A Program on Solidification and Fast Algorithms

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Solidification processes are ubiquitous in modern technology. They are important whenever a substance changes from a liquid or gas to a solid, for example when ice melts or freezes, when silicon or gallium arsenide crystals are grown for use in semiconductor devices or silver halide crystals grown for film production, when Alaskan soil freezing patterns are altered by an oil pipeline, or when zinc dendrites pierce the walls of a lead- zinc battery. Computer simulation of solidification processes, the subject of this activity, serves two purposes. When the fundamental physics is under investigation, the theoretical predictions of any proposed model must be produced and compared with other models and with experiment. Solidification is sufficiently complex that this must be done by careful numerical simulation; exact solutions almost never exist. Once the fundamental physics is well understood, numerical calculations can produce data inaccessible to experiment and in some situations can even substitute for experiment. Considerable savings in time and money can be realized if numerical simulation can be substituted for experiments. The goal of the research is to develop technology to solve solidification problems which are presently beyond the reach of numerical simulation. To achieve this goal, the investigators will combine the best numerical methods available and extend them to solve more complex problems.