Immersed Interface Method for Elasticity Problems with Interfaces

finite differences;the immersed interface method;jump conditions;interfaces;Elasticity;optimization solvers.;PCG;GMRES;preconditioned BICGSTAB;stress;strain;Galerkin method;energy form;variation form;level set method;Cartesian grids method;Gaussian quadrature;immersed finite element method

Yang, Xingzhou ; Dr. Mansoor A. Haider, Committee Member,Dr. Kazufumi Ito, Committee Member,Dr. Sharon R. Lubkin, Committee Member,Dr. Zhilin Li, Committee Chair,Computational Mathematics,Yang, Xingzhou ; Dr. Mansoor A. Haider ; Committee Member ; Dr. Kazufumi Ito ; Committee Member ; Dr. Sharon R. Lubkin ; Committee Member ; Dr. Zhilin Li ; Committee Chair ; Computational Mathematics

University:North Carolina State University

关键词: finite differences;    the immersed interface method;    jump conditions;    interfaces;    Elasticity;    optimization solvers.;    PCG;    GMRES;    preconditioned BICGSTAB;    stress;    strain;    Galerkin method;    energy form;    variation form;    level set method;    Cartesian grids method;    Gaussian quadrature;    immersed finite element method;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5035/etd.pdf?sequence=1&isAllowed=y

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【 摘 要 】

An 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.