Full identification of acoustic sources with multiple frequencies and boundary measurements. (English) Zbl 1187.65124

Alves, Carlos J. S.; Martins, Nuno F. M.; Roberty, Nilson C.

Inverse Probl. Imaging 3, No. 2, 275-294 (2009).

Authors’ abstract: We study the identification of acoustic sources in a domain \(\Omega\) from boundary data. With a single frequency, we show that identification is possible if, besides the boundary data, considerable information regarding the type of the source is considered. For the general case, we present an identification result using multiple frequencies and boundary measurements. We show that for compactly supported sources in \(\Omega\), the completion of Cauchy data has at most one solution and thus for this type of sources, identification is possible using variable frequencies and incomplete boundary measurements. A numerical method based on the reciprocity functional is proposed and tested for several numerical examples. For compact sources, a data completion method is proposed and tested in order to apply the previous method.

Reviewer: Wilhelm Heinrichs (Essen)

MSC:

65N21	Numerical methods for inverse problems for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65N80	Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs

Keywords:

inverse acoustic source problem; method of fundamental solutions; Cauchy data Fitting; reciprocity gap functional; identification; multiple frequencies; boundary measurements; numerical examples