A Multifrontal Approach for Simulating Equilibrium-Stage Processes on Supercomputers

Abstract

For the simulation of complex equilibrium-stage operations, the overall computing time is often dominated by the solution of large, sparse systems of linear equations. If the modeling equations for such separation systems are grouped by equilibrium stage, the linear systems take on an almost banded form with relatively few off-band elements. We present here a simple multifrontal approach for solving such linear systems on supercomputers. Like the frontal approach, these solvers exploit supercomputing technology by treating parts of the sparse matrix as full, thereby allowing arithmetic operations to be performed with highly vectorized and optimized BLAS dense matrix kernels. In addition, these solvers exploit the almost banded structure of the distillation matrices by using a modified threshold pivot search strategy that attempts to maintain the desirable structure of the matrix during the solution process. Results indicate that this multifrontal approach provides substantial savings in solution time compared to other techniques often used.