On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation

1993 ◽  
Vol 66 (1) ◽  
pp. 199-214 ◽  
Author(s):  
Rainer Kress ◽  
Ian H. Sloan
Keyword(s):  
Integral Equation ◽  
Helmholtz Equation ◽  
Numerical Solution ◽  
Logarithmic Integral

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.

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