TY - GEN A1 - Streubel, Tom A1 - Strohm, Christian A1 - Trunschke, Philipp A1 - Tischendorf, Caren T1 - Generic Construction and Efficient Evaluation of Network DAEs and Their Derivatives in the Context of Gas Networks N2 - We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function f and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of f can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF). T3 - ZIB-Report - 17-41 KW - compressed sparse row format KW - algorithmic differentiation KW - abs-normal form KW - piecewise linear tangent approximation KW - piecewise smooth Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64582 SN - 1438-0064 ER - TY - GEN A1 - Hasenfelder, Richard A1 - Lehmann, Lutz A1 - Radons, Manuel A1 - Streubel, Tom A1 - Strohm, Christian A1 - Griewank, Andreas T1 - Computational aspects of the Generalized Trapezoidal Rule N2 - In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side F:IR^n -> IR^n. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a non-differentiability of F. In such a situation the investigated generalized trapezoidal rule achieves a higher convergence order than the classical method. While the asymptotic behavior of the generalized method was investigated in a previous work, in the present article we develop the algorithmic structure for efficient implementation strategies and estimate the actual computational cost of the latter. Moreover, energy preservation of the generalized trapezoidal rule is proved for Hamiltonian systems with piecewise linear right hand side. T3 - ZIB-Report - 18-23 KW - Algorithmic Differentiation KW - Automatic Differentiation KW - Lipschitz Continuity KW - Piecewise Linearization KW - Nonsmooth KW - Trapezoidal Rule KW - Implementation KW - Computational Cost Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68615 SN - 1438-0064 ER - TY - CHAP A1 - Streubel, Tom A1 - Strohm, Christian A1 - Trunschke, Philipp A1 - Tischendorf, Caren T1 - Generic Construction and Efficient Evaluation of Network DAEs and Their Derivatives in the Context of Gas Networks T2 - Operations Research Proceedings 2017 N2 - We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function f and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of f can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF). KW - compressed sparse row format KW - algorithmic differentiation KW - abs-normal form KW - piecewise linear tangent approximation KW - piecewise smooth Y1 - 2018 SN - 978-3-319-89920-6 U6 - https://doi.org/10.1007/978-3-319-89920-6_83 SP - 627 EP - 632 PB - Springer International Publishing ER -