INTEGRAL EQUATIONS' APPROACH TO SCATTERING PROBLEMS

• Main Author: ROKHLIN, VLADIMIR
• Format: Others
• Language: English
• Published: 2007
• Subjects: Mathematics
• Online Access: http://hdl.handle.net/1911/19047

In the present thesis, the classical potential theory is used to derive systems of second kind integral equations corresponding to scattering of acoustic and elastic waves from both fluid and solid inclusions. These systems of integral equations are discretized by means of the Nystrom algorithm. The resulting systems of linear algebraic equations are solved by means of a version of the preconditioned generalized conjugate residual algorithm. In order to obtain the time domain result, results for a sequence of frequency values are computed with subsequent application of the Fast Fourier Transformation. The computational results presented in the present thesis indicate that the resulting numerical algorithm is suitable for fairly large-scale scattering computations in two dimensions. The 3-dimensional version of the theory is also briefly discussed.