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Forward, tangent linear, and adjoint Runge-Kutta methods for stiff chemical kinetic simulations. (English) Zbl 1202.65090
Summary: We investigate numerical methods for direct decoupled sensitivity and discrete adjoint sensitivity analysis of stiff systems based on implicit Runge-Kutta schemes. Efficient implementations of tangent linear and adjoint schemes are discussed for two families of methods: fully implicit three-stage Runge-Kutta and singly diagonally-implicit Runge-Kutta. High computational efficiency is attained by exploiting the sparsity patterns of the Jacobian and Hessian. Numerical experiments with a large chemical system used in atmospheric chemistry illustrate the power of the stiff Runge-Kutta integrators and their tangent linear and discrete adjoint models. Through the integration with the Kinetic PreProcessor KPP-2.2 these numerical techniques become readily available to a wide community interested in the simulation of chemical kinetic systems.

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L04 Numerical methods for stiff equations
34A34 Nonlinear ordinary differential equations and systems
80A30 Chemical kinetics in thermodynamics and heat transfer
80M25 Other numerical methods (thermodynamics) (MSC2010)
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