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Artificial boundary conditions of absolute transparency for two- and three-dimensional external time-dependent scattering problems

Published online by Cambridge University Press:  01 December 1998

IVAN L. SOFRONOV
IVAN L. SOFRONOV
Affiliation:
Keldysh Institute of Applied Mathematics RAS, Miusskaya sq. 4, Moscow 125047, Russia
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Abstract

For an external problem in IRd (d=2, 3) such that the unknown function satisfies the wave equation outside a finite domain, we generate artificial boundary conditions transparent to outgoing waves. These conditions permit an equivalent replacement of the original external problem by the problem inside the artificial boundary which is a circle (d=2) or a sphere (d=3): The questions of numerical implementation of the artificial conditions (that are non-local in both space and time) are considered. Special attention is paid to the reduction of necessary computational resources; in particular, a way of incorporating these conditions into numerical methods which makes the computational formulae local in time is suggested. The aspects of treating artificial boundaries of a non-spherical shape are discussed. Numerical examples of two- and three-dimensional scattering problems demonstrate the accuracy of proposed artificial boundary conditions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 9 , Issue 6 , December 1998 , pp. 561 - 588
Copyright
1998 Cambridge University Press

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