A parallelization of an equation-based algorithm for multicomponent separation calculations

Multicomponent separation calculations, whether for single columns or for complexly interlinked systems of multiple columns, represent large scale computational problems and are thus attractive applications for the parallel computing architectures of modern supercomputers. Frequently, these problems are formulated as a large set of nonlinear equations solved by a Newton-Raphson or comparable successive linearization technique. They thus require the solution of a very large system of sparse linear equations, which often represents a large fraction of the overall computing time. An efficient parallel technique for the solution of such large sparse systems, based on an ordering of equations by plate, is presented. The resulting linear systems take on an almost block tridiagonal (BTD) form, with off-BTD blocks arising from recycle streams or tower sidestreams. Extensions to a current multiprocessor scheme for BTD systems, the Sameh method, are also given.A close examination of the regular structure of the linear system reveals the possibility of a further improvement in the methd: a pretreatment of the matrix to reduce both the cost of system reduction and the overhead inherent in the parallel technique. The separate approaches result in three competing methods, which are compared on a parallel machine for a variety of problems. The results of this system of tests leads to an "advanced" method which incorporates the best features of the successful algorithms.U of I OnlyETDs are only available to UIUC Users without author permissio