scholarly journals The method of fundamental solutions with eigenfunction expansion method for nonhomogeneous diffusion equation

2006 ◽  
Vol 22 (5) ◽  
pp. 1173-1196 ◽  
Author(s):  
D. L. Young ◽  
C. W. Chen ◽  
C. M. Fan ◽  
C. C. Tsai
Keyword(s):  
Diffusion Equation ◽  
Eigenfunction Expansion ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Eigenfunction Expansion Method

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

scholarly journals Free surface groundwater flow solution using boundary collocation methods

2018 ◽  
Vol 196 ◽  
pp. 03026 ◽  
Author(s):  
Juraj Mužík ◽  
Roman Bulko
Keyword(s):  
Diffusion Equation ◽  
Groundwater Flow ◽  
Moving Boundary ◽  
Numerical Algorithms ◽  
Type Equation ◽  
Fundamental Solutions ◽  
Collocation Methods ◽  
Method Of Fundamental Solutions ◽  
Singular Boundary ◽  
State Diffusion

In this paper, two meshless numerical algorithms are developed for the solution of two-dimensional steady-state diffusion equation that describes the stationary groundwater flow. The proposed numerical methods, which are truly meshless, quadrature-free and boundary only, are based on the method of fundamental solutions and singular boundary method respectively. The diffusion equation is transformed into a Poisson-type equation with a known fundamental solution. Numerical examples with moving boundary are presented and compared to the solutions obtained by the finite element method.

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