**Dr. Tom DeLillo**

Wichita State University

**"Computational Methods for an Inverse Problem in Acoustics"**

**Abstract:**

We consider the inverse problem in acoustics of computing the normal velocities on the boundary of a region from pressure measurements on an interior surface. The pressure satisfies the Helmholtz equation in the region and is represented as a single layer potential. The problem of finding the density function from the interior pressure measurement therefore involves solving a first kind integral equation and is ill-posed. Once the density is found, the normal velocity can
be computed by applying a second kind integral operator. We will report on results using various regularization methods for this problem, including the singular value decomposition
and iterative methods such as the conjugate gradient method, when the pressure data contains noise. These problems arise in studies of acoustics in interior aircraft cabins. This is joint work with Victor Isakov, Nicolas Valdivia, and Lianju Wang at WSU and is supported by the NSF and Cessna Aircraft Company in Wichita.

#### Friday, November 5, 1999

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 1999]