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**Harvard**

Boström, A. (1986) *The null-field approach in series form - the direct and inverse problems*.

** BibTeX **

@article{

Boström1986,

author={Boström, Anders},

title={The null-field approach in series form - the direct and inverse problems},

journal={Journal of the Acoustical Society of America},

issn={0001-4966},

volume={79},

pages={1223-1229},

abstract={The direct and inverse scattering problem in two-dimensional acoustics at a fixed frequency are considered. It is shown how the null-field approach can be modified so that the Q matrix (which in a straightforward manner gives the transition matrix) is obtained as a series instead of an integral. For an obstacle which is a perturbation of a circle this series form gives an approximate, very explicit, expression for the transition matrix. A few numerical examples are given to show the utility and limitations of this approximation. For the inverse problem, the series form of Q gives a system of nonlinear polynomial equations which are solved by the imbedding method. Some numerical examples show that quite accurate results are obtained by this method in cases where the system of equations can be kept small. The linear approximation of the system of polynomial equations yields a method that works surprisingly well and which is also promising for the more difficult three-dimensional and vector problems.},

year={1986},

keywords={acoustics, scattering, inverse problem},

}

** RefWorks **

RT Journal Article

SR Print

ID 190588

A1 Boström, Anders

T1 The null-field approach in series form - the direct and inverse problems

YR 1986

JF Journal of the Acoustical Society of America

SN 0001-4966

VO 79

SP 1223

OP 1229

AB The direct and inverse scattering problem in two-dimensional acoustics at a fixed frequency are considered. It is shown how the null-field approach can be modified so that the Q matrix (which in a straightforward manner gives the transition matrix) is obtained as a series instead of an integral. For an obstacle which is a perturbation of a circle this series form gives an approximate, very explicit, expression for the transition matrix. A few numerical examples are given to show the utility and limitations of this approximation. For the inverse problem, the series form of Q gives a system of nonlinear polynomial equations which are solved by the imbedding method. Some numerical examples show that quite accurate results are obtained by this method in cases where the system of equations can be kept small. The linear approximation of the system of polynomial equations yields a method that works surprisingly well and which is also promising for the more difficult three-dimensional and vector problems.

LA eng

OL 30