The Interıor and Exterior Problems for the Generalized Poly-Axially Symmetric Helmholtz Equation

1982 ◽  
pp. 176-190
Author(s):  
İ. Ethem ANAR
Keyword(s):  
Helmholtz Equation ◽  
Axially Symmetric ◽  
Exterior Problems

On modified Green functions in exterior problems for the Helmholtz equation

1982 ◽  
Vol 383 (1785) ◽  
pp. 313-332 ◽  
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Present Note ◽  
Boundary Integral ◽  
Green Functions ◽  
Exterior Problems ◽  
The Green Function ◽  
Definition Of

The question of non-uniqueness in boundary integral equation formu­lations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of co­efficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.

scholarly journals Measures of Growth of Entire Solutions of Generalized Axially Symmetric Helmholtz Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Devendra Kumar ◽  
Rajbir Singh
Keyword(s):  
Helmholtz Equation ◽  
Lower Order ◽  
Entire Solution ◽  
Axially Symmetric ◽  
Entire Solutions ◽  
Lower Type ◽  
Order And Type

For an entire solution of the generalized axially symmetric Helmholtz equation , measures of growth such as lower order and lower type are obtained in terms of the Bessel-Gegenbauer coefficients. Alternative characterizations for order and type are also obtained in terms of the ratios of these successive coefficients.

A FINITE ELEMENT CODE FOR THE NUMERICAL SOLUTION OF THE HELMHOLTZ EQUATION IN AXIALLY SYMMETRIC WAVEGUIDES WITH INTERFACES

1999 ◽  
Vol 07 (02) ◽  
pp. 83-110 ◽  
Author(s):  
NIKOLAOS A. KAMPANIS ◽  
VASSILIOS A. DOUGALIS
Keyword(s):  
Finite Element ◽  
Helmholtz Equation ◽  
Nonlocal Boundary Condition ◽  
Bottom Topography ◽  
Nonlocal Boundary ◽  
Small Scale ◽  
Far Field ◽  
Axially Symmetric ◽  
Fortran Code ◽  
Iterative Linear Solvers

We consider the Helmholtz equation in an axisymmetric cylindrical waveguide consisting of fluid layers overlying a rigid bottom. The medium may have range-dependent speed of sound and interface and bottom topography in the interior nonhomogeneous part of the waveguide, while in the far-field the interfaces and bottom are assumed to be horizontal and the problem separable. A nonlocal boundary condition based on the DtN map of the exterior problem is posed at the far-field artificial boundary. The problem is discretized by a standard Galerkin/finite element method and the resulting numerical scheme is implemented in a Fortran code that is interfaced with general mesh generation programs from the MODULEF finite element library and iterative linear solvers from QMRPACK. The code is tested on several small scale examples of acoustic propagation and scattering in the sea and its results are found to compare well with those of COUPLE.

Fundamental solutions of the bi-axially symmetric Helmholtz equation

2018 ◽  
Vol 2018 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Tukhtasin Ergashev ◽  
◽  
Anvar Hasanov ◽  
Keyword(s):  
Helmholtz Equation ◽  
Fundamental Solutions ◽  
Axially Symmetric

Growth Estimates of Entire Function Solutions of Generalized Bi-Axially Symmetric Helmholtz Equation

2017 ◽  
Vol 8 ◽  
pp. 12-26 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Entire Function ◽  
Helmholtz Equation ◽  
Axially Symmetric ◽  
Order And Type

Growth estimates for entire function solutions of the generalized bi-axially symmetric Helmholtz equation ∂2u/∂x2 + ∂2u/∂y2 + (2µ/x)·(∂u/∂x) + (2ν/y)·(∂u/∂y) +k2u = 0, (µ,ν Є R+), in terms of their Jacobi Bessel coefficients and ratio of these coefficients have been studied. Some relations for order and type also have been obtained in terms of Taylor and Neumann coefficients. Our results generalize and extend some results of Gilbert and Howard, McCoy, Kumar and Singh.

Sign in / Sign up

Export Citation Format

Share Document