A fast compressive Fourier collocation method for high-dimensional diffusion equation
Song Yol Kim, Chu Myong Ri, Ryong Chun Jo, Un Yong Cha
Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea
Keywords: high-dimensional diffusion equation, compressive Fourier collocation, sparse FFT, fast algorithm
Abstract
In this paper, a new fast compressive Fourier collocation algorithm for high-dimensional diffusion equations is constructed. A new algorithm is based on the high-dimensional sparse and fast Fourier transform and the compressive sampling matching pursuit algorithm. The computational complexity of the proposed algorithm is proportional to d2, where d is the dimension of PDE domain. The error of the approximate solution is estimated and some numerical experiments are given.
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