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Adaptive reduction of finite element models in computational solid mechanics
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Department of mathematics and mathematical statistics , 2011.
Identifiers
URN: urn:nbn:se:umu:diva-43750ISBN: 978-91-7459-227-6OAI: oai:DiVA.org:umu-43750DiVA: diva2:415741
Opponent
Supervisors
Available from: 2011-05-12 Created: 2011-05-09 Last updated: 2012-05-29Bibliographically approved
List of papers
1. Mode superposition with submodeling
Open this publication in new window or tab >>Mode superposition with submodeling
2012 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 90, no 6, 739-751 p.Article in journal (Refereed) Published
Abstract [en]

We investigate a new approach for local enhancement of mode superpositions, which builds on the concept of submodeling. To this end, we impose a multiscale split on the reduced solution into a global part defined by the mode superposition method and a local part defined by a patch problem solved in a subspace of the finite element space associated with a subdomain around some region of interest. The patch problem yields a local correction on the modal approximation. We describe the basics of this approach and evaluate the accuracy of the approximation in elastostatic numerical examples. We also demonstrate how the submodeling technique may be applied as a post-processing operation on a set of reduced solutions, for example, from dynamics simulation, to enhance accuracy in some domain of interest. Copyright (C) 2012 John Wiley & Sons, Ltd.

Place, publisher, year, edition, pages
Malden, MA: Wiley-Blackwell, 2012
Keyword
model reduction, mode superposition, submodeling
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-55498 (URN)10.1002/nme.3340 (DOI)000303048900003 ()
Available from: 2012-05-28 Created: 2012-05-21 Last updated: 2012-05-29Bibliographically approved
2. Adaptive component mode synthesis in linear elasticity
Open this publication in new window or tab >>Adaptive component mode synthesis in linear elasticity
2011 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 86, no 7, 801-934 p.Article in journal (Refereed) Published
Abstract [en]

Component mode synthesis (CMS) is a classical method for the reduction of large-scale finite element models in linear elasticity. In this paper we develop a methodology for adaptive refinement of CMS models. The methodology is based on a posteriori error estimates that determine to what degree each CMS subspace influence the error in the reduced solution. We consider a static model problem and prove a posteriori error estimates for the error in a linear goal quantity as well as in the energy and L2 norms. Automatic control of the error in the reduced solution is accomplished through an adaptive algorithm that determines suitable dimensions of each CMS subspace. The results are demonstrated in numerical examples.

Keyword
component mode synthesis, substructuring, adaptivity, a posteriori error estimation, model reduction, finite element method
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-43738 (URN)10.1002/nme.3078 (DOI)
Available from: 2011-05-09 Created: 2011-05-09 Last updated: 2012-01-14Bibliographically approved
3. A posteriori error analysis of component mode synthesis for the elliptic eigenvalue problem
Open this publication in new window or tab >>A posteriori error analysis of component mode synthesis for the elliptic eigenvalue problem
2011 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 200, no 41-44, 2840-2847 p.Article in journal (Refereed) Published
Abstract [en]

We develop a posteriori error estimates for the error associated with model reduction of elliptic eigenvalue problems using component mode synthesis (CMS). The estimates reflect to what degree each CMS subspace influence the overall error in the reduced solution. This allows for automatic error control through adaptive algorithms that determine suitable dimensions of each CMS subspace.

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
Model reduction, Component mode synthesis, A posteriori error estimate, Adaptivity
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-43740 (URN)10.1016/j.cma.2011.05.002 (DOI)
Available from: 2011-05-09 Created: 2011-05-09 Last updated: 2012-01-14Bibliographically approved
4. A posteriori error analysis of component mode synthesis for the frequency response problem
Open this publication in new window or tab >>A posteriori error analysis of component mode synthesis for the frequency response problem
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-43742 (URN)
Available from: 2011-05-09 Created: 2011-05-09 Last updated: 2012-01-12
5. Duality-based adaptive model reduction for one-way coupled thermoelastic problems
Open this publication in new window or tab >>Duality-based adaptive model reduction for one-way coupled thermoelastic problems
2012 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 91, no 3, 306-318 p.Article in journal (Other academic) Published
Abstract [en]

 In this paper, we derive a discrete a posteriori error estimate for a thermoelastic model problem discretized using a reduced finite element method. The problem is one-way coupled in the sense that heat transfer affects elastic deformation but not vice versa. A reduced model is constructed using component mode synthesis in each of the heat transfer and linear elastic finite element solvers. The error estimate bounds the difference between the reduced and the standard finite element solution in terms of discrete residuals and corresponding dual weights. A main feature with the estimate is that it automatically gives a quantitative measure of the propagation of error between the solvers with respect to a certain computational goal. The analytical results are accompanied by a numerical example.

Keyword
model reduction, component mode synthesis, thermoelasticity, adaptive, a posteriori
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-43743 (URN)10.1002/nme.4273 (DOI)000305681300005 ()
Note
Article included in thesis in manuscript form.Available from: 2011-05-09 Created: 2011-05-09 Last updated: 2012-07-23Bibliographically approved
6. On generalized proper orthogonal decompositions
Open this publication in new window or tab >>On generalized proper orthogonal decompositions
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-43744 (URN)
Available from: 2011-05-09 Created: 2011-05-09 Last updated: 2012-01-12
7. Model reduction in rolling bearing simulation based on static load cases and the proper orthogonal decomposition
Open this publication in new window or tab >>Model reduction in rolling bearing simulation based on static load cases and the proper orthogonal decomposition
2011 (English)Other (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-43749 (URN)
Available from: 2011-05-09 Created: 2011-05-09 Last updated: 2012-01-14Bibliographically approved

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