Reliability of iterative linear equation solvers in chemical process simulation
Abstract For large-scale problems, it may be attractive to use iterative methods to solve the large, sparse, linear systems that arise in the equation-based approach to process simulation. This is because, as problem sizes grow, direct methods become extremely expensive in terms of both computation time and storage requirements. Iterative methods, however, may not be reliable for the indefinite and highly unsymmetric matrices encountered in a diverse multi-unit flowsheeting problem. An extensive computational study of the reliability of iterative linear solvers on such problems is presented here. Nine different iterative linear solvers are considered, in connection with incomplete factorization preconditioning. These are applied to a set of nine test problems. Results indicate that the ordering of rows and columns in the matrices is a crucial factor in determining the success with which iterative methods can be employed. Results also indicate that in general these multi-unit flowsheeting matrices are difficult to solve by iterative methods, and that, though there is certainly potential in the use of iterative methods, to realize this potential will require improvements in the reordering and/or preconditioning schemes used.
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