Variational methods for constructing of monotone approximations for atmospheric chemistry models
V.V. Penenko, E.A. Tsvetova
Keywords: variational principle, stiff systems ODE, integrating multipliers, discrete-analytical approximations, atmospheric chemistry, algorithms for sensitivity studies
Abstract
A new method for constructing efficient monotone numerical schemes for solving direct, adjoint, and inverse atmospheric chemistry problems is presented. It is a systhesis of a variational principles combined with splitting and decomposition methods and a constructive realization of the Eulerian integrating factors (EIM) by means of the local adjoint problem technique. To provide the efficiency of calculations, a method to decompose the multi component substances transformation operators in terms of mechanisms of reactions is also proposed. With the analytical EIMs, the decomposed systems of stiff ODEs are reduced to the equivalent systems of integral equations. To solve them, non-iterative multistage algorithms of given order of accuracy are developed. An original variational method for constructing of mutually consistent algorithms for direct and adjoint problems, and sensitivity studies for complex models with constraints is developed.
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