Applied Computational Mathematics Division


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A New Algorithm for the Automation of Phase Diagram Calculation

Maria Emelianenko
Pennsylvania State University, Department of Mathematics

Tuesday, March 22, 2005 11:00-12:00,
NIST North (820), Room 145
Gaithersburg
Tuesday, March 22, 2005 09:00-10:00,
Room 4511
Boulder

Abstract: Many existing thermodynamical software packages for phase diagram calculations (e.g. Thermocalc) lack the ability to automatically determine system properties from initial data and can produce metastable equilibria instead of stable ones or simply diverge if the initial guess is not good enough. The a priori knowledge of system properties and locations of the miscibility gaps are required from the user in order for the system to produce feasible results. Several algorithms were proposed to automate the process of finding suitable starting positions, all of which carry an increased computational cost. In this talk we discuss an attempt to improve on the existing strategies for automating phase diagram calculations by introducing a novel reduced complexity algorithm based on the adaptive critical point detection approach. The main advantage of the new scheme lies in its ability to effectively reduce the total number of trial calculations by recognizing the importance of geometry-specific properties of the Gibbs energies. The new algorithm possesses advantages over existing methods in terms of the convergence speed, the computational complexity, and the robustness. Numerical results for binary and ternary systems as well as possible higher dimensional solutions including better sampling techniques are discussed.

Speaker Bio: Maria Emelianenko is expected to receive her PhD in Mathematics from Pennsylvania State University this summer and will continue as a Postdoctoral Researcher at the Center for Nonlinear Analysis of Carnegie Mellon University. She received an MA in Mathematics from Pennsylvania State University in 2003 and an MS and BS in Applied Mathematics and Computer Science from Moscow State University (2001 and 1999, respectively). Maria's research is focused on the analysis and development of efficient numerical algorithms. She is a part of the MatCASE project at PSU which is funded by a major NSF-ITR grant to develop computational tools for multicomponent materials design. Recently, she has worked on the design of fast new algorithms for quantization and clustering with the use of concepts like Centroidal Voronoi tessellations and optimization methods for the determination of phase diagrams for multicomponent materials. Her earlier research activities include the analysis of multidimensional birth-death processes and development of efficient pricing schemes in next-generation telecommunication networks, solution of ill-conditioned systems of linear equations, and mathematical models in biology.

Presentation Slides: PDF

Contact: P. M. Ketcham

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