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A new integral equation approach to the Neumann problem in acoustic scattering
Author(s) -
Krutitskii P. A.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.269
Subject(s) - fredholm integral equation , mathematics , integral equation , neumann boundary condition , mathematical analysis , kernel (algebra) , boundary (topology) , scattering , boundary value problem , fredholm theory , electric field integral equation , summation equation , scattering theory , pure mathematics , physics , quantum mechanics
We suggest a new approach of reduction of the Neumann problem in acoustic scattering to a uniquely solvable Fredholm integral equation of the second kind with weakly singular kernel. To derive this equation we placed an additional boundary with an appropriate boundary condition inside the scatterer. The solution of the problem is obtained in the form of a single layer potential on the whole boundary. The density in the potential satisfies a uniquely solvable Fredholm integral equation of the second kind and can be computed by standard codes. Copyright © 2001 John Wiley & Sons, Ltd.