Algorithms and Parallel Computing

11.9 PROJECTION OPERATION USING THE LINEAR PROJECTION OPERATOR

In Section 11.8, we discussed how we can associate a time step value to each point in the computation domain . In this section, we discuss how we can assign a task to each point in the computation domain . This task could later be assigned to a thread for the case of multithreaded software implementation, or the task could be assigned to a PE for the case of hardware systolic implementation. It is a waste of resources (number of processors or number of threads) to associate a unique processor or thread to each point in the computation domain . The main reason is that each point is active only for one time instant and is idle the rest of the time. The basic idea then is to allocate one processor or thread to several points of . There are basically three ways of doing this:

1. Use linear projection operator matrix P to reduce the dimensions of to produce a new computation domain whose dimensions k < n. Matrix P has dimensions ...