Immersed Interface Method for Elasticity Problems with Interfaces

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dc.contributor.advisorDr. Mansoor A. Haider, Committee Memberen_US
dc.contributor.advisorDr. Kazufumi Ito, Committee Memberen_US
dc.contributor.advisorDr. Sharon R. Lubkin, Committee Memberen_US
dc.contributor.advisorDr. Zhilin Li, Committee Chairen_US
dc.contributor.advisorComputational Mathematicsen_US
dc.contributor.authorYang, Xingzhouen_US
dc.date.accessioned2010-04-02T19:06:30Z
dc.date.available2010-04-02T19:06:30Z
dc.date.issued2004-07-20en_US
dc.degree.disciplineApplied Mathematicsen_US
dc.degree.leveldissertationen_US
dc.degree.namePhDen_US
dc.description.abstractAn immersed interface method and an immersed finite element method for solving linear elasticity problems with two phases separated by an interface have been developed in this thesis. For the problem of interest, the underlying elasticity modulus is a constant in each phase but vary from phase to phase. The basic goal here is to design an efficient numerical method using a fixed Cartesian grid. The application of such a method to problems with moving interfaces driving by stresses has a great advantage: no re-meshing is needed. A local optimization strategy is employed to determine the finite difference equations at grid points near or on the interface. The bi-conjugate gradient method and the GMRES with preconditioning are both implemented to solve the resulting linear systems of equations and compared. The level set method is used to represent the interface. Numerical results are presented to show that the immersed interface method is second-order accurate.en_US
dc.identifier.otheretd-07062004-175450en_US
dc.identifier.urihttp://www.lib.ncsu.edu/resolver/1840.16/5035
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectfinite differencesen_US
dc.subjectthe immersed interface methoden_US
dc.subjectjump conditionsen_US
dc.subjectinterfacesen_US
dc.subjectElasticityen_US
dc.subjectoptimization solvers.en_US
dc.subjectPCGen_US
dc.subjectGMRESen_US
dc.subjectpreconditioned BICGSTABen_US
dc.subjectstressen_US
dc.subjectstrainen_US
dc.subjectGalerkin methoden_US
dc.subjectenergy formen_US
dc.subjectvariation formen_US
dc.subjectlevel set methoden_US
dc.subjectCartesian grids methoden_US
dc.subjectGaussian quadratureen_US
dc.subjectimmersed finite element methoden_US
dc.titleImmersed Interface Method for Elasticity Problems with Interfacesen_US

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