ABSTRACT
Because many applications are very complicated such as weather prediction, there will often be a large number of unknowns. For heat diffusion in one direction the long thin wire was broken into n smaller cells and the temperature was approximated for all the time steps in each segment. Typical values for n could range from 50 to 100. If one needs to model temperature in a tropical storm, then there will be diffusion in three directions. So, if there are n = 100 segments in each direction, then there will be n3 = 1003 = 106 cells each with unknown temperatures, velocity components and pressures. Three dimensional problems present strong challenges in memory, computational units and storage of data. The first three sections are a very brief description of serial, vector and multiprocessing computer architectures. The last three sections illustrate the use of the IBM/SP and MPI for the parallel computation of matrix products and the two and three space variable models of heat diffusion and pollutant transfer. Chapter 7 contains a more detailed description of MPI and the essential subroutines for communication among the processors. Additional introductory materials on parallel computations can be found in P. S. Pacheco [21] and more advanced topics in Dongarra, Duff, Sorensen and van der Vorst [6].
