scholarly journals Green’s function and image system for the Laplace operator in the prolate spheroidal geometry

AIP Advances ◽  
2017 ◽  
Vol 7 (1) ◽  
pp. 015024 ◽  
Author(s):  
Changfeng Xue ◽  
Shaozhong Deng
Keyword(s):  
Green’S Function ◽  
Laplace Operator ◽  
Green's Function ◽  
Prolate Spheroidal ◽  
Image System ◽  
The Laplace Operator ◽  
Spheroidal Geometry

On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle

2015 ◽  
Vol 6 (3) ◽  
Author(s):  
Makhmud A. Sadybekov ◽  
Batirkhan K. Turmetov ◽  
Berikbol T. Torebek
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Unit Ball ◽  
Explicit Form ◽  
Laplace Operator ◽  
Green's Function ◽  
Robin Problem ◽  
The Green Function ◽  
The Laplace Operator

AbstractThe paper is devoted to investigation questions about constructing the explicit form of the Green's function of the Robin problem in the unit ball of ℝ

scholarly journals Pointwise bounds for the Green's function for the Neumann-Laplace operator in $ \text{R}^3 $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Hoff
Keyword(s):  
Sobolev Space ◽  
Green’S Function ◽  
Laplace Operator ◽  
Green's Function ◽  
Neumann Boundary ◽  
Space Theory ◽  
Basic Facts ◽  
The Laplace Operator ◽  
Bounded Sets ◽  
Scaling Arguments

<p style='text-indent:20px;'>We derive pointwise bounds for the Green's function and its derivatives for the Laplace operator on smooth bounded sets in <inline-formula><tex-math id="M2">\begin{document}$ {\bf R}^3 $\end{document}</tex-math></inline-formula> subject to Neumann boundary conditions. The proofs require only ordinary calculus, scaling arguments and the most basic facts of <inline-formula><tex-math id="M3">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-Sobolev space theory.</p>

Etude numérique des modes et fréquences propres d'une cavité à l'aide de la fonction de Green

1979 ◽  
Vol 57 (2) ◽  
pp. 208-217
Author(s):  
Jacques A. Imbeau ◽  
Byron T. Darling
Keyword(s):  
Point Source ◽  
Green’S Function ◽  
Green's Function ◽  
Normal Modes ◽  
Preceding Paper ◽  
Double Precision ◽  
Prolate Spheroidal ◽  
Normal Functions ◽  
Normal Frequency ◽  
High Degree

We apply the methods developed in our preceding paper (J. A. Imbeau and B. T. Darling. Can. J. Phys. 57, 190(1979)) for calculating the Green's function of a cavity to obtain the normal modes and normal frequencies of the cavity. As the frequency of the driving point source approaches that of a normal frequency the response (Green's function) of the cavity becomes infinite, and the form of the Green's function is dominated by the normal mode. There is also a 180° reversal of phase in passing through a resonance. In this way, we are able to calculate the normal frequencies of prolate spheroidal cavities to the full precision employed in the calculations (16 significant digits for double precision of the IBM-370). The Green's functions and the normal functions are also obtainable to a high degree of precision, except in the immediate vicinity of the surface of the cavity where they suffer a well-known discontinuity.

Sign in / Sign up

Export Citation Format

Share Document