Iterative Methods for Solving the Exterior Dirichlet Problem for the Helmholtz Equation with Applications to the Inverse Scattering Problem for Low Frequency Acoustic Waves.
DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST
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A previous paper presented an iterative method for solving the exterior Dirichlet problem for the Helmholtz equation defined in the plane and used this result to provide a constructive approach for solving the low frequency inverse scattering problem for a cylinder. These results were based on the use of conformal mapping and the fact that the integral of the normal derivative of the total field over the boundary of the obstacle vanishes, neither of which is valid in the three dimensional case. The present paper shows how the previous analysis can be modified in order to extend these results to the case of the exterior Dirichlet problem for the Helmholtz equation in R3. Our results are based on choosing an appropriate fundamental solution such that the integral equation associated with the exterior Dirichlet problem can be solved by iteration for sufficiently small values of the wave number.
- Numerical Mathematics
- Radiofrequency Wave Propagation