Parallel processing of multiple scales problems

摘要

The efficient use of multiprocessor computers requires the introduction of new numerical algorithms. This presentation is concerned with the development of parallel processing algorithms for multiple scales problems associated with large scale scientific computations. We advocate the use of asymptotic analysis of the governing equations of the physical and chemical processes to gain an understanding of the important features of the solution. Then we use this information to guide the development of numerical methods, keeping in mind the need to have many nearly independent processes available for load balancing the processors. Finally in the implementation of the algorithms, we must consider the role of computer languages in maintaining the global concurrencies specified by the analyst and in identifying additional local concurrencies. In effect, we must have a complete approach, with cooperation between mathematicians, numerical analysts, and computer scientists.