On the efficient generation of taylor expansions for DAE solutions by automatic differentiation

Authors:
Andreas Griewank;Andrea Walther
Affiliations:
Department of Mathematics, Humboldt-Universität Berlin, Germany;Institute of Scientific Computing, Technische Universität Dresden, Germany
Venue:
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Year:
2004

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Abstract

Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order. The successive calculation of Taylor coefficients involves the solution of nonlinear algebraic equations by some variant of the Gauss-Newton method. Hence, one needs to evaluate certain Jacobians and several right hand sides. Without advocating a particular solver we discuss how this information can be efficiently obtained using ADOL-C or similar automatic differentiation packages.