Existence of Solutions to Poisson's Equation

2008 ◽  
Vol 51 (2) ◽  
pp. 229-235
Author(s):  
Mary Hanley
Keyword(s):  
Boundary Conditions ◽  
Poisson Equation ◽  
Existence Of Solutions ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
The Poisson Equation ◽  
Topological Condition ◽  
Necessary And Sufficient

AbstractLet Ω be a domain in ℝn (n ≥ 2). We find a necessary and sufficient topological condition on Ω such that, for anymeasure μ on ℝn, there is a function u with specified boundary conditions that satisfies the Poisson equation Δu = μ on Δ in the sense of distributions.

scholarly journals Multiscale boundary element method for Poisson’s equation

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Su Hoe Yeak ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Poisson Equation ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Numerical Example ◽  
The Poisson Equation ◽  
Method Show ◽  
Element Method

This paper applied the multiscale boundary element method for the numerical solution of the Poisson equation. The multiscale technique coupling with boundary element method will be used to solve the problem of Poisson equation efficiently and faster. Numerical example is given to illustrate the efficiency of the propose method. The solution of proposed method will be compared with boundary element method and the former method show less iteration in computation.

scholarly journals Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions

2012 ◽  
Vol 137 (13) ◽  
pp. 134108 ◽  
Author(s):  
Alessandro Cerioni ◽  
Luigi Genovese ◽  
Alessandro Mirone ◽  
Vicente Armando Sole
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Generic Boundary
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