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A Novel Numerical Scheme for Nonhomogeneous Diffusion Processes in Irregular Domain

Journal article published in 1 by Shu-Ping Hu, Der-Liang Young, Chia-Ming Fan
This paper was not found in any repository; the policy of its publisher is unknown or unclear.
This paper was not found in any repository; the policy of its publisher is unknown or unclear.

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Abstract

In this paper, a novel numerical scheme (FDMFS), which combines the finite difference method (FDM) and the method of fundamental solutions (MFS), is proposed to simulate the nonhomogeneous diffusion problem. Although the time-dependent MFS is meshless, extendable for any dimensional problems and without transformation or difference discretization for the time domain, the MFS is only useful for dealing with homogeneous partial differential equations. Therefore, we proposed the FDM with Cartesian grid to handle the non-homogeneous term of the equations. The numerical solution in FDMFS is decomposed as a particular solution and a homogeneous solution. The particular solutions are constructed using the FDM in an artificial regular domain which contains the real domain, and the homogeneous solutions can be obtained by the time-space unification MFS. Besides, the Cartesian grid for particular solution is very simple to generate automatically. We proposed three different treatments for particular solution and compared these schemes with each other. Two numerical examples are chosen to validate the proposed numerical scheme and the numerical results are compared well with analytical solutions Keywords: non-homogeneous, diffusion, finite difference method, method of fundamental solutions, irregular domain.