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Full-Text Articles in Physical Sciences and Mathematics
Nonequispaced Fast Fourier Transform, David Hughey
Nonequispaced Fast Fourier Transform, David Hughey
Theses and Dissertations
Two algorithms for fast and accurate evaluation of high degree trigonometric polynomials at many scattered points are presented. Both methods rely on highly localized kernels and the Fast Fourier Transform. The first algorithm uses the function values at uniformly distributed grid points and kernels that reproduce trigonometric polynomials, while the second method uses kernels that approximate well the function on the frequency side. Both algorithm are termed Nonequispaced Fast Fourier Transform. The first algorithm is coded in MATLAB and shown to approximate well the function to be evaluated.
Fast Methods For Variable-Coefficient Peridynamic And Non-Local Diffusion Models, Che Wang
Fast Methods For Variable-Coefficient Peridynamic And Non-Local Diffusion Models, Che Wang
Theses and Dissertations
In previous studies, scientists developed the classical solid mechanic theory. The model has been widely used in scientific research and practical production. The main assumption of the classical theory of solid mechanics is that all internal forces act through zero distance. Because of this assumption, the mathematical model always leads to partial differential equations, which meet with problems when describing the spontaneous formation of discontinuities and other singularities. A peridynamic model was proposed as a reformation of solid mechanics [40, 41, 43, 44, 45], which leads to a non-local framework that does not explicitly involve the notion of deformation gradients, …