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Title: Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations

Abstract

Several global optimization methods are reviewed that attempt to ensure that the integral Gibbs energy of a closed isothermal isobaric system is a global minimum to satisfy the necessary and sufficient conditions for thermodynamic equilibrium. In particular, the integral Gibbs energy function of a multicomponent system containing non-ideal phases may be highly non-linear and non-convex, which makes finding a global minimum a challenge. Consequently, a poor numerical approach may lead one to the false belief of equilibrium. Furthermore, confirming that one reaches a global minimum and that this is achieved with satisfactory computational performance becomes increasingly more challenging in systems containing many chemical elements and a correspondingly large number of species and phases. Several numerical methods that have been used for this specific purpose are reviewed with a benchmark study of three of the more promising methods using five case studies of varying complexity. A modification of the conventional Branch and Bound method is presented that is well suited to a wide array of thermodynamic applications, including complex phases with many constituents and sublattices, and ionic phases that must adhere to charge neutrality constraints. Also, a novel method is presented that efficiently solves the system of linear equations that exploitsmore » the unique structure of the Hessian matrix, which reduces the calculation from a O(N3) operation to a O(N) operation. As a result, this combined approach demonstrates efficiency, reliability and capabilities that are favorable for integration of thermodynamic computations into multi-physics codes with inherent performance considerations.« less

Authors:
 [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1325485
Alternate Identifier(s):
OSTI ID: 1341113
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Computational Materials Science
Additional Journal Information:
Journal Volume: 118; Journal Issue: C; Journal ID: ISSN 0927-0256
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Gibbs energy minimization; necessary and sufficient conditions; global optimization; global minimum

Citation Formats

Piro, M. H. A., and Simunovic, S. Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations. United States: N. p., 2016. Web. doi:10.1016/j.commatsci.2016.02.043.
Piro, M. H. A., & Simunovic, S. Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations. United States. https://doi.org/10.1016/j.commatsci.2016.02.043
Piro, M. H. A., and Simunovic, S. Thu . "Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations". United States. https://doi.org/10.1016/j.commatsci.2016.02.043. https://www.osti.gov/servlets/purl/1325485.
@article{osti_1325485,
title = {Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations},
author = {Piro, M. H. A. and Simunovic, S.},
abstractNote = {Several global optimization methods are reviewed that attempt to ensure that the integral Gibbs energy of a closed isothermal isobaric system is a global minimum to satisfy the necessary and sufficient conditions for thermodynamic equilibrium. In particular, the integral Gibbs energy function of a multicomponent system containing non-ideal phases may be highly non-linear and non-convex, which makes finding a global minimum a challenge. Consequently, a poor numerical approach may lead one to the false belief of equilibrium. Furthermore, confirming that one reaches a global minimum and that this is achieved with satisfactory computational performance becomes increasingly more challenging in systems containing many chemical elements and a correspondingly large number of species and phases. Several numerical methods that have been used for this specific purpose are reviewed with a benchmark study of three of the more promising methods using five case studies of varying complexity. A modification of the conventional Branch and Bound method is presented that is well suited to a wide array of thermodynamic applications, including complex phases with many constituents and sublattices, and ionic phases that must adhere to charge neutrality constraints. Also, a novel method is presented that efficiently solves the system of linear equations that exploits the unique structure of the Hessian matrix, which reduces the calculation from a O(N3) operation to a O(N) operation. As a result, this combined approach demonstrates efficiency, reliability and capabilities that are favorable for integration of thermodynamic computations into multi-physics codes with inherent performance considerations.},
doi = {10.1016/j.commatsci.2016.02.043},
journal = {Computational Materials Science},
number = C,
volume = 118,
place = {United States},
year = {Thu Mar 17 00:00:00 EDT 2016},
month = {Thu Mar 17 00:00:00 EDT 2016}
}

Journal Article:

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