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Advanced Software for the Calculation of Thermochemistry, Kinetics, and Dynamics and Theoretical Chemical Dynamics Studies for Elementary Combustion Reactions

PI:
Albert Wagner (Argonne National Laboratory [ANL])
Donald Thompson (Oklahoma State University [OSU])
Co-PIs:
Stephen Gray, Ron Shepard, and Michael Minkoff (ANL)
ISIC co-PIs: CCTTSS:
Lois McInnes [ANL]
Dave Bernholdt [Oak Ridge National Laboratory])
TOPS:
Michael Minkoff [ANL] and Barry Smith [ANL]

Summary

Our project has evolved into the development of software for kinetics and dynamics that can properly scale to teraflop computing. Because kinetics and dynamics act as a bridge between computationally intensive electronic structure calculations and similarly intensive computational fluid dynamics (CFD) calculations, not surprisingly the infrastructure software being developed by our efforts has broad utility and has benefited from Integrated Software Infrastructure Centers (ISIC) support. The two projects (as listed above) have become one integrated effort that shares resources. Below, we describe the kinetics/dynamics efforts and then the infrastructure efforts pursued by our integrated project.

Kinetics/Dynamics

The calculation of reaction rate constants is fundamental to the accurate simulation of chemical phenomena from combustion to smog. Rate constants are typically calculated approximately by a variety of methods. Exact calculations via quantum dynamics are computationally very intensive, with the consequence that approximate theories are not fully calibrated. The most direct way to calculate exact rate constants is the Cumulative Reaction Probability (CRP) approach. Formalisms for both time-independent and time-dependent CRP calculations exist, with different numerics and different implications for the calibration of approximate methods. We are pursuing both CRP approaches.

Time Independent CRP: A time independent CRP calculation can be formulated as an iterative solution to the eigenvalues of the reaction probability operator. Each iteration requires the resolution of two separate Green’s functions via the iterative solution of associated linear equations. A parallelized CRP code has been developed on top of the PETSc library (in collaboration with the TOPS ISIC). The GMRES method iteratively resolves the Green’s functions while the Lanczos method iteratively resolves the eigenvalues. The code is being tested on a model problem that has the property of being expandable to any number of reacting atoms (with associated internal degrees of freedom [DOF]) but has an analytic CRP solution. With this model, the code is scalable over a hundred or more processors with time to solutions at NERSC measured at about ten minutes per eigenvalue for a 7 DOF problem. Current versions of the code use only diagonal preconditioning for resolving the Green’s functions. Future work will examine more global preconditioners including the Subspace Projected Approximated Matrix approach (see below) and optimal block orthogonal preconditioning (in collaboration with W. Poirier under DOE/MICS support).

Time Dependent CRP: A parallel, four-atom, 6 DOF, time-dependent CRP code has been developed. We parallelized over several DOF using the message passing interface OpenMP which allows both shared memory for all the processors within a node but message passing between processors on different nodes. Runs involving up to 256 processors (16 processors per 16 nodes) have been performed and code tuning is in progress. The OpenMP strategy of intra-node shared memory parallelization and inter-node message passing parallelization maps well onto CRP problems with more atoms and more DOF. After code tuning and tests on selected applications, the scalability of the code with processor/node combinations and with higher DOF will be explored.

Infrastructure:

All kinetics/dynamics studies compute the response of molecules to intermolecular forces that can be represented by a potential energy surface (PES). A PES is a function of every internal DOF. In its simple 2D form, a PES looks like a mountainous landscape. The path that connects two valleys by passing over the lowest point in an intervening mountain chain describes on the PES the most favorable reaction route that converts stable reactant molecules into stable product molecules. The kinetics/dynamics codes compute how molecules move over the PES landscape while electronic structure calculations provide the "altitude" of each point on the landscape. The terascale application of electronic structure calculations is the subject of most of the SciDAC projects funded by Basic Energy Sciences. We are developing convenient ways to produce and use PESs that reduce the number of electronic structure calculations needed for accurate kinetics/dynamics. In addition, we are developing preconditioner approaches for the numerics of kinetics/dynamics applications but with implications for electronic structure applications. These efforts are described below.

Interpolative Moving Least Squares (IMLS) PES fitting methods: The minimization of ab initio electronic structure calculations needed to characterize a high dimensional PES is an interpolation/extrapolation problem. In an ANL/OSU collaboration, we are exploring higher order IMLS solutions to this problem. IMLS methods use weighted polynomial least squares fits to the ab initio points that are unusually weighted by functions that depend on where the PES fit is desired. While position-dependent weights mean that the least squares fit must be done from scratch at each location a PES fit is needed, such weights greatly improve fit accuracy by adding non-linear flexibility to the polynomial fit. The IMLS approach can be compactly programmed for any number of DOF and for any polynomial degree. The weights have a structure that allows only "nearest neighbor" ab initio points to significantly influence the fit. Consequently software strategies can be used to make the fit evaluation a local, rather than global, process. Initial results on few dimensional applications indicate that the number of ab initio points required is better than inversely proportional to the degree of the IMLS polynomial. Scaling studies are in progress. IMLS technology could be useful in other applications, such as response surfaces used in incorporating kinetics into CFD calculations.

POTLIB 2001: POTLIB 2001 is a program library of PESs with a common, published user interface for every library entry. To further improve the convenience and access of the library, we are collaborating with the POTLIB librarian (R. Duchovic [Indiana University Purdue University at Fort Wayne]) and the CCTTSS ISIC to make POTLIB and a suite of application codes common component architecture (CCA) compliant. The CCA model supports language interoperability (e.g., FORTRAN or C++) and algorithmic complexity in sequential, massively parallel, and distributed computing environments. A CCA system of POTLIB/application codes would allow seamless use of any POTLIB PES with any system application code in a language or environment independent way. To date, we have rendered one PES entry in POTLIB CCA compliant, have done timings to confirm that the CCA overhead is negligible, and are now converting the entire POTLIB library.

Subspace Projected Approximate Matrix (SPAM) method: The SPAM method is a multigrid-like preconditioner for large-scale iterative eigensolvers where matrix-vector products dominate the solution. Projection operators allow the use of a sequence of approximating user-specified preconditioners incorporating any kind of mathematical or physical insight into the specific application the user has. The sequence acts to accelerate the iterative convergence of the exact problem. Fortran95 "black box" code for symmetric, Hermitian, or real generalized symmetric eigenvalue problems have been developed. Parallel extensions are being developed based on distributed-memory message passing (e.g. MPI), on the global array library, and on the PETSc environment. This work is in conjunction with the TOPS ISIC. SPAM applications to problems in polyatomic vibrational spectroscopy, CRP kinetics studies (see above), and electronic structure methods (e.g., COLUMBUS Program System) are in progress.

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