Summary of Research (1994-2007)

My interest in this area started at the “Center for Global and Regional Environmental Research” (CGRER) of the University of Iowa with which I continue to keep close ties. There I worked in an interdisciplinary team together with Gregory Carmichael from the Chemical Engineering Department and several Ph.D. students in chemical engineering, computer science, and applied mathematics. The goal of this group was to develop a “Third Generation Model” for atmospheric chemistry. The requirements for such a model had been formulated by a panel of scientists (including Gregory Carmichael and myself) assembled by EPA [48]. It involves setting up a parabolic system consisting of about 300 nonlinear PDEs and finding efficient numerical methods for solving it. This is a 3-D reactive transport problem with about 100 chemical species and 200 chemical reactions. Since transport and chemical reactions operate at different time scales, an operator split technique is applied with different integration methods for transport and chemistry. In fact chemistry is solved by integrating at each point of the space grid a (very stiff) initial value ODE problem for a period of time equal to the time step of the transport integrator. Since up to 90% of computer time in atmospheric chemistry simulations is used in integrating chemistry, our group initially focussed its efforts on improving the chemistry integrators. This research effort lead to the reduction of the chemistry integration time by an order of magnitude and contributed to a better theoretical understanding of the behavior of numerical integrators for chemical rate equations. The results of our research are contained in several papers ([23, 24, 25, 27, 35, 80, 81, 84, 85, 86]). In order to easily test different chemistry models and different integration schemes our group developed a symbolic preprocessor for chemical rate equations, kpp, which makes it very easy to build new chemistry models, automatically computes Jacobians, and determines a close to optimal reordering of chemical species in order to improve the sparsity of the LU factors to be used by implicit integrators. kpp is available on the Internet at htpp://people.cs.vt.edu/ ̃asandu and has being used by many research teams around the world. A paper on kpp was published in [26]. At present we are working on extending the capabilities of kpp in several directions and we are actively seeking external funding for this project. Sensitivity analysis is another important aspect in modeling atmospheric chemistry. Estimating the sensitivity of the model with respect to initial conditions and parameters defining the model is crucial for interpreting the results and for model optimization. We proved that automatic differentiation can be a useful tool in computing sensitivities and we proposed a novel way of applying the software package ADIFOR to this effect [23, 80, 81]. At present we are looking at efficient ways of building adjoint models for our problem. The use of automatic differentiation in the numerical solution of stiff ODEs is investigated in [34].