Applied Mathematics
Inverse Problems
Inverse problems are a major area of both theoretical and computational research in the department. The theoretical analysis of such problems requires a solid knowedge of such areas of mathematics as partial differential equations and Fourier analysis. Aircraft acoustics and crack detection are just two applications investigated by research groups in the department.
Acoustical Holography
Nearfield Acoustical Holography is the inverse problem in acoustics of computing the normal velocities on the boundary of a region from measurements of the acoustical pressure on an interior surface. Methods for solving this problem are important for the reduction of noise levels in airplane cabins. A group of several faculty and graduate students have developed such methods with support from the National Science Foundation as well as a local aircraft company. The figure shows the reconstruction of normal velocity in comparison with the original normal velocity distribution.
(DeLillo)