dc.contributor.advisor Duraiswami, Ramani en_US dc.contributor.author Adelman, Ross en_US dc.date.accessioned 2017-01-24T06:32:51Z dc.date.available 2017-01-24T06:32:51Z dc.date.issued 2016 en_US dc.identifier doi:10.13016/M23J9H dc.identifier.uri http://hdl.handle.net/1903/18943 dc.description.abstract The Laplace and Helmholtz equations are two of the most important partial differential equations (PDEs) in science, and govern problems in electromagnetism, acoustics, astrophysics, and aerodynamics. The boundary element method (BEM) is a powerful method for solving these PDEs. The BEM reduces the dimensionality of the problem by one, and treats complex boundary shapes and multi-domain problems well. The BEM also suffers from a few problems. The entries in the system matrices require computing boundary integrals, which can be difficult to do accurately, especially in the Galerkin formulation. These matrices are also dense, requiring O(N^2) to store and O(N^3) to solve using direct matrix decompositions, where N is the number of unknowns. This can effectively restrict the size of a problem. Methods are presented for computing the boundary integrals that arise in the Galerkin formulation to any accuracy. Integrals involving geometrically separated triangles are non-singular, and are computed using a technique based on spherical harmonics and multipole expansions and translations. Integrals involving triangles that have common vertices, edges, or are coincident are treated via scaling and symmetry arguments, combined with recursive geometric decomposition of the integrals. The fast multipole method (FMM) is used to accelerate the BEM. The FMM is usually designed around point sources, not the integral expressions in the BEM. To apply the FMM to these expressions, the internal logic of the FMM must be changed, but this can be difficult. The correction factor matrix method is presented, which approximates the integrals using a quadrature. The quadrature points are treated as point sources, which are plugged directly into current FMM codes. Any inaccuracies are corrected during a correction factor step. This method reduces the quadratic and cubic scalings of the BEM to linear. Software is developed for computing the solutions to acoustic scattering problems involving spheroids and disks. This software uses spheroidal wave functions to analytically build the solutions to these problems. This software is used to verify the accuracy of the BEM for the Helmholtz equation. The product of these contributions is a fast and accurate BEM solver for the Laplace and Helmholtz equations. en_US dc.language.iso en en_US dc.title Fast and Accurate Boundary Element Methods in Three Dimensions en_US dc.type Dissertation en_US dc.contributor.publisher Digital Repository at the University of Maryland en_US dc.contributor.publisher University of Maryland (College Park, Md.) en_US dc.contributor.department Computer Science en_US dc.subject.pqcontrolled Computer science en_US dc.subject.pqcontrolled Applied mathematics en_US dc.subject.pquncontrolled Acoustic scattering en_US dc.subject.pquncontrolled Boundary element method en_US dc.subject.pquncontrolled Fast multipole method en_US dc.subject.pquncontrolled Helmholtz equation en_US dc.subject.pquncontrolled Laplace equation en_US dc.subject.pquncontrolled Spheroidal wave functions en_US
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