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Title: Fast Fourier Transform on Multipoles Algorithm for Elasticity and Stokes Flow
Authors: HE XUEFEI
Keywords: boundary element, Fast Fourier Transform on Multipoles, FFTM, Navier, Stokes, nonlinear
Issue Date: 20-Aug-2008
Citation: HE XUEFEI (2008-08-20). Fast Fourier Transform on Multipoles Algorithm for Elasticity and Stokes Flow. ScholarBank@NUS Repository.
Abstract: In this thesis, the fast Fourier transform on multipole (FFTM) is used to accelerate the matrix-vector product in the boundary element method (BEM) for solving three dimensional Laplace equation, Navier equation, Stokes equation and non-linear Poisson-type equation. The FFTM method uses multipole moments and local expansions, together with the fast Fourier transform (FFT), to accelerate the far field computation. In this work, a new formulation for handling the double layer kernel using the direct formulation is presented. The FFTM algorithm is extended to solve elasticity problems, governed by the Navier equation. The memory requirement of original FFTM algorithm tends to be high. To reduce the memory cost, a new compact storage of the translation matrices is proposed. This reduces the memory usage significantly, allowing large elasticity problems to be solved efficiently. To extend the FFTM to solve the Stokes equation, the same technique, as that for the Navier equation, is used to derive the translation operators. The resulting multipole translations for Stokes equation are similar to the Navier equation. The BEM becomes less attractive when used to solve non-linear equation. In this thesis, the non-linear Poisson-type equation is solved by the FFTM. In each iteration of the fast algorithm, a particular solution is calculated by the FFT, the resulted Laplace equation is solved by the FFTM and the interior values are updated by the FFTM.
Appears in Collections:Ph.D Theses (Open)

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