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Dorostkar, Ali
Publications (10 of 14) Show all publications
Neytcheva, M., Holmgren, S., Bull, J. R., Dorostkar, A., Kruchinina, A., Nikitenko, D., . . . Voevodin, V. (2018). Multidimensional performance and scalability analysis for diverse applications based on system monitoring data. In: Parallel Processing and Applied Mathematics: Part I. Paper presented at PPAM 2017 (pp. 417-431). Springer
Open this publication in new window or tab >>Multidimensional performance and scalability analysis for diverse applications based on system monitoring data
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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
Dorostkar, A. (2017). Analysis and Implementation of Preconditioners for Prestressed Elasticity Problems: Advances and Enhancements. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>Analysis and Implementation of Preconditioners for Prestressed Elasticity Problems: Advances and Enhancements
2017 (English)Doctoral 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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. p. 61
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1580
Keywords
FEM, Saddle point matrix, Preconditioning, Schur complement, Generalized Locally Toeplitz, Prestressed elasticity
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-331852 (URN)978-91-513-0116-7 (ISBN)
Public defence
2017-12-08, Room 2446, TDB, Lägerhyddsvägen 2, 75237, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2017-11-13 Created: 2017-10-18 Last updated: 2018-03-07
Dorostkar, A. (2017). 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
Donatelli, M., Dorostkar, A., Mazza, M., Neytcheva, M. & Serra-Capizzano, S. (2017). Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem. Computers and Mathematics with Applications, 74, 1015-1028
Open this publication in new window or tab >>Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem
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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
Donatelli, M., Dorostkar, A., Mazza, M., Neytcheva, M. & Serra-Capizzano, S. (2016). A block multigrid strategy for two-dimensional coupled PDEs.
Open this publication in new window or tab >>A block multigrid strategy for two-dimensional coupled PDEs
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2016 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-001
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-274750 (URN)
Available from: 2016-01-22 Created: 2016-01-25 Last updated: 2019-01-22Bibliographically approved
Dorostkar, A., Neytcheva, M. & Serra-Capizzano, S. (2016). Spectral analysis of coupled PDEs and of their Schur complements via Generalized Locally Toeplitz sequences in 2D. Computer Methods in Applied Mechanics and Engineering, 309, 74-105
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
Dorostkar, A. (2015). Developments in preconditioned iterative methods with application to glacial isostatic adjustment models. (Licentiate dissertation). Uppsala University
Open this publication in new window or tab >>Developments in preconditioned iterative methods with application to glacial isostatic adjustment models
2015 (English)Licentiate 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.

Place, publisher, year, edition, pages
Uppsala University, 2015
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2015-002
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-253718 (URN)
Supervisors
Available from: 2015-05-29 Created: 2015-06-01 Last updated: 2017-08-31Bibliographically approved
Dorostkar, A., Neytcheva, M. & Lund, B. (2015). Numerical and computational aspects of some block-preconditioners for saddle point systems. Parallel Computing, 49, 164-178
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
Dorostkar, A., Neytcheva, M. & Lund, B. (2015). On some block-preconditioners for saddle point systems and their CPU–GPU performance.
Open this publication in new window or tab >>On some block-preconditioners for saddle point systems and their CPU–GPU performance
2015 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2015-003
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-242560 (URN)
Projects
eSSENCE
Available from: 2015-01-26 Created: 2015-01-27 Last updated: 2018-01-11Bibliographically approved
Dorostkar, A., Neytcheva, M. & Serra-Capizzano, S. (2015). Schur complement matrix and its (elementwise) approximation: A spectral analysis based on GLT sequences. In: Large-Scale Scientific Computing: . Paper presented at LSSC 2015 (pp. 419-426). Springer
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
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