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1 Computer Assisted Mechanics and Engineering Sciences

1 2004

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Solving wave problems in infinite domain by using variable local DtN operators

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Premrov M. , Špacapan I.

Computer Assisted Mechanics and Engineering Sciences

2004

tom Vol. 11, No. 2-3

145-153

This paper presents an iterative method for solving two-dimensional wave problems in infinite domains. The method yields a solution that satisfies Sommerfeld's radiation condition, as required for the correct solution of infinite domains excited only locally. This problem occurs in the solution of the wave equation in infinite domains when using an asymptotic local DtN (Dirichlet-to-Neumann) map in computational procedures applied to a finite domain. We are demonstrating that the amplitudes of the reflected fictive harmonics depend upon the wave number, the location of the fictive boundary, as well as on the DtN operator used in the computations. A constant value of the operator cannot sufficiently eliminate the amplitudes of all reflected waves, while the results are poor especially for higher harmonics. Thus, we are proposing an iterative method, which varies the tangential dependence of the operator in each computational step.