (IGA) for the Stokes problem. Starting from an inf-sup stable discontinuous Galerkin (DG) formulation, the method seeks for an approximation in a highly continuous trial space that minimizes the residual measured in a dual norm of the discontinuous test space. We consider two-dimensional Stokes problems with manufactured solutions and the cavity flow problem. We explore the results obtained by considering highly continuous isogeometric trial spaces, and discontinuous test spaces. We compare by the Pareto front the resulting numerical accuracy and the computational cost, expressed by the number of floating-point operations performed by the direct solver algorithm.

AB - We investigate a residual minimization (RM) based stabilized isogeometric finite element method (IGA) for the Stokes problem. Starting from an inf-sup stable discontinuous Galerkin (DG) formulation, the method seeks for an approximation in a highly continuous trial space that minimizes the residual measured in a dual norm of the discontinuous test space. We consider two-dimensional Stokes problems with manufactured solutions and the cavity flow problem. We explore the results obtained by considering highly continuous isogeometric trial spaces, and discontinuous test spaces. We compare by the Pareto front the resulting numerical accuracy and the computational cost, expressed by the number of floating-point operations performed by the direct solver algorithm.

KW - Computational cost

KW - Direct solvers

KW - Discontinuous Galerkin

KW - Isogeometric analysis

KW - Residual minimization

KW - Stokes problem

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DO - 10.1007/978-3-030-50417-5_15

M3 - Conference contribution

AN - SCOPUS:85088215366

SN - 9783030504168

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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EP - 211

BT - Computational Science – ICCS 2020 - 20th International Conference, Proceedings

A2 - Krzhizhanovskaya, Valeria V.

A2 - Závodszky, Gábor

A2 - Lees, Michael H.

A2 - Sloot, Peter M.A.

A2 - Dongarra, Jack J.

A2 - Brissos, Sérgio

A2 - Teixeira, João

PB - Springer Science and Business Media Deutschland GmbH

T2 - 20th International Conference on Computational Science, ICCS 2020

Y2 - 3 June 2020 through 5 June 2020

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Łoś M, Rojas S, Paszyński M, Muga I, Calo VM. A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem. In Krzhizhanovskaya VV, Závodszky G, Lees MH, Sloot PMA, Sloot PMA, Sloot PMA, Dongarra JJ, Brissos S, Teixeira J, editors, Computational Science – ICCS 2020 - 20th International Conference, Proceedings. Springer Science and Business Media Deutschland GmbH. 2020. p. 197-211. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-50417-5_15

A stable discontinuous galerkin based isogeometric residual minimization for the stokes problem

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