A Domain Decomposition Finite-Difference Method Utilizing Characteristic Basis Functions for Solving Electrostatic Problems

2008 ◽  
Vol 50 (4) ◽  
pp. 946-952 ◽  
Author(s):  
Bing-Zhong Wang ◽  
R. Mittra ◽  
Wei Shao
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Domain Decomposition ◽  
Difference Method ◽  
Basis Functions ◽  
Electrostatic Problems

Heat Diffusion in Heterogeneous Bodies Using Heat-Flux-Conserving Basis Functions

1988 ◽  
Vol 110 (2) ◽  
pp. 276-282 ◽  
Author(s):  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Solution Method ◽  
Basis Functions ◽  
Heat Diffusion ◽  
Simple Geometry ◽  
The Finite Difference Method

The generalized analytical derivation presented here enables one to obtain solutions to the diffusion equation in complex heterogeneous geometries. A new method of constructing basis functions is introduced that preserves the continuity of temperature and heat flux throughout the domain, specifically at the boundary of each inclusion. A set of basis functions produced in this manner can be used in conjunction with the Green’s function derived through the Galerkin procedure to produce a useful solution method. A simple geometry is selected for comparison with the finite difference method. Numerical results obtained by this method are in excellent agreement with finite-difference data.

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