Two Numerical Problems in Chemical Dynamics Simulation

Abstract

In this talk we describe two problems in chemical simulation. The first involved the calculation of Potential Energy Surfaces -- a high-dimensional data-fitting problem which is central to large-scale calculations of chemical reaction paths. We are exploring the use of Interpolating Moving Least-Squares (IMLS) methods of high-dimension and present some of the applications and results thus far. The second problem involves the calculation of reaction-rate coefficients in an ab initio manner. Reaction rate coefficients can be obtained from exact quantum cumulative reaction probabilities (CRP) by eigenvalue calculations. We are using parallel software libraries to parallelize large-scale CRP calculations. These calculations involve Lanczos methods to obtain the eigenvalues of the probability operator. The evaluation of two linear solves of Greens functions are required at each iteration. These, in turn, are solved iteratively via GMRES. Thus the matrix-vector multiply is a key computational kernel. Results for the underlying matrix-vector operations via tensor matrices are discussed in single-processor experiments up to ten dimensions.