dc.contributor.author Kärkkäinen, Kari dc.date.accessioned 2008-01-09T12:55:54Z dc.date.available 2008-01-09T12:55:54Z dc.date.issued 2005 dc.identifier.isbn 951-39-2395-9 dc.identifier.other oai:jykdok.linneanet.fi:982891 dc.identifier.uri https://jyx.jyu.fi/handle/123456789/13270 dc.description.abstract Kari Kärkkäinen tutki tehokkaita ja käyttökelpoisia ratkaisumenetelmiä vapaita pintoja sisältäville malleille. Hän tarkastelee väitöksessään numeerisessa simuloinnissa käytettävien vapaan pinnan ratkaisumenetelmien tehokkuutta ja niiden parantamista käyttäen matemaattista lähestymistapaa. Kärkkäinen ehdottaa ratkaisumenetelmää, jonka avulla vapaan pinnan tehtävien ratkaiseminen on helpompaa. Menetelmää voi myös soveltaa erilaisiin tilanteisiin. fi dc.description.abstract This work is devoted to the development of efficient and robust solution algorithms for a class of free boundary problems. This consists of mathematical analysis of different model problems and the description of numerical implementation to generic free boundary problems along with the numerical results. The free boundary problems that are investigated in this work are elliptic stationary boundary value problems with overdetermined boundary conditions. Overdetermined boundary conditions are satisfied only in a special geometry which is a solution to the free boundary problem. The free boundary problems are nonlinear and can not be solved straightforwardly. Algorithms to solve this kind of free boundary problems are iterative, the solution is sought by iterating geometries. The suggested algorithm is based on the combination of continuous shape sensitivity analysis and automatic differentiation of discrete equations. The discrete linearized equations are derived tuning the finite element method to correspond to the continuous shape linearization of the problem. Efficiency of the presented algorithms are tested and illustrated through numerous numerical examples. en dc.format.extent 84 sivua dc.language.iso eng dc.publisher University of Jyväskylä dc.relation.ispartofseries Jyväskylä studies in computing dc.relation.isversionof ISBN 951-39-2354-1 dc.title Shape sensitivity analysis for numerical solution of free boundary problems dc.type Diss. dc.identifier.urn URN:ISBN:951-39-2395-9 dc.type.dcmitype Text en dc.type.ontasot Väitöskirja fi dc.type.ontasot Doctoral dissertation en dc.contributor.tiedekunta Informaatioteknologian tiedekunta fi dc.contributor.tiedekunta Faculty of Information Technology en dc.contributor.yliopisto University of Jyväskylä en dc.contributor.yliopisto Jyväskylän yliopisto fi dc.contributor.oppiaine Tietotekniikka fi dc.relation.issn 1456-5390 dc.relation.numberinseries 58 dc.rights.accesslevel openAccess fi dc.subject.yso matemaattiset mallit dc.subject.yso simulointi dc.subject.yso matematiikka dc.subject.yso algoritmit dc.subject.yso raja-arvo dc.subject.yso numeeriset menetelmät
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