Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth...

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Autores principales:	Jaroslav Haslinger, Radek Kučera, Kristina Motyčková, Václav Šátek
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Stokes problem threshold leak boundary conditions interior-point method semi-smooth Newton method Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7cb5bb4b26884e9f956cfecb3b890ef2
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id	oai:doaj.org-article:7cb5bb4b26884e9f956cfecb3b890ef2
record_format	dspace
spelling	oai:doaj.org-article:7cb5bb4b26884e9f956cfecb3b890ef22021-11-25T18:17:06ZNumerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms10.3390/math92229062227-7390https://doaj.org/article/7cb5bb4b26884e9f956cfecb3b890ef22021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2906https://doaj.org/toc/2227-7390The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.Jaroslav HaslingerRadek KučeraKristina MotyčkováVáclav ŠátekMDPI AGarticleStokes problemthreshold leak boundary conditionsinterior-point methodsemi-smooth Newton methodMathematicsQA1-939ENMathematics, Vol 9, Iss 2906, p 2906 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Stokes problem threshold leak boundary conditions interior-point method semi-smooth Newton method Mathematics QA1-939
spellingShingle	Stokes problem threshold leak boundary conditions interior-point method semi-smooth Newton method Mathematics QA1-939 Jaroslav Haslinger Radek Kučera Kristina Motyčková Václav Šátek Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms
description	The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.
format	article
author	Jaroslav Haslinger Radek Kučera Kristina Motyčková Václav Šátek
author_facet	Jaroslav Haslinger Radek Kučera Kristina Motyčková Václav Šátek
author_sort	Jaroslav Haslinger
title	Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms
title_short	Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms
title_full	Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms
title_fullStr	Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms
title_full_unstemmed	Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms
title_sort	numerical modeling of the leak through semipermeable walls for 2d/3d stokes flow: experimental scalability of dual algorithms
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/7cb5bb4b26884e9f956cfecb3b890ef2
work_keys_str_mv	AT jaroslavhaslinger numericalmodelingoftheleakthroughsemipermeablewallsfor2d3dstokesflowexperimentalscalabilityofdualalgorithms AT radekkucera numericalmodelingoftheleakthroughsemipermeablewallsfor2d3dstokesflowexperimentalscalabilityofdualalgorithms AT kristinamotyckova numericalmodelingoftheleakthroughsemipermeablewallsfor2d3dstokesflowexperimentalscalabilityofdualalgorithms AT vaclavsatek numericalmodelingoftheleakthroughsemipermeablewallsfor2d3dstokesflowexperimentalscalabilityofdualalgorithms
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Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

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