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Developments in preconditioned iterative methods with application to glacial isostatic adjustment models
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.
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: urn:nbn:se:uu:diva-253718OAI: oai:DiVA.org:uu-253718DiVA: diva2:815768
Supervisors
Available from: 2015-05-29 Created: 2015-06-01 Last updated: 2017-08-31Bibliographically approved
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, 12-23 p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Springer, 2014
Series
Lecture Notes in Computer Science, 8805
National Category
Computer Science 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: 2017-01-25Bibliographically 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, 164-178 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
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: 2017-12-04Bibliographically 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: 2015-12-28Bibliographically 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: 2015-12-28Bibliographically approved

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Dorostkar, Ali

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