Dynamic Grid Manipulation for PDEs (Partial Differential Equations) on Hypercube Parallel Processors.
Abstract
Adaptive methods for partial differential Equations can be considered as a problem in managing a dynamic graph on a parallel processor. The properties we want for this graph are that edges in the graph, as much as possible, map to nearest neighbor links in the parallel processor, and that changes to the graph not require a major re-arrangement of the mapping of the nodes of the graph onto the processor. We will discuss a simple restricted set of transformations which are easy to implement on a message passing parallel processor, and discuss in detail the design choices made. These transformations are based on maintaining a graph of bounded node degree at the cost of a small amount of global communication. In designing adaptive algorithms of parallel processors, the communication speeds of the processors can have a major effect on the design. Different hypercubes can be characterized by three parameters: the floating point speed, the I/O startup time, and the I/O transfer rate. One aspect of algorithm design which is influenced by interprocessor communication is data structure granularity. We will discuss how this affects the choice of algorithm as a function of the three parameters for our algorithm and relate this to our experiments. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1986
- Accession Number
- ADA168679
Entities
People
- William D. Gropp
Organizations
- Yale University