Algorithms for Approximate Solution of ODE Ensembles Using Clustering and Sensitivity Matrices

Algorithms for solving ensembles of ODEs with sets of different input data arising from modeling chemical kinetics are considered with an operator splitting scheme for multiphysical calculations. The efficiency of an algorithm combining clustering of an input data ensemble and estimating of the solution within the cluster is evaluated by using a sensitivity matrix obtained by solving adjoint equations. The algorithm is implemented on the basis of numerical schemes consistent in the sense of a discrete Lagrange identity for solving ODE systems of the production-destruction type. The contribution of the clustering and the sensitivity matrix to the performance of the algorithm is evaluated. The results of testing with atmospheric chemistry scenarios show that the algorithm reduces the calculation time with an acceptable decrease in accuracy.