Dear Colleagues,

We continue our Colloquium in the Math Department.

Yongzhi Steve Xu,

Department of Mathematics,

University of Tennessee at Chattanooga

Thursday, February 12, EMCS 233, 3:00pm.

Sound Wave Equation and Polarized Maxwell's Equations --- Modeling,
Analysis, and Numerical Simulations

Abstract.

The propagation of Sound waves in an ocean is governed by the sound wave
equation, while the propagation of light waves in fiber optic is
governed by Maxwell's equations. Under some conditions, both can be
simplified to the Helmholtz equation in a layered half space. We combine
analytical and numerical methods to study the two physical phenomena.

This talk present our resent research results of modeling, analysis and
numerical simulations of the sound wave and light wave propagation and
scattering. Movies of numerical simulations made by Mat lab will be
shown. Two design problems of marine acoustics and fiber optics will be
discussed as toy models of computational engineering.

We have carefully tailored the talk to use undergraduate mathematics.
Students may see how calculus (math 151, math 161), multi-calculus (math
255), differential equations (math 245), Fourier transform (math 460),
contour integrals (math 470), numerical methods (math 308, math 418),
and other mathematics can be combined to solve complicated problems.


Boris P Belinskiy

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748