Accession Number : AD0746067

Title :   Low Frequency Neumann Scattering Problems in Two Dimensions.

Descriptive Note : Scientific rept.,

Corporate Author : DELAWARE UNIV NEWARK DEPT OF MATHEMATICS

Personal Author(s) : Ahner,John F.

Report Date : JUN 1972

Pagination or Media Count : 34

Abstract : A new method is given to solve the exterior Neumann scattering problem in the plane. This method depends upon a new integral equation formulation of the Helmholtz equation with prescribed Neumann boundary conditions for piecewise smooth, simple closed curves, which is continuous as the field point approaches the curve gamma from the exterior, is continuous for all points on gamma including those portions where gamma is not smooth and the integrand is bounded, even at the singularities of the free space Green's function. It is proven that for sufficiently small but nonzero values of the wave number, if gamma is strictly convex, the field on gamma may be found by a standard Neumann series. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), (*INTEGRAL EQUATIONS, POTENTIAL THEORY), ITERATIONS, COMPLEX VARIABLES, CONVEX SETS, SPECIAL FUNCTIONS(MATHEMATICAL), SCATTERING, THEOREMS, INEQUALITIES, SERIES(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE