Structural analysis and solution of systems of algebraic design equations
Article first published online: 17 JUN 2004
Copyright © 1984 American Institute of Chemical Engineers
Volume 30, Issue 4, pages 609–622, July 1984
How to Cite
Book, N. L. and Ramirez, W. F. (1984), Structural analysis and solution of systems of algebraic design equations. AIChE J., 30: 609–622. doi: 10.1002/aic.690300412
- Issue published online: 17 JUN 2004
- Article first published online: 17 JUN 2004
- Manuscript Accepted: 23 JUN 1983
- Manuscript Revised: 6 JUN 1983
- Manuscript Received: 3 JAN 1983
A new method for expressing the structure of a system of equations is developed using a type of occurrence matrix entitled the functionality matrix. The functionality matrix indicates not only the occurrence of variables in equations but also the functional form in which they occur. Since the difficulty of solving an equation for a variable is related to its functional form, analysis of the functionality matrix provides explicit information on the difficulty of solution of the solution of the equation.
A methodology for the solution of design problems by digital computers is described. This methodology operates on the functionality matrix which describes the set of design equations. Algorithms using this methodology interact and guide the designer in an efficient selection of design variables and redundant equations. Once design variables and redundant equations are selected, a computational method is presented for ordering and solving the equations.