Integral equation methods for the Helmholtz equation

1982 ◽  
Vol 5 (1) ◽  
pp. 506-517 ◽  
Author(s):  
Jean Giroire
Keyword(s):  
Integral Equation ◽  
Helmholtz Equation ◽  
Integral Equation Methods

Transmission problems for the vector Helmholtz equation

1987 ◽  
Vol 105 (1) ◽  
pp. 61-76 ◽  
Author(s):  
Peter Wilde
Keyword(s):  
Integral Equation ◽  
Helmholtz Equation ◽  
Boundary Integral Equation ◽  
Existence And Uniqueness ◽  
Boundary Integral ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Transmission Problems ◽  
Integral Equation Methods

SynopsisTransmission problems for the vector Helmholtz equation are considered. By using boundary integral equation methods, existence and uniqueness theorems in the form of Fredholm's alternative are established.

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.

A Comparison of Two Integral Equation Methods for High Subsonic Lifting Flows

1975 ◽  
Vol 26 (1) ◽  
pp. 56-58 ◽  
Author(s):  
D Nixon
Keyword(s):  
Integral Equation ◽  
Unique Solution ◽  
Subsonic Flow ◽  
Integral Equation Methods ◽  
High Subsonic Flow

SummaryA comparison is made of two recently published integral equation methods for calculating the high subsonic flow around lifting and non-lifting aerofoils. It is shown that one method leads to a non-unique solution.

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