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1	Fast algorithms for frequency domain wave propagation Tsuji, Paul Hikaru 22 February 2013 (has links) High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time. / text Fast algorithms Boundary element methods Boundary integral equations Fast multipole methods Nedelec elements Spectral element methods Finite element methods Preconditioners Perfectly matched layers Radiation conditions Time harmonic Frequency domain Wave propagation Maxwell's equations Helmholtz equation Linear elasticity Elastic wave equation Computational electromagnetics Computational acoustics Electromagnetic cloaking Seismic velocity models Overthrust Salt dome

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Fast algorithms for frequency domain wave propagation