The radially symmetric Green’s function for Dirichlet problem of Pennes equation outside of a circular domain

2020 ◽  
Vol 123 (1) ◽  
pp. 89-107
Author(s):  
J. A. López Molina
Keyword(s):  
Dirichlet Problem ◽  
Green’S Function ◽  
Green's Function ◽  
Circular Domain ◽  
Pennes Equation

Integral Equation Approach for Computing Green’s Function on Doubly Connected Regions via the Generalized Neumann Kernel

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Siti Zulaiha Aspon ◽  
Ali Hassan Mohamed Murid ◽  
Mohamed M. S. Nasser ◽  
Hamisan Rahmat
Keyword(s):  
Integral Equation ◽  
Dirichlet Problem ◽  
Linear System ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Integral ◽  
Generalized Neumann Kernel ◽  
Integral Equation Approach ◽  
Gauss Elimination ◽  
Neumann Kernel

This research is about computing the Green’s function on doubly connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystrӧm method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica plots of Green’s functions for several test regions are also presented.

scholarly journals Green’s function of the Dirichlet problem for the differential operator on a star-shaped graph at m

2019 ◽  
Vol 101 (1) ◽  
pp. 14-28
Author(s):  
Ghulam Hazrat Aimal Rasa ◽  
◽  
G. S. Auzerkhan ◽  
M. N. Konyrkulzhayeva ◽  
◽  
...  
Keyword(s):  
Dirichlet Problem ◽  
Differential Operator ◽  
Green’S Function ◽  
Green's Function ◽  
Shaped Graph

DIRICHLET PROBLEM OF POISSON EQUATIONS AND VARIATIONAL PRINCIPLE ON A TYPE OF FRACTAL SETS

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050090
Author(s):  
YIPENG WU ◽  
KUI YAO ◽  
LEI MU ◽  
ZHILONG CHEN
Keyword(s):  
Dirichlet Problem ◽  
Variational Principle ◽  
Green’S Function ◽  
Green's Function ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Fractal Sets ◽  
Poisson Equations ◽  
Level 3

This paper studied the level-3 Sierpinski gasket. We solved Dirichlet problem of Poisson equations and proved variational principle on the level-3 Sierpinski gasket by expressing Green’s function explicitly.

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