Let D in R^3 be a bounded simply connected domain with smooth boundary F(D) contained in the three dimensional euclidean space, whose acoustic properties are given by a surface acoustic impedance X(x), x in F(D). The obstacle D when hit by an incoming time harmonic plane acoustic wave generates a scattered acoustic field whose leading term at large distance from the obstacle is given by a spherical wave multiplied by a term called far field pattern. In this paper we consider the problem of recovering F(D) and X from the knowledge of several far field patterns and of the corresponding incoming waves. We propose a method to solve this problem based on the so called Herglotz function method that generalizes the work of Colton and Monk [1]. Finally some numerical experiments on test problems are shown.
A new method to reconstruct the boundary conditions of the Helmholtz equation
MAPONI, Pierluigi;MISICI, Luciano;
1994-01-01
Abstract
Let D in R^3 be a bounded simply connected domain with smooth boundary F(D) contained in the three dimensional euclidean space, whose acoustic properties are given by a surface acoustic impedance X(x), x in F(D). The obstacle D when hit by an incoming time harmonic plane acoustic wave generates a scattered acoustic field whose leading term at large distance from the obstacle is given by a spherical wave multiplied by a term called far field pattern. In this paper we consider the problem of recovering F(D) and X from the knowledge of several far field patterns and of the corresponding incoming waves. We propose a method to solve this problem based on the so called Herglotz function method that generalizes the work of Colton and Monk [1]. Finally some numerical experiments on test problems are shown.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
