(575a) A Parallel System for Describing and Analyzing Complex Chemical Kinetics

Goyal, A., Purdue University
Cao, J., Purdue University
Midkiff, S. P., Purdue University

The quantitative models of the kinetics is important for a number of significant chemical processes such as vulcanization, oil refining, combustion and atmospheric chemistry, etc., where a large number of individual species can participate in a combinatorially large number of reactions. The description of these systems can require 100s to 1000s of ODEs that can have up to 1,000,000 terms, where 10 to 20 model parameters must be determined optimization of the model with a set of experimental data. Traditional methods of formulation and solution of problems of this complexity are not feasible. To address these problems, we have developed a cyber-system that exploits high performance parallel computing to expedite model generation and evaluation. The first component of the system is a Chemical Compiler that allows the researcher to specify chemical reactions in a near English language and generates the complex set of reactions. The second component of the system is the Rate Constant Information Processor that allows incorporation of equivalence rules for the rate constants obtained from insights from quantum chemistry simulations. The resulting reactions and model parameters are then parsed to Equation Generator which efficiently generates 100's of ODEs. Since the resulting ODEs are quite computationally demanding, efficient generation of these ODE's is required. An Equation Optimizer was developed that uses algebraic laws (associativity and distributivity) and common sub-expression elimination. Finally, the kinetic constants must be determined via optimization by comparing the predictions of the kinetic model versus a set of experimental data, which requires the solution of the ODEs many times. A Parallel Optimization Module has been developed, including dynamic load balancing, where 90% efficiency in speedup has been obtained. The Optimization Module has three level of parallelization: (i) the ODE solution for each member of the experimental data sets is parallelized; (ii) The computational intensive operation in optimization is calculation of the Jacobian matrix that requires solution of m+1 ODEs for m model parameters, which can be parallelized; and, (iii) the ODE solver can also be parallelized if additional speed is required. Using these tools for a vulcanization kinetic problem with 350 species with over 600,000 terms and 10 kinetic constants, we are able to formulate a new kinetic model in about an hour and determine the optimized parameter set in an additional 6 to 8 hours. This problem showcases how the various features of Teragrid can be used to bring power of high performance computing in solving complex kinetic problems that have not been addressed to-date.