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UMBC High Performance Computing Facility
Please note that this page is under construction. We are documenting the 240-node cluster maya that will be available after Summer 2014. Currently, the 84-node cluster tara still operates independently, until it becomes part of maya at the end of Summer 2014. Please see the 2013 Resources Pages under the Resources tab for tara information.
Parallel Simulations of the Linear Boltzmann Equation for Models in Microelectronics Manufacturing
Matthias K. Gobbert and Michael Reid, Department of Mathematics and Statistics, UMBC, and Timothy S. Cale, Process Evolution, Ltd. and School of Materials, Arizona State University

Production steps in the manufacturing of microelectronic devices involve gas flow at a wide range of pressures. We develop a kinetic transport and reaction model based on a system of time-dependent linear Boltzmann equations. These kinetic equations have the property that velocity appears as an independent variable, in addition to position and time. A deterministic numerical solution for realistic three-dimensional application problems requires the discretization of the three-dimensional velocity space, the three-dimensional position space, and time.

We design a spectral Galerkin method to discretize the velocity space by specially chosen basis functions. The basis functions in the expansion lead to a system of hyperbolic conservation laws with constant diagonal coefficient matrices for each of the linear Boltzmann equations. These systems of conservation laws are solved using the discontinuous Galerkin finite element method. Stability and convergence of the method are verified analytically and demonstrated numerically. As an application example, we simulate chemical vapor deposition at the feature scale in two and three spatial dimensions and analyze the effect of pressure. Finally, we present parallel performance results which indicate that the implementation of the method possesses excellent scalability on a Beowulf cluster with a high-performance Myrinet interconnect.


  1. Michael J. Reid and Matthias K. Gobbert, Parallel Performance Studies for a Hyperbolic Test Problem, Technical Report number HPCF-2008-3, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2008. (HPCF machines used: hpc and kali.) PDF