Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
Lena Scholz, Andreas Steinbrecher · Linköping electronic conference proceedings · 2014
Differential-algebraic equations naturally arise in the modeling of dynamical processes, in particular using MODELICA as modeling language.In general, the model equations can be of higher index, i.e., they can contain hidden constraints which lead to instabilities and order reductions in the numerical integration.Therefore, a regularization or remodeling of the model equations is required.One way to obtain the required information on the hidden constraints is a structural analysis based on the sparsity pattern of the system.For the determination of a regular index-reduced system formulation then, usually, a crucial step is the so-called state selection.In this paper, we will present a new approach for the remodeling of dynamical systems that uses the information obtained from the structural analysis to construct a regularized overdetermined system formulation.This overdetermined system can then be solved using specially adapted numerical integrators, in such a way that the state selection can be performed within the numerical integrator during runtime of the simulation.