A MULTIFRONTAL APPROACH FOR SIMULATING EQUILIBRIUM-STAGE PROCESSES ONSUPERCOMPUTERS

For the simulation of complex equilibrium-stage operations, the overal l computing time is often dominated by the solution of large, sparse s ystems of linear equations. If the modeling equations for such separat ion systems are grouped by equilibrium stage, the linear systems take on an almost banded form with relatively few off-band elements. We pre sent here a simple multifrontal approach for solving such linear syste ms on supercomputers. Like the frontal approach, these solvers exploit supercomputing technology by treating parts of the sparse matrix as f ull, thereby allowing arithmetic operations to be performed with highl y vectorized and optimized BLAS dense matrix kernels. In addition, the se solvers exploit the almost banded structure of the distillation mat rices by using a modified threshold pivot search strategy that attempt s to maintain the desirable structure of the matrix during the solutio n process. Results indicate that this multifrontal approach provides s ubstantial savings in solution time compared to other techniques often used.