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SELECTE f %EB2 B MUDṼ NSAB Nilional A#,ronatilics and Space Administration Lnn.ley Resnrch Center... more SELECTE f %EB2 B MUDṼ NSAB Nilional A#,ronatilics and Space Administration Lnn.ley Resnrch Center I Iylfvon. Virqfnis 23665-5225 m % TMU1'ON TA 'T .-

Math Comput, 1994

Domain decomposition methods are iterative methods for the solution of linear or nonlinear system... more Domain decomposition methods are iterative methods for the solution of linear or nonlinear systems that use explicit information about the geometry, discretization, and/or partial di erential equation (PDE) that gave rise to the (non)linear system. A large amount of research in domain decomposition methods for partial di erential equations has been carried out in the past dozen years. Recently, these techniques have begun to be applied to \real-world" engineering problems. This summary introduces the basic ideas in domain decomposition methods for PDEs. Though no particular applications are discussed, references to several recent uses of domain decomposition are given.

Monthly Weather Review, Aug 1, 2002

A computationally efficient mass-conservative transport scheme over the sphere is proposed and te... more A computationally efficient mass-conservative transport scheme over the sphere is proposed and tested. The scheme combines a conservative finite-volume method with an efficient semi-Lagrangian scheme based on the dimension splitting ''cascade'' method. In the regions near the poles where the conservative cascade procedure breaks down, a globally conservative, but locally approximate scheme is used. This procedure is currently restricted to polar meridional Courant numbers less than one. The resulting conservative cascade scheme is evaluated using a solid-body rotation test and deformational flow test, and found to be both accurate and efficient. Compared to the traditional semi-Lagrangian scheme employing a bicubic-Lagrange interpolator, the proposed scheme is considerably more accurate and almost twice as fast while conserving mass exactly.

INTRODUCTIONThe use of computer simulations as an optimal design tool which lessens the costs in ... more INTRODUCTIONThe use of computer simulations as an optimal design tool which lessens the costs in timeand effort in experimental and physical testing has become prevalent in aerospace design(e.g., the design of the Boeing 777) and development of automotive mass productionitems. It is also commonly found in the design of production and assembly lines whererepetitive motion related to parts assembly is

Acta Crystallographica Section A Foundations of Crystallography

Lecture Notes in Pure and Applied Mathematics, 1991

This was the fourteenth such workshop to be held at NCSU, and brought together 36 graduate studen... more This was the fourteenth such workshop to be held at NCSU, and brought together 36 graduate students from 24 universities.

Grant DMS-0635449 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, f... more Grant DMS-0635449 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s)

We consider optimizations that are required for efficient execution of code segments that consist... more We consider optimizations that are required for efficient execution of code segments that consists of loops over distributed data structures. The PARTI (Parallel Automated Runtime Toolkit at ICASE) execution time primitives are designed to carry out these optimizations and can be used to implement a wide range of scientific algorithms on distributed memory machines. These primitives allow the user to

Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposit... more Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups.

[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992

ABSTRACT The flow dynamics of a homogeneous gas inside a vertical, cylindrical reactor are modele... more ABSTRACT The flow dynamics of a homogeneous gas inside a vertical, cylindrical reactor are modeled with a commercially available computational fluid dynamics code. The transport process in chemical vapor deposition are described using conservation of mass, momentum, energy, and mass transfer equations. Navier-Stokes equations for a Newtonian fluid and laminar flow are used to describe the momentum conservation. The buoyancy effect is included in the model through the gravitational term in the momentum equation. The thermal (Soret) effect is included in the model to account for binary diffusion in the presence of large temperature gradients typical of chemical vapor deposition (CVD) process. Results of a 2-D, steady, axisymmetrical flow are presented using a finite element method with non-uniform Cartesian meshes. The formulation of the optimal reactor design problem for CVD is discussed

The fluid dynamics in a vertical reactor for high pressure vapor transport (HPVT) of compound sem... more The fluid dynamics in a vertical reactor for high pressure vapor transport (HPVT) of compound semiconductors is modeled. The modeling is for the growth of IIIV -V 2 chalcopyrite ZnGeP 2 and addresses the flow of dense phosphorus gas at 3:42 Theta 10 5 Pascals pressure. Effects of density variations on p-polarized reflectance spectroscopy are also examined. The mathematical model for transport processes is described by the full gasdynamic equations (Navier Stokes equations coupled with an equation for energy). In addition, buoyancy effects are included in the model through the gravitational term in the momentum equation. Numerical results of a 3-D steady flow are presented using a finite element discretization with non-uniform, quadrilateral elements. The numerical simulations were performed to study the effects of gravitational-induced buoyancy-driven convection flows in HPVT crystal growth. Introduction Non-linear optical interactions in birefringent materials find applications in ...

Optimal Design and Control, 1995

The optimal boundary temperature control of the stationary thermally coupled incompressible Navie... more The optimal boundary temperature control of the stationary thermally coupled incompressible Navier- Stokes equation is considered. Well-posedness and existence of the optimal control and a necessary optimality condition are obtained. Optimization algorithms based on the augmented Lagrangian method with second order update are discussed. A test example motivated by control of transport process in the high pressure vapor transport (HPVT) reactor is presented to demonstrate the applicability of our theoretical results and proposed algorithm.

Math Comput, 1994

Monthly Weather Review, Aug 1, 2002

Acta Crystallographica Section A Foundations of Crystallography

Lecture Notes in Pure and Applied Mathematics, 1991

[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992

Optimal Design and Control, 1995