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A fast enriched FEM for Poisson equations involving interfaces

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dc.contributor.advisor Jamie Peraire. en_US
dc.contributor.author Huynh, Thanh Le Ngoc en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.date.accessioned 2009-04-29T17:19:36Z
dc.date.available 2009-04-29T17:19:36Z
dc.date.copyright 2008 en_US
dc.date.issued 2008 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/45278
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. en_US
dc.description Includes bibliographical references (leaves 55-56). en_US
dc.description.abstract We develop a fast enriched finite element method for solving Poisson equations involving complex geometry interfaces by using regular Cartesian grids. The presence of interfaces is accounted for by developing suitable jump conditions. The immersed boundary method (IBM) and the immersed interface method (IIM) are successfully used to solve these problems when combined with a fast Fourier transform. However, the IBM and the IIM, which are developed from the finite difference method, have several disadvantages including the characterization of the null spaces and the inability to treat complex geometries accurately. We propose a solution to these difficulties by employing the finite element method. The continuous Galerkin solution approximations at the interface elements are modified using the enriched basis functions to make sure that the optimal convergence rates are obtained. Here, the FFT is applied in the fast Poisson solver to significantly accelerate the computational processes for solving the global matrix system. With reasonably small interfaces, the operational cost is almost linearly proportional to the number of the Cartesian grid points. The method is further extended to solve problems involving multi-materials while preserving the optimal accuracy. Several benchmark examples are shown to demonstrate the performance of the method. en_US
dc.description.statementofresponsibility by Thanh Le Ngoc Huynh. en_US
dc.format.extent 56 leaves en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Computation for Design and Optimization Program. en_US
dc.title A fast enriched FEM for Poisson equations involving interfaces en_US
dc.title.alternative Fast enriched finite element method for Poisson equations involving interfaces en_US
dc.type Thesis en_US
dc.description.degree S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 310976551 en_US


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