• home
• current students
• graduate
• events

Presenter: Dr. Susan C. Hagness - Electrical and Computer Engineering, University of Wisconsin-Madison
Supervisor:

Date: Thu, October 31, 2002
Time: 15:00:00 - 16:00:00
Place: Engineering Office Wing, Room EOW 430

ABSTRACT

Abstract

Over the past decade, the finite-difference time-domain (FDTD) method has become one of the most powerful full-wave techniques for solving Maxwell's equations of electrodynamics. The algorithmic simplicity, robustness, and potential for great volumetric complexity afforded by FDTD modeling has prompted an expanding level of interest in this technique. Currently, hundreds of papers are published worldwide each year on FDTD theory and its applications. This expansion continues unabated as engineers and scientists from outside the traditional electromagnetics community become aware of the power of FDTD.

This talk highlights two of the latest frontiers in FDTD algorithms. First, I will discuss the latest advances in unconditionally stable alternating-direction-implicit (ADI) FDTD schemes. To date, ADI-FDTD has been shown to be a computationally efficient approach for problems where very fine meshes with respect to the wavelength are required for at least part of the computational domain. However, there are critical accuracy limitations of ADI-FDTD that have not been revealed by previously published numerical dispersion analyses. I will address the limitation imposed by the truncation error on the time step of the ADI-FDTD scheme. This points to the important caveat that while the present ADI-FDTD scheme overcomes the difficulty of the overly restrictive Courant stability bound associated with several classes of problems such as those commonly encountered in low-frequency bioelectromagnetics, large errors may arise when the time step is increased beyond the Courant limit even though the time step may adequately resolve key temporal features.

The second frontier is the development of highly accurate FDTD algorithms. The specific application of interest here is the modeling of electromagnetic wave interactions with nonlinear optical materials for which numerical phase velocity errors are particularly problematic due to the phase sensitivity of frequency conversion processes. Rather than resorting to extremely fine FDTD grids and excessively long computation times to overcome this difficulty, we have recently developed a pseudospectral time-domain method with fourth-order accuracy in time (PSTD-4) for solving Maxwell's equations in nonlinear media. Due to its drastically reduced numerical dispersion error, PSTD-4 offers high levels of accuracy with coarser grid resolutions and larger time steps compared to FDTD. Accordingly, preliminary results show that PSTD-4 is significantly more computationally efficient than the standard FDTD algorithm for modeling frequency conversion in novel structures such as nonlinear photonic crystals.

For more information contact:
Dr. Maria Stuchly (721-6029)