Browsing by Author "Lowekamp, Bruce B."
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- The Cellular Automata Paradigm for the Parallel Solution of HeatTransfer ProblemsLowekamp, Bruce B.; Watson, Layne T.; Cramer, Mark S. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1994-04-01)This paper describes the numerical solution of heat transfer problems using cellular automata. While traditional methods offer high performance on uniprocessor machines, their performance is limited on distributed memory multiprocessors by communication bottlenecks caused by the interdependence of the equations. Using a cellular automata formulation, these bottlenecks can be avoided, and performance greater than that obtained by parallelizing traditional algorithms can be achieved. This paper gives an overview of the cellular automata paradigm and specific examples of solutions to a hyperbolic and a parabolic problem. The accuracy of the method is verified by comparisons of the results with analytical solutions and with results produced by other techniques.
- Nonlinear Thermal Waves: Part II - Analytical Solutions for PulsesCramer, Mark S.; Lowekamp, Bruce B.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1994-12-01)The weak shock theory developed by Cramer (1994) is used to derive explicit solutions for the evolution of one-dimensional weakly, nonlinear, weakly relaxing heat pulses in rigid conductors. Formulas and differential equations governing the evolution of general heat inputs are derived and applied to the special cases of a square-wave heat input and a finite width sine-wave heat input. Numerical solutions to the exact Maxwell-Cattaneo theory are also presented and show excellent agreement with these analytical solutions.