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Bängtsson, Erik

Open this publication in new window or tab >>Finite element block-factorized preconditioners### Bängtsson, Erik

### Neytcheva, Maya

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##### 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)
#####

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Available from: 2007-04-16 Created: 2007-04-16 Last updated: 2011-11-18Bibliographically approved

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.

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.

Open this publication in new window or tab >>Robust Preconditioners Based on the Finite Element Framework### Bängtsson, Erik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_1_j_idt183_some",{id:"formSmash:j_idt179:1:j_idt183:some",widgetVar:"widget_formSmash_j_idt179_1_j_idt183_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_1_j_idt183_otherAuthors",{id:"formSmash:j_idt179:1:j_idt183:otherAuthors",widgetVar:"widget_formSmash_j_idt179_1_j_idt183_otherAuthors",multiple:true}); 2007 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2007. p. 84
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 296
##### Keywords

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

### Margenov, Svetozar

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##### Supervisors

### Neytcheva, Maya

### Lötstedt, Per

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Available from: 2007-04-20 Created: 2007-04-20 Last updated: 2011-10-26Bibliographically approved

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.

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.

Bulgarian Academy of Sciences, Institute for Parallel Processing.

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, Division of Scientific Computing.

Open this publication in new window or tab >>A comparison between two approaches to solve the equations of linear isostasy### Bängtsson, Erik

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

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##### 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)
#####

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Available from: 2008-02-21 Created: 2008-02-21 Last updated: 2018-01-12Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.

Open this publication in new window or tab >>A comparison between two solution techniques to solve the equations of linear isostasy### Bängtsson, Erik

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

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##### 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)
#####

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Available from: 2008-02-21 Created: 2008-02-21 Last updated: 2018-01-12Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.

Open this publication in new window or tab >>An agglomerate multilevel preconditioner for linear isostasy saddle point problems### Bängtsson, Erik

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_4_j_idt183_some",{id:"formSmash:j_idt179:4:j_idt183:some",widgetVar:"widget_formSmash_j_idt179_4_j_idt183_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_4_j_idt183_otherAuthors",{id:"formSmash:j_idt179:4:j_idt183:otherAuthors",widgetVar:"widget_formSmash_j_idt179_4_j_idt183_otherAuthors",multiple:true}); 2006 (English)In: Large-Scale Scientific Computing, Berlin: Springer-Verlag , 2006, p. 113-120Conference 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 ()
#####

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Available from: 2008-07-22 Created: 2008-07-22 Last updated: 2018-01-13Bibliographically approved

Open this publication in new window or tab >>A consistent stabilized formulation for a nonsymmetric saddle-point problem### Bängtsson, Erik

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_5_j_idt183_some",{id:"formSmash:j_idt179:5:j_idt183:some",widgetVar:"widget_formSmash_j_idt179_5_j_idt183_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_5_j_idt183_otherAuthors",{id:"formSmash:j_idt179:5:j_idt183:otherAuthors",widgetVar:"widget_formSmash_j_idt179_5_j_idt183_otherAuthors",multiple:true}); 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)
#####

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Available from: 2007-02-03 Created: 2007-02-03 Last updated: 2011-11-17Bibliographically approved

Open this publication in new window or tab >>Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problems### Bängtsson, Erik

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_6_j_idt183_some",{id:"formSmash:j_idt179:6:j_idt183:some",widgetVar:"widget_formSmash_j_idt179_6_j_idt183_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_6_j_idt183_otherAuthors",{id:"formSmash:j_idt179:6:j_idt183:otherAuthors",widgetVar:"widget_formSmash_j_idt179_6_j_idt183_otherAuthors",multiple:true}); 2005 (English)In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 21, p. 73-81Article in journal (Refereed) Published
##### National Category

Computational Mathematics Computer Sciences
##### Identifiers

urn:nbn:se:uu:diva-73790 (URN)10.1002/cnm.728 (DOI)
#####

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Available from: 2006-05-13 Created: 2006-05-13 Last updated: 2018-01-14Bibliographically approved

Open this publication in new window or tab >>Numerical simulations of glacial rebound using preconditioned iterative solution methods### Bängtsson, Erik

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_7_j_idt183_some",{id:"formSmash:j_idt179:7:j_idt183:some",widgetVar:"widget_formSmash_j_idt179_7_j_idt183_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_7_j_idt183_otherAuthors",{id:"formSmash:j_idt179:7:j_idt183:otherAuthors",widgetVar:"widget_formSmash_j_idt179_7_j_idt183_otherAuthors",multiple:true}); 2005 (English)In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 50, p. 183-201Article 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)
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Available from: 2006-05-13 Created: 2006-05-13 Last updated: 2018-01-14Bibliographically approved

Open this publication in new window or tab >>Robust preconditioned iterative solution methods for large-scale nonsymmetric problems### Bängtsson, Erik

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_8_j_idt183_some",{id:"formSmash:j_idt179:8:j_idt183:some",widgetVar:"widget_formSmash_j_idt179_8_j_idt183_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt179_8_j_idt183_otherAuthors",{id:"formSmash:j_idt179:8:j_idt183:otherAuthors",widgetVar:"widget_formSmash_j_idt179_8_j_idt183_otherAuthors",multiple:true}); 2005 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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)
#####

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##### Supervisors

### Neytcheva, Maya

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Available from: 2005-11-03 Created: 2006-05-14 Last updated: 2017-08-31Bibliographically approved

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.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.

Open this publication in new window or tab >>Numerical solution methods for glacial rebound models### 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.### Bängtsson, Erik

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

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##### 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)
#####

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#####

Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-01-25Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.