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Numerical and Scientific Computing
^ Center for Simulation of Advanced Rockets
M. T. Heath,* E. de Sturler, P. E. Saylor, X. M. Jiao, A. Pinar
U.S. Department of Energy, B341494

The center carries out a wide variety of research in combustion, fluid dynamics, structural analysis, and computer science. Research in numerical computation focuses on solvers for large linear systems and on data transfer between disparate meshes. Work on linear solvers includes development of direct and iterative methods for symmetric and nonsymmetric linear systems and eigenvalue problems. Specific emphases include grid-based solvers, enhanced sparse matrix-vector products, preconditioners, and improved error estimates that enable sharper stopping criteria. Also under development are algorithms for mesh association and data interpolation at component interfaces.

^ Ultimate Speed of Quantum-Well Optoelectronic Devices
K. Hess,* U. Ravaioli* (Elect. & Comput. Engr.), T. Kerkhoven, D. Bailey, H. Song, J. Bude, G. Kosinovsky
U.S. Office of Naval Research, SDI-IST/N00014-86-K-0512

This research focuses on opportunities in optoelectronics that arise from the possibility of bandgap engineering. The goal is to simulate new forms of semiconductor heterolayers and thereby advise as to the optimum materials and structural forms that will lead to ultrahigh switching speeds in single devices and in optoelectronic integrated circuits. Researchers investigate the dynamic equations of lasers, detectors, and modulators, and transient electronic transport in structures that are prototypical for optoelectronic devices. This numerical approach, mostly based on Monte Carlo methods, goes far beyond conventional device modeling. Researchers also simulate optoelectronic processes pertinent to femtosecond spectroscopy transients.

^ Multidimensional Computation of Electronic Properties of Semiconductor Microstructures of High-Performance Heterojunction Devices
T. Kerkhoven;* J. P. Leburton,* U. Ravaioli* (Elect. & Comput. Engr.); Y. Saad,* J. Arends
National Science Foundation, EET-87-19100

The goal of this research is to design numerical programs for the simulation of multidimensional quantum wells. The numerical model consists of Poisson's equation coupled with Schrodinger's equation. Poisson's equation is solved as an elliptic boundary value problem, while Schrodinger's equation defines an eigenvalue problem. The model is nonlinear and requires repeated solution of such eigenvalue problems. Researchers compare the performance of Lanczos procedures with subspace iteration and examine the use of inverse iteration. Consistency of the two problems is obtained in an outer iteration that will be accelerated with a conjugate gradient procedure.

^ Inclusion of Overshoot Effects in the Drift-Diffusion Semiconductor Model
U. Ravaioli* (Elect. & Comput. Engr.), T. Kerkhoven, E. Kan
National Center for Computational Electronics; National Science Foundation, EET 88-09023

Researchers cooperate on the development of a numerical program in which overshoot effects are included in the drift-diffusion model. The model is extended by the introduction of mobility functions for which field dependence is computed by Monte Carlo simulation. The Scharfetter-Gummel discretization is adapted so that it can be applied to the modified model.

^ Preconditioning Radiation Transport
P. E. Saylor,* D. Smolarski, D. Swesty
National Aeronautics and Space Administration, NCCS 5-153

Scalable methods are under development for preconditioning certain large linear systems arising from astrophysical applications.

^ Termination Criteria for Iterative Methods
P. E. Saylor,* K. Warnick
Center for the Simulation of Advanced Rockets; Center for Computational Electromagnetics; Lawrence Livermore National Laboratory

Following some suggestions from Karl Warnick, a goal of this research was to derive a comparison between termination criteria for the conjugate gradient method derived from Gaussian Quadrative (Dahlquist, Eisenstat, Golub, et al.) and termination criteria based on norm estimates.

^ NASA Grand Challenge Coalescing Neutron Star Binaries
P. Saylor*
National Aeronautics and Space Administration, NCCS 5-153

The objective of this project is the simulation of the collision of binary neutron stars. The code implements general relativity coupled with the equations of fluid mechanics, called hydro, and has been submitted to NASA Earth and Space Sciences.

^ Analysis and Improvement of Jacobi-Davidson Type Methods
E. de Sturler,* E. Martinez (Chem.), R. Martin (Physics), A. Najarian (Comput. Sci.), A. Stathopoulos (College of William and Mary)
National Science Foundation, Focused Research Group Grant, DMR-997655

An important new class of eigenvalue solvers for very large, sparse problems is formed by methods of Jacobi-Davidson type. The Jacobi-Davidson method has been introduced only recently, and although it has proven successful for a variety of problems it still may converge slowly. Indeed, under some circumstances the method may not converge at all. In a recent paper, this research team showed why this happens, and offered a solution that remedies the problem. However, to improve the method in an efficient way and improve the convergence more generally, research is needed to better understand the underlying mathematics. These methods have applications in physics, chemistry, and materials science.

^ Curriculum Development in Computational Materials Science and Nanoscale Science and Engineering
E. de Sturler,* D. Ceperley, D. Johnson, R. Martin, T. Martinez, M. Parks, P. Saylor
National Science Foundation, EEC-0088101

This project encompasses development of course materials (lecture notes, demos, practical assignments, numerical experiments) on Krylov subspace methods for linear systems and eigenvalue problems, nonlinear problems, multigrid methods, and fast multipole methods for summer school (summer 2001) and general curriculum in College of Engineering.

^ Parallel Linear Solvers and Preconditioners for Rocket Simulations and Other Applications
E. de Sturler,* D. Parsons, A. Namazifard; R. Lehoucq (Sandia National Laboratories); E. Chow (Lawrence Livermore National Laboratory)
U.S. Department of Energy, B341494

This project aims at the further analysis and development of very robust and efficient (parallel) linear solvers and preconditioners for very large, sparse problems. Such research is of paramount importance to address the huge systems and sequences of systems that result from the problems addressed in the ASCI project. One important topic is to understand and effectively use the truncation schemes that are used to make optimal iterative methods for non-Hermitian problems tractable. Another important topic is the mathematical study of methods based on the nonsymmetric Lanczos process. These methods are popular because they are cheap per iteration. However, they may behave erratically and their convergence is not guaranteed. One goal of this research is to make these methods much more reliable.

^ Programming Environment for Multi-Application Simulations
E. de Sturler,* M. Bhandarkar, M. Campbell, M. Heath, J. Hoeflinger, J. Jiao, L. Kale, D. Padua, D. Reed, J. Zheng
U.S. Department of Energy, B341494

This project involves the design of a programming environment for the coupling and flexible use of stand-alone applications to jointly simulate the physical and mechanical processes taking place in solid propellant rockets. The simulation of solid propellant rockets requires a variety of complex physical processes to be simulated. In contrast to many other integration or software environment efforts, researchers aim to integrate these applications mainly at the application level itself. Simulation programs will interact through the exchange of boundary data. The applications do not have to share common data structures, common meshes, or even use the same finite element or finite volume approximation scheme.

^ Surface Parameterization for Mesh Generation
E. de Sturler,* A. Sheffer
U.S. Department of Energy (CSAR, de Sturler & Sheffer), B341494; National Science Foundation (CPSD, Sheffer), DMS 98-73945

This project is focused on development of new methods for two-dimensional parameterization of triangulated surfaces and generation of smooth three-dimensional surface meshes. The methods are based on constrained optimization with angles as primary variables. This project also involves research on a variety of meshing issues, nonlinear solvers, optimization, and computational geometry. The methods developed can also be applied to texture mapping (computer graphics) and potentially to other applications.

^ Iterative Methods and Matrix Function Approximation in Material Science Simulations
E. de Sturler;* D. Johnson, A. Smirnov (Mat. Sci. & Engr.); R. Yu (Theoret. & Appl. Mech.)
National Science Foundation, Focused Research Group Grant, DMR-997655

This research is focused on study of a variety of techniques related to iterative methods for linear systems for problems arising in material science. An important topic is formed by cheap methods to compute selected coefficients of the inverses of matrices.

^ Geometric Methods for Numerical Computing: Graph Partitioning, Mesh Generation, and Parallel Computation
S. H. Teng*
National Science Foundation CAREER Award

This proposed research program focuses on the development of geometric methods and their numerical applications. It involves the design of efficient algorithms for fundamental problems and their software implementation. The research has two principal directions. Some effort will focus on determining how to use underlying geometric structures and numerical conditions to generate unstructured meshes and partition them for subsequent parallel numerical simulation. A second direction is to apply mesh partitioning techniques to the solution of sparse-linear systems, to adaptive and hierarchical computations, and to dynamic load balancing for N-body simulations.


Summary of Engineering Research