VECTOR AND PARALLEL STRATEGIES FOR SPARSE MATRIX PROBLEMS IN EQUATION-BASED CHEMICAL PROCESS FLOWSHEETING

Advanced computer architectures provide a new challenge and opportunity in the area of process simulation, design, and optimization (flowsheeting). The use of supercomputing will not only provide the ability to more realistically handle units involving complex phenomena, but also provide truly interactive design capabilities. It is necessary to rethink approaches and algorithms used in the area of process flowsheeting in order to fully utilize the potential of these computers, however. One of the key computational steps in equation-based flowsheeting is the solution of large, sparse sets of linear equations. The goal of this thesis is to develop strategies for effectively using vector processing and multiprocessing architectures in solving the sparse matrices that arise in equation-based flowsheeting.; In order to vectorize sparse matrix codes it is necessary to operate on regularly indexed vectors. This is possible through the use of gather/scatter or by locating parts of the matrix that are dense. The frontal approach can be an effective method for solving flowsheeting matrices on vector computers. The key to effectively applying the frontal approach to flowsheeting matrices is to use a matrix reordering that keeps the size of the frontal matrix small. The reverse-BLOKS reordering is very good at keeping the size of the frontal matrix small.; Parallelism may be exploited in the solution of sparse flowsheeting matrices by decomposing the matrix by ordering into BoDF or BoBDF. Good speedups may be achieved by either method. For small flowsheeting matrices, BoDF performs better than BoBDF. Even when no attempt is made specifically to take advantage of the structure of flowsheeting matrices, BoDF is able to exploit some of that structure. The speedup in BoBDF depends greatly on the number of units in the flowsheet, however, and for large flowsheeting matrices the BoBDF performs very well and outperforms matrix solution using BoDF.