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Bängtsson, Erik
Publications (10 of 14) Show all publications
Bängtsson, E. & Neytcheva, M. (2007). Finite element block-factorized preconditioners. .
Open this publication in new window or tab >>Finite element block-factorized preconditioners
2007 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2007-008
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-10631 (URN)
Available from: 2007-04-16 Created: 2007-04-16 Last updated: 2011-11-18Bibliographically approved
Bängtsson, E. (2007). Robust Preconditioners Based on the Finite Element Framework. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis.
Open this publication in new window or tab >>Robust Preconditioners Based on the Finite Element Framework
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Robust preconditioners on block-triangular and block-factorized form for three types of linear systems of two-by-two block form are studied in this thesis.

The first type of linear systems, which are dense, arise from a boundary element type of discretization of crack propagation problems. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method.

The second type of algebraic systems, which are sparse, indefinite and nonsymmetric, arise from a finite element (FE) discretization of the partial differential equations (PDE) that describe (visco)elastic glacial isostatic adjustment (GIA). The Schur complement approximation in the block preconditioners is constructed by assembly of local, exactly computed Schur matrices. The quality of the approximation is verified in numerical experiments.

When the block preconditioners for the indefinite problem are combined with an inner iterative scheme preconditioned by a (nearly) optimal multilevel preconditioner, the resulting preconditioner is (nearly) optimal and robust with respect to problem size, material parameters, number of space dimensions, and coefficient jumps.

Two approaches to mathematically formulate the PDEs for GIA are compared. In the first approach the equations are formulated in their full complexity, whereas in the second their formulation is confined to the features and restrictions of the employed FE package. Different solution methods for the algebraic problem are used in the two approaches. Analysis and numerical experiments reveal that the first strategy is more accurate and efficient than the latter.

The block structure in the third type of algebraic systems is due to a fine-coarse splitting of the unknowns. The inverse of the pivot block is approximated by a sparse matrix which is assembled from local, exactly inverted matrices. Numerical experiments and analysis of the approximation show that it is robust with respect to problem size and coefficient jumps.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2007. 84 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 296
Keyword
FEM, iterative solution method, algebraic multilevel preconditioner, sparse approximate inverse, block preconditioner, Schur complement approximation, nonsymmetric saddle point matrix, isostatic glacial adjustment, pre-stress advection, elasticity, viscoelasticity, (in)compressible solid, ABAQUS, BEM/DDM
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-7828 (URN)978-91-554-6870-5 (ISBN)
Public defence
2007-05-11, Room 2247, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2007-04-20 Created: 2007-04-20 Last updated: 2011-10-26Bibliographically approved
Bängtsson, E. & Lund, B. (2006). A comparison between two approaches to solve the equations of linear isostasy. Institute for Parallel Processing, Bulgarian Academy of Sciences.
Open this publication in new window or tab >>A comparison between two approaches to solve the equations of linear isostasy
2006 (English)Report (Other academic)
Place, publisher, year, edition, pages
Institute for Parallel Processing, Bulgarian Academy of Sciences, 2006
Series
BIS-21++ Report, 2006-03
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-20384 (URN)
Available from: 2008-02-21 Created: 2008-02-21 Last updated: 2018-01-12Bibliographically approved
Bängtsson, E. & Lund, B. (2006). A comparison between two solution techniques to solve the equations of linear isostasy. .
Open this publication in new window or tab >>A comparison between two solution techniques to solve the equations of linear isostasy
2006 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-051
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-19829 (URN)
Available from: 2008-02-21 Created: 2008-02-21 Last updated: 2018-01-12Bibliographically approved
Bängtsson, E. & Neytcheva, M. (2006). An agglomerate multilevel preconditioner for linear isostasy saddle point problems. In: Large-Scale Scientific Computing: (pp. 113-120). Berlin: Springer-Verlag.
Open this publication in new window or tab >>An agglomerate multilevel preconditioner for linear isostasy saddle point problems
2006 (English)In: Large-Scale Scientific Computing, Berlin: Springer-Verlag , 2006, 113-120 p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Berlin: Springer-Verlag, 2006
Series
Lecture Notes in Computer Science, 3743
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-78987 (URN)10.1007/11666806_11 (DOI)000236456400011 ()
Available from: 2008-07-22 Created: 2008-07-22 Last updated: 2018-01-13Bibliographically approved
Bängtsson, E. (2005). A consistent stabilized formulation for a nonsymmetric saddle-point problem. .
Open this publication in new window or tab >>A consistent stabilized formulation for a nonsymmetric saddle-point problem
2005 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2005-030
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-76700 (URN)
Available from: 2007-02-03 Created: 2007-02-03 Last updated: 2011-11-17Bibliographically approved
Bängtsson, E. & Neytcheva, M. (2005). Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problems. Communications in Numerical Methods in Engineering, 21, 73-81.
Open this publication in new window or tab >>Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problems
2005 (English)In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 21, 73-81 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-73790 (URN)10.1002/cnm.728 (DOI)
Available from: 2006-05-13 Created: 2006-05-13 Last updated: 2018-01-14Bibliographically approved
Bängtsson, E. & Neytcheva, M. (2005). Numerical simulations of glacial rebound using preconditioned iterative solution methods. Applications of Mathematics, 50, 183-201.
Open this publication in new window or tab >>Numerical simulations of glacial rebound using preconditioned iterative solution methods
2005 (English)In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 50, 183-201 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-73787 (URN)10.1007/s10492-005-0013-3 (DOI)
Available from: 2006-05-13 Created: 2006-05-13 Last updated: 2018-01-14Bibliographically approved
Bängtsson, E. (2005). Robust preconditioned iterative solution methods for large-scale nonsymmetric problems. (Licentiate dissertation). Uppsala University.
Open this publication in new window or tab >>Robust preconditioned iterative solution methods for large-scale nonsymmetric problems
2005 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We study robust, preconditioned, iterative solution methods for large-scale linear systems of equations, arising from different applications in geophysics and geotechnics.

The first type of linear systems studied here, which are dense, arise from a boundary element type of discretization of crack propagation in brittle material. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method.

The second type of algebraic systems are nonsymmetric and indefinite and arise from finite element discretization of the partial differential equations describing the elastic part of glacial rebound processes. An equal order finite element discretization is analyzed and an optimal stabilization parameter is derived.

The indefinite algebraic systems are of 2-by-2-block form, and therefore block preconditioners of block-factorized or block-triangular form are used when solving the indefinite algebraic system. There, the required Schur complement is approximated in various ways and the quality of these approximations is compared numerically.

When the block preconditioners are constructed from incomplete factorizations of the diagonal blocks, the iterative scheme show a growth in iteration count with increasing problem size. This growth is stabilized by replacing the incomplete factors with an inner iterative scheme with a (nearly) optimal order multilevel preconditioner.

Place, publisher, year, edition, pages
Uppsala University, 2005
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2005-006
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-86353 (URN)
Supervisors
Available from: 2005-11-03 Created: 2006-05-14 Last updated: 2017-08-31Bibliographically approved
Neytcheva, M., Bängtsson, E. & Lund, B. (2004). Numerical solution methods for glacial rebound models. .
Open this publication in new window or tab >>Numerical solution methods for glacial rebound models
2004 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2004-016
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-48253 (URN)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-01-25Bibliographically approved
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