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He, Xin

Open this publication in new window or tab >>Numerical solution of the time-dependent Navier–Stokes equation for variable density–variable viscosity: Part I### Axelsson, Owe

### He, Xin

### Neytcheva, Maya

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Mathematical Modelling and Analysis, ISSN 1392-6292, E-ISSN 1648-3510, Vol. 20, p. 232-260Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-248502 (URN)10.3846/13926292.2015.1021395 (DOI)000351931100006 ()
#####

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Available from: 2015-03-30 Created: 2015-03-30 Last updated: 2017-12-04Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>On preconditioning of incompressible non-Newtonian flow problems### He, Xin

### Neytcheva, Maya

### Vuik, Cornelis

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 33, p. 33-58Article in journal (Refereed) Published
##### National Category

Computational Mathematics Computer Sciences
##### Identifiers

urn:nbn:se:uu:diva-237758 (URN)10.4208/jcm.1407-m4486 (DOI)000346401000003 ()
#####

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Available from: 2014-12-01 Created: 2014-12-04 Last updated: 2018-01-11Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>Parallel implementation of the Sherman–Morrison matrix inverse algorithm### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Holm, Marcus

### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: Applied Parallel and Scientific Computing, Berlin: Springer-Verlag , 2013, p. 206-219Conference paper, Published paper (Refereed)
##### Place, publisher, year, edition, pages

Berlin: Springer-Verlag, 2013
##### Series

Lecture Notes in Computer Science ; 7782
##### National Category

Computer Sciences Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-198520 (URN)10.1007/978-3-642-36803-5_15 (DOI)000343867800015 ()978-3-642-36802-8 (ISBN)
##### Conference

PARA 2012: State of the Art in Scientific and Parallel Computing
#####

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#####

##### Projects

UPMARCeSSENCE
Available from: 2013-02-18 Created: 2013-04-17 Last updated: 2018-01-11Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.

Open this publication in new window or tab >>Efficiently parallel implementation of the inverse Sherman–Morrison algorithm### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Holm, Marcus

### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2012 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-017
##### National Category

Computer Sciences Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-179219 (URN)
#####

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##### Projects

UPMARCeSSENCE
Available from: 2012-08-08 Created: 2012-08-09 Last updated: 2018-01-12Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.

Open this publication in new window or tab >>Numerical solution of the time-dependent Navier–Stokes equation for variable density–variable viscosity### Axelsson, Owe

### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2012 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-019
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-179351 (URN)
#####

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Available from: 2012-08-12 Created: 2012-08-13 Last updated: 2012-09-12Bibliographically approved

Open this publication in new window or tab >>On preconditioning incompressible non-Newtonian flow problems### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2012 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-016
##### National Category

Computational Mathematics Computer Sciences
##### Identifiers

urn:nbn:se:uu:diva-179218 (URN)
#####

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Available from: 2012-08-07 Created: 2012-08-09 Last updated: 2018-01-12Bibliographically approved

Open this publication in new window or tab >>On some Numerical Methods and Solution Techniques for Incompressible Flow Problems### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2012 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2012. p. 56
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 954
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing with specialization in Numerical Analysis
##### Identifiers

urn:nbn:se:uu:diva-179410 (URN)978-91-554-8429-3 (ISBN)
##### Public defence

2012-09-24, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 14:00 (English)
##### Opponent

### Bai, Zhong-Zhi

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##### Supervisors

### Neytcheva, Maya

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Available from: 2012-09-03 Created: 2012-08-14 Last updated: 2013-01-22Bibliographically approved

The focus of this work is on numerical solution methods for solving the incompressible Navier-Stokes equations, which consist of a set of coupled nonlinear partial differential equations.

In general, after linearization and finite element discretization in space, the original nonlinear problem is converted into finding the solutions of a sequence of linear systems of equations. Because of the underlying mathematical model, the coefficient matrix of the linear system is indefinite and nonsymmetric of two-by-two block structure. Due to their less demands for computer resources than direct methods, iterative solution methods are chosen to solve these linear systems. In order to accelerate the convergence rate of the iterative methods, efficient preconditioning techniques become essential. How to construct numerically efficient preconditioners for two-by-two block systems arising in the incompressible Navier-Stokes equations has been studied intensively during the past decades, and is also a main concern in this thesis.

The Navier-Stokes equations depend on various problem parameters, such as density and viscosity, that themselves may vary in time and space as in multiphase systems. In this thesis we follow the following strategy. First, we consider the stationary Navier-Stokes equations with constant viscosity and density, and contribute to the search of efficient preconditioners by analyzing and testing the element-by-element approximation method of the Schur complement matrix and the so-called augmented Lagrangian method. Second, the variation of the viscosity is an important factor and affects the behavior of the already known preconditioners, proposed for two-by-two block matrices. To this end, we choose the augmented Lagrangian method and analyse the impact of the variation of the viscosity on the resulting preconditioner. Finally, we consider the Navier-Stokes equations with their full complexity, namely, time dependence, variable density and variable viscosity. Fast and reliable solution methods are constructed based on a reformulation of the original equations and some operator splitting techniques. Preconditioners for the so-arising linear systemsare also analyzed and tested.

Chinese Academy of Sciences, Academy of Mathematics and Systems Sciences.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.

Open this publication in new window or tab >>Preconditioning the incompressible Navier-Stokes equations with variable viscosity### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 30, p. 461-482Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-179408 (URN)10.4208/jcm.1201-m3848 (DOI)000311467400002 ()
#####

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Available from: 2012-09-24 Created: 2012-08-14 Last updated: 2017-12-07Bibliographically approved

Open this publication in new window or tab >>On an augmented Lagrangian-based preconditioning of Oseen type problems### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Serra Capizzano, Stefano

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 51, p. 865-888Article in journal (Refereed) Published
##### National Category

Computational Mathematics Computer Sciences
##### Identifiers

urn:nbn:se:uu:diva-156201 (URN)10.1007/s10543-011-0334-4 (DOI)000297362000005 ()
#####

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Available from: 2011-06-07 Created: 2011-07-17 Last updated: 2019-01-22Bibliographically approved

Open this publication in new window or tab >>Preconditioning the incompressible Navier-Stokes equations with variable viscosity### He, Xin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Neytcheva, Maya

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2011 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-006
##### National Category

Computational Mathematics Computer Sciences
##### Identifiers

urn:nbn:se:uu:diva-151675 (URN)
#####

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Available from: 2011-04-05 Created: 2011-04-15 Last updated: 2018-01-12Bibliographically approved