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Acoustic scattering study and Fredholm integral equation

Author: XuJianLi
Tutor: WangLianTang
School: Northwestern University
Course: Applied Mathematics
Keywords: Wave scattering problem Integral equation Tikhonov regularization method Potential theory Far field pattern
CLC: O241.82
Type: Master's thesis
Year: 2011
Downloads: 37
Quote: 0
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Abstract


As an important branch of the inverse problem of the field of mathematical physics , in the past two decades , for the wave scattering problem , the research phase of the forward problem for the study of the inverse problem to more mature , the solution method is also diverse . This paper focuses on the Impedance and Neumann boundary conditions under positive numerical solution of the problem of acoustic scattering . Impedance boundary conditions , sound waves are scattered potential theory integral equation is solved using the method of moments , rather than integral -core processing , and finally to easy sex ; numerical examples ; positive scattering of sound waves Neumann boundary condition , the use of radial basis function approximation of the value of the scattered wave to solve by numerical examples show that the method based on Tikhonov regularization thinking , given a the numerical solution of the Fredholm integral equation , numerical results show that the numerical stability and effectiveness of the algorithm .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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