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

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(N 3) 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
 [1] ;  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Computational Materials Science
Additional Journal Information:
Journal Volume: 118; Journal Issue: C; Journal ID: ISSN 0927-0256
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Nuclear Energy (NE)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Gibbs energy minimization; necessary and sufficient conditions; global optimization; global minimum
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1341113