@unpublished{KreimeierSauterStreubeletal.2021, author = {Kreimeier, Timo and Sauter, Henning and Streubel, Tom and Tischendorf, Caren and Walther, Andrea}, title = {Solving Least-Squares Collocated Differential Algebraic Equations by Successive Abs-Linear Minimization - A Case Study on Gas Network Simulation}, year = {2021}, abstract = {This paper studies the numerical simulation of gas networks with regulating elements using differential algebraic equations (DAEs) in combination with least-squares collocation. In contrast to classical collocation methods, more collocation points than degrees of freedom for the collocation polynomials are used. Recently, it has been shown that such a least-squares collocation has a regularizing effect for DAEs, in particular for DAEs with higher index. In each time step of the numerical integration, one has to solve a system of nonlinear equations that is nonsmooth due to the regulating elements in the gas networks. We consider four solvers one of which explicitly exploits the inherent nonsmooth nature. Numerical results are given for three different test cases with increasing complexity illustrating the feasibility of the proposed approach to approximate a solution of the DAE and the advantageous performance of the nonsmooth solver that is based on the concept of abs-linearization.}, language = {en} } @unpublished{SauterTischendorf2021, author = {Sauter, Henning and Tischendorf, Caren}, title = {Optimal control of gas network DAEs}, year = {2021}, language = {en} } @unpublished{SauterTischendorf2021, author = {Sauter, Henning and Tischendorf, Caren}, title = {Least squares collocation for the simulation of gas network DAEs}, year = {2021}, language = {en} }