Efficient solution of linear systems arising in the linearization of the VTN-phase stability problem using the Sherman-Morrison iterations

We derive a simple procedure for solving systems of linear equations arising from the linearization of the VTN-phase stability problem. Using the structure of the Hessian matrix, the solution is obtained by sequential usage of the Sherman-Morrison formula. The great advantage of the method is that t...

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Bibliographic Details
Published inFluid phase equilibria Vol. 527; p. 112832
Main Authors Smejkal, Tomáš, Mikyška, Jiří
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2021
Subjects
Newton-Raphson method
Optimization
Phase stability testing
Sherman-Morrison iterations
TPD function
VTN specification
Sherman-Morrison iterations
VTN specification
TPD function
Newton-Raphson method
Optimization
Phase stability testing
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Summary:We derive a simple procedure for solving systems of linear equations arising from the linearization of the VTN-phase stability problem. Using the structure of the Hessian matrix, the solution is obtained by sequential usage of the Sherman-Morrison formula. The great advantage of the method is that the system of equation can be solved without even assembling the system. The performance and the speed-up of the computation is demonstrated on several examples of different complexity.
ISSN:0378-3812
1879-0224
DOI:10.1016/j.fluid.2020.112832