FastDer++, efficient automatic differentiation for non-linear PDE solvers
Mathematics and Computers in Simulation - Special issue: Selected papers of the IMACS/IFAC fourth international symposium on mathematical modelling and simulation in agricultural and bio-industries
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By employing automatic differentiation (AD), solvers for nonlinear systems of PDEs can be developed which relieve the user from the extra work of linearising a nonlinear PDE system and at the same time improve performance. This is achieved by extending common AD techniques using operator overloading to take advantage of the fact that in a FEM/FD/FV framework, a limited number of functions and their partial derivatives with respect to the unknowns have to be evaluated many times. The extension is implemented in C++ for both forward and reverse modes, and compared to hand coded evaluation of derivatives and two state-of-the-art AD implementations, ADIC [84] and ADOL-C [242, 243]. An application is discussed which dramatically reduces the cost of solver development.