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.
Ind. Eng. Chem. Res., 36, 144-151 (1997)