An Integral Equation Method for Solving Mixed Boundary Value Problems

1971 ◽  
Vol 20 (4) ◽  
pp. 642-658 ◽  
Author(s):  
D. L. Jain ◽  
R. P. Kanwal
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Integral Equation Method ◽  
Equation Method ◽  
Mixed Boundary Value Problems

On mixed boundary value problems for the Helmholtz equation

1977 ◽  
Vol 77 (1-2) ◽  
pp. 65-77 ◽  
Author(s):  
R. Kress ◽  
G. F. Roach
Keyword(s):  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Theoretic Approach ◽  
Mixed Boundary Value Problems

SynopsisExistence and uniqueness theorems are obtained for a class of mixed boundary value problems associated with the three-dimensional Helmholtz equation. In this context the boundary of the region of interest is assumed to consist of the union of a finite number of disjoint, closed, bounded Lyapunov surfaces on some of which are imposed Dirichlet conditions whilst Neumann conditions are imposed on the remainder. An integral equation method is adopted throughout. The required boundary integral equations are generated by a modified layer theoretic approach which extends the work of Brakhage and Werner [1] and Leis [2, 3].

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