A domain decomposition strategy and parallel gradient-type iterative solution scheme have been developed and implemented for computation of complex 3D viscous flow problems involving heat transfer and surface tension effects. Special attention has been paid to the kernels for the computationally intensive matrix-vector products and dot products, to memory management, and to overlapping communication and computation. Details of these implementation issues are described together with associated performance and scalability studies. Representative Rayleigh- Bénard and microgravity Marangoni flow calculations on the Cray T3D are presented, and performance results verifying a sustained rate in excess of 16 gigaflops on 512 nodes of the T3D have been obtained. The work is currently being extended to the T3E and we have begun carrying out further performance benchmarks and scalability studies on this platform. Preliminary performance studies have recently been carried out and sustained rates above 50 gigaflops and 100 gigaflops have been achieved on the 512 node T3E-600 and 1024 node T3E-900 configurations respectively.

An efficient numerical solution scheme based on a new mapped finite difference discretization and iterative strategies is developed for submicron semiconductor devices. As a representative model we consider a nonparabolic hydrodynamic system. The discretization is formulated in a mapped reference domain, and incorporates a transformed Scharfetter-Gummel treatment for the current density and energy flux. This permits the use of graded, nonuniform curvilinear grids in the physical domain of interest, which has advantages when gridding irregular domain shapes or grading meshes for steep solution profiles. The solution of the discrete system is carried out in a fully coupled, implicit form, and nonsymmetric gradient-type iterative strategies are investigated. Numerical results demonstrating the performance and reliability of the scheme are presented for test problems.

A new Taylor-Galerkin finite element method and adaptive, time-iterative scheme are developed for simulating single-carrier submicron-scale semiconductor device transport with the hydrodynamic model under the assumptions of parabolic energy bands. Boundary conditions are applied using characteristic projections. Numerical studies are conducted to investigate the sensitivity of the given model to some of the parameters contained in typical heat flux and relaxation time models for a one-dimensional, representative test problem.

We present a parallel finite element solver for mesh-connected multicomputers (ie., message-passing, distributed-memory multiprocessors) and provide a theoretical proof tht the algorithms used are highly scalable and close to optimal. Further, the algorithms are written in an object-oriented language (ESP C++) to enhance reusability of code. Performance results are presented for a Motorola multicomputer and a network of Sun workstations.

A three-dimensional process simulator in which both the standard nonlinear diffusion model and a five-species kinetic model are implemented to model phosphorus diffusion in silicon is described. The reaction-diffusion equations are discretized using finite differences in space and the numerical method of lines. The resulting ordinary differential equations are solved using the system integrator LSODP. LSODP uses a backward difference formula for time integration and a Krylov projection method to solve the linear system in the inner Newton loop. Comparisons of the two diffusion models are run on several test problems. Results show that the Krylov approach works well for the mildly asymmetric system of the single species, but requires a large dimension (K/sub m/ approximately=20) subspace for the five-species model.>

An adaptive mesh refinement scheme and dynamic data structure were developed in conjunction with a flux-upwind Petrov-Galerkin finite-element formulation for analysis of semiconductor device equations. The electrostatic potential equation and carrier-current continuity equations are iteratively decoupled in the solution algorithm. Incremental continuation in applied bias is used to improve the nonlinear solution iteration and to produce an efficient and robust scheme. The adaptive refinement scheme also uses an element-by-element conjugate gradient solution algorithm that performs efficiently on parallel and vector processors. Sample numerical results for MOS and bipolar devices indicate the effectiveness of the flux or streamline upwind Petrov-Galerkin (FUPG) method and demonstrate its superiority over traditional Scharfetter-Gummel (SG) approaches.>