Algorithms for structuring design calculations

Ramirez, W. Fred; Vestal, Charles R.

doi:10.1016/0009-2509(72)85102-9

Cited by 14 publications

(15 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Building on the initial work of Rudd and Watson (1968), recent work (Ramirez and Vestal, 1972), has shown how structural information contained in equation sets can be used to develop algorithms for minimizing and simplifying iterative loops. It is the interest of this paper to develop techniques for using this same structural information to aid in the study of convergence properties of iterative loops.…”

Section: Conclusion and Significancementioning

confidence: 99%

“…Application of the iterative variable selection and computational structuring algorithm of Ramirez and Vestal (1972) shows that there is one essential iterative variable. The computational sequence is: with x2 assumed, compute x1 from Equation (7); now with x1 known, compute x3 from Equation (8); and finally a new guess for x2 is obtained from Equation (9).…”

Section: Conclusion and Significancementioning

confidence: 99%

“…This means that there is one degree of freedom, or equivalently, that there is one desi n variable to be chosen. Ramirez and Vestal (1972) kave presented algorithms for the selection of design variables and the determination of a computational sequence for solving the system of equations. Their work is based on the dual objective of decomposing the system in order to minimize the number of iterative variables necessary for solution and to minimize the number of nested iterative calculations.…”

Section: Focpto = V~o ( a H )~-~/~~X C A~mentioning

confidence: 99%

“…Equation 1 With the choice of Fo as the design variable we now use the structuring algorithm of Ramirez and Vestal ( 1972) to determine the computational sequence for the CFSTR whose plant structural matrix is given in Figure 3. Starting at hierarchy level 1, there are no equations with a minimum frequency of one.…”

Section: Focpto = V~o ( a H )~-~/~~X C A~mentioning

confidence: 99%

See 3 more Smart Citations

Convergence properties of systems of algebraic equations—explicit loops

Friedman

Ramirez

1973

AIChE Journal

View full text Add to dashboard Cite

Techniques are developed for using the structural information contained in algebraic equation sets to aid in the study of convergence properties of iterative equation loops.The concept of inverse mapping is applied directly in order to study convergence properties of sequences. For problems in which there exist both a direct and inverse path for the computation of iterative loops, direct substitution techniques will converge via one path and diverge via the other path. When an inverse path existed, the direct substitution method was superior to simultaneous solution techniques for the problems studied. Not all iterative loops have an inverse path. For problems in which inverse paths do not originally exist, rearrangement of the equations of an iterative loop can result in a modified loop for which an inverse path does exist. The digraph representation of an iterative loop aids in deciding whether rearrangements are feasible for a particular problem. When inverse paths cannot conveniently be obtained, direct substitution cannot be successfully used and simultaneous solution techniques such as quasi-linearization are recommended. SCOPEParticularly in the mathematical description of design problems, it is necessary to solve a large set of algebraic equations. Recently much has been Published on how the structural information contained in equation sets can be used to develop algorithms for minimizing and simplifying iterative loops (Ramire2 and Vestal, 1972). However, little has been published on how this structural information influences the convergence properties of systems of algebraic equations. Structural information is important in the study of convergence properties. In this paper we present a direct method for applying the mapping concepts of functional analysis in order to show how structural information relates to, and aids in the study of, solution strategies for algebraic equation sets. The method presented is easy to use and should be of use to practicing engineers.

show abstract

Section: Conclusion and Significancementioning

confidence: 99%

Section: Conclusion and Significancementioning

confidence: 99%

Section: Focpto = V~o ( a H )~-~/~~X C A~mentioning

confidence: 99%

Section: Focpto = V~o ( a H )~-~/~~X C A~mentioning

confidence: 99%

See 2 more Smart Citations

Convergence properties of systems of algebraic equations—explicit loops

Friedman

Ramirez

1973

AIChE Journal

View full text Add to dashboard Cite

show abstract

“…In doing so, they developed the solution path and (unknowingly) selected a set of unknown variables for which the Jacobian was nonsingular. Researchers such as Lee & Rudd [1966], Himmelblau [1967], Christensen & Rudd [1969], Ramirez & Vestal [1972], Friedman & Ramirez [1973], Stadtherr et a1. [1974], Ramirez [1976, 19841, andRamirez [1989] contributed immensely to our understanding of equation management.…”

Section: Introductionmentioning

confidence: 99%

Innovative equation management techniques for implementation in kinematics and dynamics courses

Egelhoff

Blackketter²,

Glumbix³

FIE '98. 28th Annual Frontiers in Education Conference. Moving From 'Teacher-Centered' to 'Learner-Centered' Education. Confere

View full text Add to dashboard Cite

The scope of this paper is the description of techniques and algorithms which engineers use in mathematically modeling physical systems. This work builds on recently developed algorithms that can be used to guide students in solving and understanding the mathematical modeling of physical systems. The techniques have been developed for general use in. a number of applications, especially in a Kinematics and Dynamics course. The techniques allow easy manipulation of equations, and systems of governing equations, in complex situations. The algorithms and techniques generally guarantee, and actually restrict, the student to speciji a design variables set in a manner that solutions are possible. This paper documents that the selection of design variables is d$$cult, anti-intuitive, and in some cases it is humanly impossible to generate all of the possible combinations of constraints.While currently the algorithms are implemented in a computer program, the techniques can also be applied to hand calculations. By way of demonstration, a Kinematics and Dynamics design sofiare program was developed which exemplifies the usefulness, and more importantly, the key benefits o f t h e developed algorithms. The intention is to show that the algorithms are applicable to any set of equations and can be used to enhance students problem solving abilities.

show abstract

Steady state chemical process simulation

1975

View full text Add to dashboard Cite

In recent years process simulation by computer has become an accepted tool in the design and control of chemical processes, but there are still uncertainties and conflicting views about the real benefits relative to cost in both chemical industry and in education. This article surveys the literature of the last three years, exploring the answers to the question: How has chemical process simulation by computer fulfilled expectations in industry and education and what are the major areas of research identifiable at this time? It is concluded that process simulation remains a very dynamic field with a continuous expansion in the areas of application and in the number of users. New subjects requiring research are replacing older areas which have matured.

show abstract

Algorithms for structuring design calculations

Cited by 14 publications

References 7 publications

Convergence properties of systems of algebraic equations—explicit loops

Convergence properties of systems of algebraic equations—explicit loops

Innovative equation management techniques for implementation in kinematics and dynamics courses

Steady state chemical process simulation

Contact Info

Product

Resources

About