Fast,Scalable master equation solution algorithms.III,Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

摘要

In this paper we propose a novel fast and linearly scalabel method for solving master equatons arising in the context of gas-phase reactive systems,based on an existent stiff ordinary differential equation integrator.The required solution of a linear system involving the Jacobian matrix is achieved using the Gmres iteration preconditioned usign the diffusion approximation to the master equation.In this way we avoid the cubic scaling of traditional master equatin solution methods and maintain the low temperature robustness of numerical integration.The method is tested using a master equation modelling the formation of progargyl from the reaction of singlet methylene with acetylene,proceeding through long lived isomerizing intermediates.