This project studies the use of wavelets and fast multipole methods and their modifications to solve surface integral equations. The developed code will eventually be used to study the solution of multiple scattering from rough surfaces. Wavelet transforms can be used to generate a sparse matrix from a dense matrix. The resultant sparse matrix can be manipulated much more efficiently and inverted with less computer time. The fast multiple method can be used to expedite matrix-vector multiples in an iterative algorithm like the conjugate gradient method.

In this project, we study the use of the distorted Born iterative method and the local shape function method to study the inversion of well-logging tools. These new methods can invert a profile of much higher contrast than conventional technique where a linearization approximation is made. To expedite the inversion, the forward problem is solved with the CG-FFHT (conjugate gradient fast Fourier Hankel transform) method. Alternatively, a finite-element method with a frontal solver is also used to invert well-logging data.

In this project, we study efficient methods to model 3-D geometries involving lossy inhomogeneous media. We study the use of differential equation solvers and integral equation solvers to achieve this goal. Differential equations are solved with the finite-element method, finite-difference method together with iterative methods like conjugate gradient method, biconjugate gradient method, and spectral Lanczos method. Integral equations are solved with method of moments and the multilevel fast multipole algorithms. These solutions will help model the response of a well-logging tool in a complex environment. In the inverse problem, we will apply the Born iterative and distorted Born iterative method to solve inverse problems related to well-logging using efficient forward solvers.

In this project, we use fast algorithms to study the multiple scattering of acoustic waves by random media. The effect of inclusions in the atmosphere on the effect of acoustic wave propagation will be studied using supercomputers. First, a small number of inclusions will be studied. Then the solution for N randomly distributed inclusions will be studied. The resultant computer program will be used as a computer simulation model for the propagation of low-frequency, high-energy acoustic waves through random inclusions or random media. The effect of the half-space and interface will be studied.

The goals of this multimillion dollar project are: (1) to substantially advance our knowledge in developing fast algorithms for solving integral equations of electromagnetic scattering with reduced computational complexity and memory requirements; (2) to enhance our ability to solve partial differential equations of magnetic scattering by reducing grid-dispersion error and modeling error; (3) hybridization with high-frequency methods to further expand the class of problems we can handle in addition to fast numerical methods; (4) parallelization of our algorithms on massively parallel machines and distributed systems to harness maximal throughput from present day computers; (5) development of computational engines as workhorses and application-specific modules for easy interfacing with real-world applications problems.

This project investigates efficient methods to solve the volume integral equation of scattering for inhomogeneous bodies in two and three dimensions. The forward solver is then used to solve inverse scattering problems involving many unknowns. The proposed forward scattering and inverse scattering solvers use iterative methods. In certain instances, recursive methods or nesting methods will be used.

This project proposes to build and design a multifrequency and broadband radar for nondestructive evaluation of the quality and condition of concrete. The system will consist of several transmitter antennas with many receiver antennas. It has the advantage of producing a superior image of voids and reinforcement bars in a concrete with a higher resolution. Such a system will be used for rapid nondestructive evaluation of constructed works.

Quantum-well InGaAs and InGaAsP semiconductors using strained effects will be applied in the design and f abrication of optoelectronic devices and systems including laser diodes and electroabsorption modulators. We will focus on the fundamental research issues of these opto electronic devices and their high-speed applications for navy needs. The full advantage of strained quantum-well semiconductors for applications in semiconductor lasers and electroabsorption modulators will be explored both theoretically and experimentally. Novel designs of quantum-well lasers using different types of strain and hetero struc tures will be realized for high-performance operation.

Wide-bandwidth microwave modulation of semiconductor strained quantum-well lasers using distributed feedback structures plays an important role in high bit-rate optical communication systems. The goals of this project are (1) to design and fabricate high bandwidth quantum-well lasers using strain effects and (2) to combine microwave and optical measurement techniques to investigate the physics and device performance of quantum-well lasers under high-speed modulation conditions. The proposed project is interdisciplinary in nature because optoelectronic device technology and microwave and optical measurement techniques will be introduced to the study of high-frequency modulation of quantum-well lasers for optical communication systems.

The feasibility of using optical fibers with a polarimetric technique to detect internal strain in concrete has been investigated both theoretically and experimentally in our previous work. Compressive strain on birefringent optical fiber changes the polarization of the light propagating through the fiber. The output power measured at a given polarization can be calibrated according to the strain applied. Based on this knowledge, we can design weight sensors for railcars, using the weight of a railcar to induce a strain on the embedded fiber-optic cable. The goal of this project is to research, model, and test potential fiber optic designs in weighing railcars in motion.

Fundamental linear and nonlinear gains and their polarization dependencies in strained semiconductor quantum wells will be investigated theoretically and experimentally. We will design strained quantum wells such that the gains of both TE and TM polarizations have nearly the same magnitude using InGaAs/InGaAlAs and InGaAs/InGaAsP material systems. Strained quantum wells have important technological applications in optoelectronic devices. With our comprehensive study, polarization-insensitive semiconductor optical amplifiers using strained quantum wells will be designed.

It has been found that fibers can effectively monitor rail integrity. The simplest, most effective approach involves attaching fiber to a length of track, shining light into the fiber, and monitoring the light intensity out of the fiber with a photodetector. If the rail buckles or breaks, the fiber will be affected, reducing the light intensity that the detector measures. Thus, a decision can be made concerning the integrity of a particular length of track based on the detected light intensity. This project is to research, model, and test fiber-optic designs for monitoring the integrity and performance of structures such as railroad bridges and tracks.

This research is to develop a numerical simulation tool for the investigation of the interactions between high-power electromagnetic fields and complex electronic systems deployed in a large complex platform. A clear understanding of such interactions is instrumental in developing electronic systems capable of functioning normally in a high-intensity ambient electromagnetic environment.

The interaction of electromagnetic fields with biological objects such as a human body is an important issue in MRI and microwave hyperthermia applications. Better understanding of such interactions cannot only provide vital safety information, but can also enable engineers to design better and new devices. In this project, we develop highly accurate and efficient three-dimensional computational methods for simulation of the interaction of electromagnetic fields with biological objects.

The goal of this project is to develop a finite-element method using vector elements for electromagnetic analysis of electronic devices, circuits, antennas, and radar scattering. Special emphasis is on the method's accuracy, efficiency, and versatility. Both frequency and time-domain methods will be investigated and their performance will be evaluated. Specific applications will be demonstrated.

In this project, we develop hybrid numerical methods to compute electromagnetic scattering from realistic three-dimensional targets. These hybrid methods combine the high-frequency techniques, such as the shooting-and-bouncing-ray technique, and the low-frequency technique, such as the finite-element method and integral equation methods, to take the advantages and eliminate the disadvantages of both. As a result, they are accurate and efficient and can be applied to large complex targets.

A four-arm sinuous zigzag antenna can provide simultaneous reception/transmission of two polarizations over a very wide band of frequencies. Despite the usefulness of this antenna, very little analysis has been published. Of particular interest are unidirectional versions obtained by adding ground planes and/or conducting cavities to antennas of conical shape. In this project the moment method is used in the supercomputer solution for the currents on the arms of sinuous antennas and on surrounding structures.