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  • 1. Donatelli, Marco
    et al.
    Dorostkar, Ali
    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.
    Mazza, Mariarosa
    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
    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.
    A block multigrid strategy for two-dimensional coupled PDEs2016Report (Other academic)
  • 2. Donatelli, Marco
    et al.
    Dorostkar, Ali
    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.
    Mazza, Mariarosa
    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
    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.
    Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem2017In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 74, p. 1015-1028Article in journal (Refereed)
  • 3.
    Dorostkar, Ali
    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.
    Analysis and Implementation of Preconditioners for Prestressed Elasticity Problems: Advances and Enhancements2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this work, prestressed elasticity problem as a model of the so-called glacial isostatic adjustment (GIA) process is studied. The model problem is described by a set of partial differential equations (PDE) and discretized with a mixed finite element (FE) formulation. In the presence of prestress the so-constructed system of equations is non-symmetric and indefinite. Moreover, the resulting system of equations is of the saddle point form.

    We focus on a robust and efficient block lower-triangular preconditioning method, where the lower diagonal block is and approximation of the so-called Schur complement. The Schur complement is approximated by the so-called element-wise Schur complement. The element-wise Schur complement is constructed by assembling exact local Schur complements on the cell elements and distributing the resulting local matrices to the global preconditioner matrix.

    We analyse the properties of the element-wise Schur complement for the symmetric indefinite system matrix and provide proof of its quality. We show that the spectral radius of the element-wise Schur complement is bounded by the exact Schur complement and that the quality of the approximation is not affected by the domain shape.

    The diagonal blocks of the lower-triangular preconditioner are combined with inner iterative schemes accelerated by (numerically) optimal and robust algebraic multigrid (AMG) preconditioner. We observe that on distributed memory systems, the top pivot block of the preconditioner is not scaling satisfactorily. The implementation of the methods is further studied using a general profiling tool, designed for clusters.

    For nonsymmetric matrices we use the theory of Generalized Locally Toeplitz (GLT) matrices and show the spectral behavior of the element-wise Schur complement, compared to the exact Schur complement. Moreover, we use the properties of the GLT matrices to construct a more efficient AMG preconditioner. Numerical experiments show that the so-constructed methods are robust and optimal.

    List of papers
    1. Numerical and computational aspects of some block-preconditioners for saddle point systems
    Open this publication in new window or tab >>Numerical and computational aspects of some block-preconditioners for saddle point systems
    2015 (English)In: Parallel Computing, ISSN 0167-8191, E-ISSN 1872-7336, Vol. 49, p. 164-178Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-253717 (URN)10.1016/j.parco.2015.06.003 (DOI)000364892500012 ()
    Available from: 2015-06-26 Created: 2015-06-01 Last updated: 2018-01-11Bibliographically approved
    2. Spectral analysis of coupled PDEs and of their Schur complements via Generalized Locally Toeplitz sequences in 2D
    Open this publication in new window or tab >>Spectral analysis of coupled PDEs and of their Schur complements via Generalized Locally Toeplitz sequences in 2D
    2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 309, p. 74-105Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-296265 (URN)10.1016/j.cma.2016.05.042 (DOI)000383828400004 ()
    Available from: 2016-06-08 Created: 2016-06-14 Last updated: 2019-01-22Bibliographically approved
    3. Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences
    Open this publication in new window or tab >>Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences
    2015 (English)In: Large-Scale Scientific Computing, Springer, 2015, p. 419-426Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Springer, 2015
    Series
    Lecture Notes in Computer Science ; 9374
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-267963 (URN)10.1007/978-3-319-26520-9_47 (DOI)000373881700047 ()978-3-319-26519-3 (ISBN)
    Conference
    LSSC 2015
    Funder
    Knut and Alice Wallenberg Foundation
    Available from: 2015-11-29 Created: 2015-11-30 Last updated: 2019-01-22Bibliographically approved
    4. Multidimensional performance and scalability analysis for diverse applications based on system monitoring data
    Open this publication in new window or tab >>Multidimensional performance and scalability analysis for diverse applications based on system monitoring data
    Show others...
    2018 (English)In: Parallel Processing and Applied Mathematics: Part I, Springer, 2018, p. 417-431Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Springer, 2018
    Series
    Lecture Notes in Computer Science ; 10777
    National Category
    Computer Sciences Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-331839 (URN)10.1007/978-3-319-78024-5_37 (DOI)000458563300037 ()978-3-319-78023-8 (ISBN)
    Conference
    PPAM 2017
    Projects
    eSSENCE
    Available from: 2018-03-23 Created: 2017-10-18 Last updated: 2019-03-14Bibliographically approved
    5. Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem
    Open this publication in new window or tab >>Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem
    Show others...
    2017 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 74, p. 1015-1028Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-323893 (URN)10.1016/j.camwa.2017.05.024 (DOI)000411546900011 ()
    Funder
    Knut and Alice Wallenberg Foundation
    Available from: 2017-06-03 Created: 2017-06-10 Last updated: 2019-01-22Bibliographically approved
    6. Function-based algebraic multigrid method for the 3D Poisson problem on structured meshes
    Open this publication in new window or tab >>Function-based algebraic multigrid method for the 3D Poisson problem on structured meshes
    2017 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2017-022
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-331778 (URN)
    Available from: 2017-10-18 Created: 2017-10-18 Last updated: 2017-10-19Bibliographically approved
  • 4.
    Dorostkar, Ali
    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.
    Developments in preconditioned iterative methods with application to glacial isostatic adjustment models2015Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This study examines the block lower-triangular preconditioner with element-wise Schur complement as the lower diagonal block applied on matrices arising from an application in geophysics. The element-wise Schur complement is a special approximation of the exact Schur complement that can be constructed in the finite element framework. The preconditioner, the exact Schur complement and the element-wise Schur complement are analyzed mathematically and experimentally.

    The preconditioner is developed specifically for the glacial isostatic adjustment (GIA) model in its simplified flat Earth variant, but it is applicable to linear system of equations with matrices of saddle point form.

    In this work we investigate the quality of the element-wise Schur complement for symmetric indefinite matrices with positive definite pivot block and show spectral bounds that are independent of the problem size. For non-symmetric matrices we use generalized locally Toeplitz (GLT) sequences to construct a function that asymptotically describes the spectrum of the involved matrices.

    The theoretical results are verified by numerical experiments for the GIA model. The results show that the so-obtained preconditioned iterative method converges to the solution in constant number of iterations regardless of the problem size or parameters.

    List of papers
    1. CPU and GPU performance of large scale numerical simulations in Geophysics
    Open this publication in new window or tab >>CPU and GPU performance of large scale numerical simulations in Geophysics
    Show others...
    2014 (English)In: Euro-Par 2014: Parallel Processing Workshops, Part I, Springer, 2014, p. 12-23Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Springer, 2014
    Series
    Lecture Notes in Computer Science ; 8805
    National Category
    Computer Sciences Geophysics
    Identifiers
    urn:nbn:se:uu:diva-238254 (URN)10.1007/978-3-319-14325-5_2 (DOI)000354783500002 ()978-3-319-14324-8 (ISBN)
    Conference
    1st Workshop on Applications of Parallel Computation in Industry and Engineering
    Projects
    UPMARCeSSENCE
    Available from: 2014-12-10 Created: 2014-12-10 Last updated: 2018-01-11Bibliographically approved
    2. Numerical and computational aspects of some block-preconditioners for saddle point systems
    Open this publication in new window or tab >>Numerical and computational aspects of some block-preconditioners for saddle point systems
    2015 (English)In: Parallel Computing, ISSN 0167-8191, E-ISSN 1872-7336, Vol. 49, p. 164-178Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-253717 (URN)10.1016/j.parco.2015.06.003 (DOI)000364892500012 ()
    Available from: 2015-06-26 Created: 2015-06-01 Last updated: 2018-01-11Bibliographically approved
    3. Spectral analysis of coupled PDEs and of their Schur complements via the notion of generalized locally Toeplitz sequences
    Open this publication in new window or tab >>Spectral analysis of coupled PDEs and of their Schur complements via the notion of generalized locally Toeplitz sequences
    2015 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2015-008
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-245770 (URN)
    Available from: 2015-02-25 Created: 2015-02-28 Last updated: 2019-01-22Bibliographically approved
    4. Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences
    Open this publication in new window or tab >>Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences
    2015 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2015-011
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-247553 (URN)
    Available from: 2015-03-20 Created: 2015-03-20 Last updated: 2019-01-22Bibliographically approved
  • 5.
    Dorostkar, Ali
    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.
    Function-based algebraic multigrid method for the 3D Poisson problem on structured meshes2017Report (Other academic)
  • 6.
    Dorostkar, Ali
    et al.
    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.
    Lukarski, Dimitar
    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.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    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.
    Notay, Yvan
    Schmidt, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    CPU and GPU performance of large scale numerical simulations in Geophysics2014In: Euro-Par 2014: Parallel Processing Workshops, Part I, Springer, 2014, p. 12-23Conference paper (Refereed)
  • 7.
    Dorostkar, Ali
    et al.
    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.
    Lukarski, Dimitar
    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.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    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.
    Notay, Yvan
    Schmidt, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Parallel performance study of block-preconditioned iterative methods on multicore computer systems2014Report (Other academic)
  • 8.
    Dorostkar, Ali
    et al.
    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.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Numerical and computational aspects of some block-preconditioners for saddle point systems2015In: Parallel Computing, ISSN 0167-8191, E-ISSN 1872-7336, Vol. 49, p. 164-178Article in journal (Refereed)
  • 9.
    Dorostkar, Ali
    et al.
    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.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    On some block-preconditioners for saddle point systems and their CPU–GPU performance2015Report (Other academic)
  • 10.
    Dorostkar, Ali
    et al.
    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
    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.
    Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences2015In: Large-Scale Scientific Computing, Springer, 2015, p. 419-426Conference paper (Refereed)
  • 11.
    Dorostkar, Ali
    et al.
    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
    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.
    Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences2015Report (Other academic)
  • 12.
    Dorostkar, Ali
    et al.
    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
    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.
    Spectral analysis of coupled PDEs and of their Schur complements via Generalized Locally Toeplitz sequences in 2D2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 309, p. 74-105Article in journal (Refereed)
  • 13.
    Dorostkar, Ali
    et al.
    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
    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.
    Spectral analysis of coupled PDEs and of their Schur complements via the notion of generalized locally Toeplitz sequences2015Report (Other academic)
  • 14.
    Neytcheva, Maya
    et al.
    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.
    Holmgren, Sverker
    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.
    Bull, Jonathan R.
    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.
    Dorostkar, Ali
    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.
    Kruchinina, Anastasia
    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.
    Nikitenko, Dmitry
    Popova, Nina
    Shvets, Pavel
    Teplov, Alexey
    Voevodin, Vadim
    Voevodin, Vladimir
    Multidimensional performance and scalability analysis for diverse applications based on system monitoring data2018In: Parallel Processing and Applied Mathematics: Part I, Springer, 2018, p. 417-431Conference paper (Refereed)
1 - 14 of 14
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