Waves Seminar Series

Department of Mathematical Sciences and Center for Applied Mathematics and Statistics

New Jersey Institute of Technology

Fall 2010

Talks in this series are held Wednesdays in Cullimore 611 at 2:45 pm unless noted otherwise. If you have any questions about a particular colloquium, please contact the person hosting the speaker. For general questions about the seminar schedule, please contact Richard Moore.

Date

Speaker and title

Host

9/9, 2:30pm

Special day/time!

Nathan Gibson, Oregon State University, Polynomial Chaos Approach for Simulations in Dispersive Media (abstract)

Peter Petropoulos

9/9, 3:00pm

Special day/time!

Vrushali Bokil, Oregon State University, Analysis of High Order Staggered FDTD Methods for Maxwell's Equations in Dispersive Media (abstract)

Peter Petropoulos

10/6

Arnaud Goullet, New Jersey Institute of Technology, Evolution of large amplitude internal solitary waves using a regularized model (abstract)

Shahriar Afkhami

September 9, Nathan Gibson, Oregon State University, Polynomial Chaos Approach for Simulations in Dispersive Media

Time-domain electromagnetic simulations involving anomalously dispersive media, such as biological tissue, are not straight-forward. One popular approach for representing the polarization is the Cole-Cole (1936) model, a heuristic generalization of the standard Debye (1929) model which corresponds to a first order linear auxiliary ODE. The Cole-Cole model corresponds to a fractional order ODE which presents computational challenges.

We examine an alternative approach based on using the Debye model, but with a probability distribution of relaxation times.  The idea of distributions of relaxation times dates back to von Schweidler in 1907, preceding even Debye.

Recent advances in the generalized Polynomial Chaos method make the idea of a random polarization attractive. We will describe this modeling approach and then introduce a discretization of the system coupled with Maxwell's equations.  We will present a stability analysis of the overall method and numerically demonstrate convergence rates.

September 9, Vrushali Bokil, Oregon State University, Analysis of High Order Staggered FDTD Methods for Maxwell's Equations in Dispersive Media

We consider spatial high order staggered finite difference time domain (FDTD) methods for Maxwell's equations coupled with a Debye or Lorentz polarization model. We study the stability properties of, and the phase error present in these schemes.

We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the first order spatial derivative operator. This alternative representation allows the derivation of a concise formula for the numerical dispersion relation for all (even) order schemes applied to each model, including the limiting (infinite order) case. We further derive a closed-form analytical stability condition for these schemes as a function of the order of the method.

October 6, Arnaud Goullet, New Jersey Institute of Technology, Evolution of large amplitude internal solitary waves using a regularized model

After a brief overview on internal waves in the ocean, we will introduce a regularized model for the evolution of strongly nonlinear internal waves. The ocean is simplified to a two-layer model with different fluid densities. The fluid is considered to be inviscid, irrotational and with constant density in each layer. The time evolution equations are solved numerically using a pseudo-spectral method along with a fourth order Runge-Kutta time integration scheme. We will show some preliminary results on nonlinear interaction between internal solitary waves. By including the effect of varying bottom topography, we will present some numerical simulations on the interaction of large solitary waves with bottom topography.

 


Links to Old Seminar Schedules

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