| Abstract: | Composite grid problems arise in important application areas, e.g. reactor simulation. Related physical phenomena are inherently parallel and their simulations are computationally intensive. Unfortunately, parallel languages, such as High Performance Fortran, provide little support for these problems. We illustrate topological connections via a coupling statement, develop a programming style and transformation system to support composite grid code development, and develop an algorithm that automatically determines distributions for composite grid problems with small meshes. A mesh is classified as small if the amount of computational work associated with the mesh is less than the amount of work to be assigned to a single processor. Precompiler transformations, such as cloning for alignment specification, are described. Excerpts from a High Performance Fortran program before and after transformation illustrate user programming style and transformation issues. Our distribution algorithm's alignment and distribution specifications are input to the transformed High Performance Fortran programs which applies the mapping for execution of the simulation code. Some advantages of this approach are: transformations are applied before compilation and allow communication optimization; data distribution may be determined for any number of problems without recompilation; user determined distribution for parallelization is unnecessary; portability is improved. We validate the topology-based data distribution algorithm using a number of reactor configurations. Two random distribution algorithms provide a basis of comparison with measures of load balance and communication cost. Experiments show that the topology-based distribution algorithm almost always obtains load balance at least as good as, and often significantly better than, random algorithms while reducing the total communication per iteration from 50% to as much as a factor of ten. |
