Abstract
This paper is concerned with the application of the localized Fourier collocation method (LFCM), a newly-developed meshless collocation method, for the numerical solution of high-order partial differential equations (PDEs). In the present method, the entire computational domain is divided into a set of overlapping subdomains in which the Fourier series expansion and moving-least square approximation are applied to construct the local systems of linear equations. By satisfying the governing equations and the corresponding boundary conditions, a sparse and banded stiffness matrix can be established which makes the method very attractive for large-scale engineering simulations. Preliminary numerical experiments for fourth-order PDEs in both two- and three-dimensions are presented to demonstrate the accuracy and efficiency of the present method.
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