A robust path tracking algorithm for homotopy continuation

Choi, Soo Hyoung; Harney, David Anthony; Book, Neil L.

doi:10.1016/0098-1354(95)00199-9

Cited by 32 publications

(21 citation statements)

References 7 publications

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“…The subscripts 0 at T k + 1 and P k + 1 in formulas (14) mean that these values lie not on the binodal line but in its close vicinity, and at each ((k + 1)th) predictor step, they serve as initial approximations for Newton's method.…”

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

“…In iterations at a predictor step (k > 0), the sign of the parameter σ k is also controlled [13,14].…”

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

“…The problem is solved by the two-step predictorcorrector algorithm using an Euler predictor step followed by Newton correction steps [13,14]. The homotopy function is taken to be (13) Here, is the solution of problem (10) of "deformed" equilibrium, when ≠ 1.…”

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

“…Steps of such an algorithm in predictor iterations are performed according to the scheme (14) where and define the point in the binodal line that is found in the kth iteration and ប k is the parameter that controls the admissible step length. The derivatives dT/ds and dP/ds are determined by solving the set of equations…”

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

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Calculation of binodal lines for a multicomponent mixture by the homotopy method

Yermakova¹,

Sazhina

Anikeev³

2005

Theor Found Chem Eng

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Equations are proposed for binodal lines of a multicomponent mixture in the T -P and P -V planes. A numerical method for solving the equations of the thermodynamics model is described, which is based on the homotopy method and uses the physical parameters of the system, in particular, temperature and pressure, as parameters of continuation of solution. Calculation results illustrating the features of the phase states of binary and multicomponent mixtures are presented.

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Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

“…In iterations at a predictor step (k > 0), the sign of the parameter σ k is also controlled [13,14].…”

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

Section: Construction Of Trajectories Of Solutionsmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of binodal lines for a multicomponent mixture by the homotopy method

Yermakova¹,

Sazhina

Anikeev³

2005

Theor Found Chem Eng

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“…Furthermore, an engineeringfriendly point of view can be found in numerous articles (e.g. Choi et al, 1996;Kuno and Seader, 1988;Seader et al, 1990;Seider et al, 1991;Seydel and Hlavacek, 1987;Wayburn and Seader, 1987).…”

Section: Introductionmentioning

confidence: 99%

Modified bounded homotopies to enable a narrow bounding zone

Malinen

Tanskanen

2008

Chemical Engineering Science

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Pinch‐based shortcut method for the conceptual design of adiabatic absorption columns

Redepenning

Marquardt

2016

AIChE Journal

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Shortcut methods are valuable tools for the fast evaluation of key performance indicators in the early phase of conceptual process design. For the design of absorption columns, operation at minimum solvent demand represents a thermodynamically sound indicator, which is, however, difficult to determine because an infinite number of separation stages need to be considered. Instead, the suggested shortcut model exploits the existence of the pinch point to identify operation at minimum solvent demand. Existing shortcut concepts, such as the well‐known equation of Kremser (Natl Pet News, 22, 43–49, 1930), are significantly outperformed by the novel shortcut model, which can be gradually refined to any desired accuracy. Integration into a stepwise procedure results in reliable solutions. The model covers rigorous thermodynamics; no simplifications regarding phase equilibrium, heat effects, or number of components are required. The performance of the method is illustrated by several case studies with up to seven components. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1213–1225, 2017

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A robust path tracking algorithm for homotopy continuation

Cited by 32 publications

References 7 publications

Calculation of binodal lines for a multicomponent mixture by the homotopy method

Calculation of binodal lines for a multicomponent mixture by the homotopy method

Modified bounded homotopies to enable a narrow bounding zone

Pinch‐based shortcut method for the conceptual design of adiabatic absorption columns

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