Past Research Projects

1 Boundary Truncation Techniques for Finite Methods (1990-2000)

Dr. Lee has performed extensive research in the area of outer boundary conditions for electromagnetic scattering. In the early 1990’s, Dr. Lee was a co-developer of an efficient and accurate boundary truncation method called the bymoment method. Dr. Lee was also one of the leading researchers for another innovative technique called the measured equation of invariance. When this method was first proposed by Dr. Ken Mei, it received a great deal of attention in the electromagnetics community, although it was not well understood. Dr. Lee and his students provided much of the theoretical foundations associated with this method and showed ways to improve it. Dr. Lee has also worked on the development of another method which uses an anisotropic perfectly matched layer (PML) to absorb the outgoing wave. This concept is now one of the major methods used in both finite element and finite difference methods to absorb out-going waves. Recently, Dr. Lee has extended the PML to the finite element time domain method.

2 Domain decomposition algorithms for parallel computers (1991-1994)

In 1991, Dr. Lee introduced a domain decomposition approach which he called the partitioning technique for modeling electrically large geometries. In this method, a large computation domain is broken down into a large number of smaller domains. Within each small domain, a boundary value problem is solved with the finite element method independent of the other domains. The domains were then coupled through a matrix generated from an application of boundary conditions at the interfaces between the domains. This approach provided tremendous savings in terms of memory and allowed for ideal implementation on the parallel computer. We were able to demonstrate dramatically improved speedup on the touchstone Delta parallel system, which was state-of-the art at that time.

3 Hybrid FDTD-Ray methods for Cavity Scattering (1991-1994)

Dr. Lee developed a novel hybrid method which couples a numerical technique (FDTD) to an asymptotic technique (ray methods such as shooting and bouncing ray (SBR) or generalized ray expansion (GRE)) where the weaknesses of one method are countered by the strengths of the other. Thus, a combined approach allowed one to solve problems which any single method could not handle. Such an approach was ideal for cavity scattering since the long duct could be accurately modeled by asymptotic methods while the complex engine termination could be modeled numerically. Through the use of FDTD, we were able to obtain broadband information with a single computation run, and we were also able to model penetrable structures such as absorbers that may be present in the engine. By the end of this project, we were able to perform the largest ever wide-band cavity scattering problems at that time, which included realistic fan blade terminations.

4 Improved Algorithms to Minimize Numerical Dispersion Error in Finite Difference Methods (1995-2000)

Dr. Lee has written a number of important papers on the numerical dispersion error within finite element and finite difference methods when applied to Maxwell's equations. These papers demonstrate the fundamental limitations of finite methods for modeling electrically large objects, and they provide a guide for choosing the discretization size as well as the order of the basis function for finite elements or the order of the approximation for finite differences. He has developed new finite element basis functions and new finite difference schemes which produce smaller numerical dispersion errors than the traditional methods for electromagnetic applications. These reduced dispersion schemes do not increase the computation costs while significantly reducing the error.

5 Scattering from Sea Ice (1997-1999)

Dr. Lee began working in the Byrd Polar Research Center in 1997 to help in understanding scattering from sea ice. There were two aspects to this project. The first was to characterize the electrical properties of ice over a wide bandwidth. To do this, we constructed a probe composed of two antennas. Next, we simulated the probe using the FDTD method where one antenna transmitted the signal to the other antenna. By simulating the probe in materials with different parameters, we were able to obtain a table of data for comparison against measurements. When the actual measurements were taken, we were able to predict the permittivity and conductivity of ice from the tables. The second aspect was to study the scattering from sea ice through the use of Monte Carlo simulations with a FDTD model of sea ice. From this study, we were able to do the first numerical study of sea ice scattering. This second part of this work was done in collaboration with Dr. Joel Johnson.

6 Reduced order modeling for finite element methods (1998-2002)

Dr. Lee has began looking at reduced order models to reduce the computation costs for obtaining wideband data with frequency domain methods. These methods allow one to solve the problem at a small number of frequency points (sometimes just one) and then through a small number of additional calculations to obtain solutions over a large number of frequencies. A major difficulty with most of these methods is that stagnation occurs, i.e., the solution converges only in a small band around the frequency where the solution is calculated. In this project, we were able to remove the stagnation in the Galerkin asymptotic waveform evaluation (GAWE) method. We also developed an optimized approach to obtain a wideband solution given solutions at multiple frequency points. These two advances allowed us to significantly increase the efficiency of the reduced order model. Dr. Jin-Fa Lee was a collaborator on this project.

7 Design and Analysis of Resonators for Ultra High Field Magnetic Resonance Imaging (1998-2002)

Dr. Lee became involved in the analysis and design of RF coils for high field magnetic resonance imaging (MRI) systems when Ohio State created the most powerful MRI system (8 Tesla) for human imaging. Within the MRI community, there was a general feeling that MRI above 4 Tesla was not realizable because of the predicted non-uniformity in the radio frequency (RF) magnetic field (producing poor images) and the predicted excessive power requirements for imaging. These predictions were not based on rigorous calculations, but instead based on extrapolations at lower fields. Our belief was that there is no true physical limitations at 8 Tesla, but it required important advances in RF coil design. It was clear that previous RF coil designs would be inadequate for high field, and the coil designs was probably the main limitations on the success of the project. Since 1998, Dr. Lee has worked with the MRI researchers at OSU and has been able to produce an accurate numerical model of the coil operating in the presence of a human head with the use of the FDTD method. This model allowed us to understand the performance of the head coil and therefore to design one which works in real life. Dr. Lee’s group produced the first model to accurately account for the interactions between the coil and the human head. He has been able to show what the true limitations are at the high fields and also corrects many misconceptions about the power requirements at 8 Tesla and what are the causes of the non-uniformity. Some findings from this research are:

1. Performance of birdcage coils: We showed that nonuniformities in birdcage coils were greater than many designers believed. We also showed that the interactions between the coil and the head can significantly impact coil performance. These nonuniformities were shown to increase at higher fields.

2. We proposed a new concept in RF coil design in which an array of coils is used to excite the head. Each coil is excited independently with a different magnitude and phase. By properly choosing the excitation parameters, we demonstrate that a fairly uniform magnetic field can be achieved.

3. Through a series of numerical and experimental studies, we showed that dielectric resonance effects were not present at high field. At the time the prevailing view within the community was that dielectric resonance was a major limiting factor which would prevent imaging at high field.

4. We provided the most comprehensive theoretical and numerical study of the TEM resonator available and showed its viability for use in imaging at 8 Tesla.

5. Another major prediction was that the RF power required for imaging increases with the square of the static magnetic field strength. Thus at 8 Tesla, a major concern was that the power requirements for imaging for produce to much heating in the patient to be done safely. Through the use of numerical simulations, we were able to show that the power does not have the behavior at higher fields, and in fact, there is strong evidence that it may even decrease at some point.