uu.seUppsala University Publications
Change search
Refine search result
1 - 7 of 7
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1. Babaoglu, Ceni
    et al.
    Bazarganzadeh, Mahmoudreza
    Department of Mathematics, Stockholm University.
    Some properties of two-phase quadrature domains2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 10, p. 3386-3396Article in journal (Refereed)
  • 2.
    Bazarganzadeh, Mahmoudreza
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Free Boundary Problems of Obstacle Type, a Numerical and Theoretical Study2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of five papers and it mainly addresses the theory and schemes to approximate the quadrature domains, QDs. The first deals with the uniqueness and some qualitative properties of the two QDs. The concept of two phase QDs, is more complicated than its one counterpart and consequently introduces significant and interesting open.

    We present two numerical schemes to approach the one phase QDs in the paper. The first method is based on the properties of the free boundary the level set techniques. We use shape optimization analysis to construct second method. We illustrate the efficiency of the schemes on a variety of experiments.

    In the third paper we design two finite difference methods for the approximation of the multi phase QDs. We prove that the second method enjoys monotonicity, consistency and stability and consequently it is a convergent scheme by Barles-Souganidis theorem. We also present various numerical simulations in the case of Dirac measures.

    We introduce the QDs in a sub domain of and Rn study the existence and uniqueness along with a numerical scheme based on the level set method in the fourth paper.

    In the last paper we study the tangential touch for a semi-linear problem. We prove that there is just one phase free boundary points on the flat part of the fixed boundary and it is also shown that the free boundary is a uniform C1-graph up to that part.

    List of papers
    1. Some properties of two-phase quadrature domains
    Open this publication in new window or tab >>Some properties of two-phase quadrature domains
    2011 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 10, p. 3386-3396Article in journal (Refereed) Published
    National Category
    Mathematical Analysis
    Identifiers
    urn:nbn:se:uu:diva-163099 (URN)10.1016/j.na.2011.02.014 (DOI)
    Available from: 2012-02-07 Created: 2011-12-07 Last updated: 2017-12-08Bibliographically approved
    2. Numerical Approximation of One Phase Quadrature Domains
    Open this publication in new window or tab >>Numerical Approximation of One Phase Quadrature Domains
    2013 (English)In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 29, no 5, p. 1709-1728Article in journal (Other academic) Published
    Abstract [en]

    In this work, we present two numerical schemes for a free boundary problem called one phase quadrature domain. In the first method by applying the proprieties of given free boundary problem, we derive a method that leads to a fast iterative solver. The iteration procedure is adapted in order to work in the case when topology changes. The second method is based on shape reconstruction to establish an efficient Shape-Quasi-Newton-Method. Various numerical experiments confirm the efficiency of the derived numerical methods.

    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-170221 (URN)10.1002/num.21773 (DOI)000322203200013 ()
    Available from: 2012-03-13 Created: 2012-03-09 Last updated: 2017-12-07Bibliographically approved
    3. Numerical Schemes for Multi Phase Quadrature Domains
    Open this publication in new window or tab >>Numerical Schemes for Multi Phase Quadrature Domains
    2014 (English)In: International Journal of Numerical Analysis & Modeling, ISSN 1705-5105, Vol. 11, no 4, p. 726-744Article in journal (Refereed) Published
    Abstract [en]

    In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the numerical implementation of the resulting approach and present computational tests.

    Keywords
    Quadrature domain; Free boundary problem; Finite difference method; Degenerate elliptic equation
    National Category
    Mathematics
    Research subject
    Numerical Analysis
    Identifiers
    urn:nbn:se:uu:diva-183391 (URN)000343624500004 ()
    Available from: 2012-12-07 Created: 2012-10-25 Last updated: 2017-12-07Bibliographically approved
    4. Quadrature domains in a subdomain of R^n, theory and a numerical approach
    Open this publication in new window or tab >>Quadrature domains in a subdomain of R^n, theory and a numerical approach
    (English)Manuscript (preprint) (Other academic)
    Keywords
    free boundary problems, quadrature domain, level set method
    National Category
    Mathematics
    Research subject
    Mathematics with specialization in Applied Mathematics; Numerical Analysis
    Identifiers
    urn:nbn:se:uu:diva-183392 (URN)
    Available from: 2012-12-07 Created: 2012-10-25 Last updated: 2012-12-07Bibliographically approved
    5. Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
    Open this publication in new window or tab >>Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
    2014 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 1, p. 21-42Article in journal (Refereed) Published
    Abstract [en]

    We study minimizers of the functional where B_{1}^{{\mathchoice {\raise .17ex\hbox {\scriptstyle +}} {\raise .17ex\hbox {\scriptstyle +}} {\raise .1ex\hbox {\scriptscriptstyle +}} {\scriptscriptstyle +}}}=\{x\in B_{1}: x_{1}>0\} , u=0 on {xB 1:x 1=0}, \lambda^{{\mathchoice {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .1ex\hbox {\scriptscriptstyle \pm }} {\scriptscriptstyle \pm }}} are two positive constants and 0<p<1. In two dimensions, we prove that the free boundary is a uniform C 1 graph up to the flat part of the fixed boundary and also that two-phase points cannot occur on this part of the fixed boundary. Here, the free boundary refers to the union of the boundaries of the sets {xu(x)>0}.

    National Category
    Mathematical Analysis
    Identifiers
    urn:nbn:se:uu:diva-170218 (URN)10.1007/s11512-012-0179-3 (DOI)000332797200003 ()
    Available from: 2012-03-13 Created: 2012-03-09 Last updated: 2017-12-07Bibliographically approved
  • 3. Bazarganzadeh, Mahmoudreza
    Quadrature domains in a subdomain of R^n, theory and a numerical approachManuscript (preprint) (Other academic)
  • 4.
    Bazarganzadeh, Mahmoudreza
    Department of Mathematics, Stockholm University.
    Some properties of one and twophase quadrature domains2010Licentiate thesis, monograph (Other academic)
  • 5.
    Bazarganzadeh, Mahmoudreza
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Bozorgnia, Farid
    Numerical Approximation of One Phase Quadrature Domains2013In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 29, no 5, p. 1709-1728Article in journal (Other academic)
    Abstract [en]

    In this work, we present two numerical schemes for a free boundary problem called one phase quadrature domain. In the first method by applying the proprieties of given free boundary problem, we derive a method that leads to a fast iterative solver. The iteration procedure is adapted in order to work in the case when topology changes. The second method is based on shape reconstruction to establish an efficient Shape-Quasi-Newton-Method. Various numerical experiments confirm the efficiency of the derived numerical methods.

  • 6.
    Bazarganzadeh, Mahmoudreza
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Lindgren, Erik
    Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions2014In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 1, p. 21-42Article in journal (Refereed)
    Abstract [en]

    We study minimizers of the functional where B_{1}^{{\mathchoice {\raise .17ex\hbox {\scriptstyle +}} {\raise .17ex\hbox {\scriptstyle +}} {\raise .1ex\hbox {\scriptscriptstyle +}} {\scriptscriptstyle +}}}=\{x\in B_{1}: x_{1}>0\} , u=0 on {xB 1:x 1=0}, \lambda^{{\mathchoice {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .1ex\hbox {\scriptscriptstyle \pm }} {\scriptscriptstyle \pm }}} are two positive constants and 0<p<1. In two dimensions, we prove that the free boundary is a uniform C 1 graph up to the flat part of the fixed boundary and also that two-phase points cannot occur on this part of the fixed boundary. Here, the free boundary refers to the union of the boundaries of the sets {xu(x)>0}.

  • 7.
    Bozorgnia, Farid
    et al.
    Mathematics department.
    Bazarganzadeh, Mahmoudreza
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Numerical Schemes for Multi Phase Quadrature Domains2014In: International Journal of Numerical Analysis & Modeling, ISSN 1705-5105, Vol. 11, no 4, p. 726-744Article in journal (Refereed)
    Abstract [en]

    In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the numerical implementation of the resulting approach and present computational tests.

1 - 7 of 7
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf