Coordination of distributed/parallel multiple-grid domain decomposition

A workable approach for the solution of many (numerical and non-numerical) problems is domain decomposition. If a problem can be divided into a number of sub-problems that can be solved in a distributed/parallel fashion, the overall performance can significantly improve. In this paper, we discuss one of our experiments using the new coordination language M<font size=-1>ANIFOLD</font> to solve an instance of the classical optimization problem by domain decomposition. We demonstrate the applicability of M<font size=-1>ANIFOLD</font> in expressing the solutions to domain decomposition problems in a generic way and its utility in producing executable code that can carry out such solutions in both distributed and parallel environments. The multiple-grid domain decomposition method used in this paper is based on adaptive partitioning of the domain and results in highly irregular grids as shown in the examples. The implementation of the distributed/parallel approach presented in this paper looks very promising and its coordinator modules are generally applicable.