Keywords: Differential-Algebraic Equations; Quasi-Linear; Modelica; Translation; Regularization; Solver; QUALIDAES
Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015
R. Altmeyer and A. Steinbrecher. Regularization and numerical simulation of dynamical systems modeled with Modelica. Preprint 29-2013, Institut f√ľr Mathematik, TU Berlin, 2013.
K.E. Brenan, S.L. Campbell, and L.R. Petzold. Numerical Solution of Initial-Value Problems in Differential Algebraic Equations, volume 14 of Classics in Applied Mathematics. SIAM, Philadelphia, PA, 1996.
P. Deuflhard. Newton methods for nonlinear problems. Affine invariance and adaptive algorithms, volume 35 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 2004.
C.W. Gear. Differential-algebraic equation index transformations. SIAM Journal on Scientific and Statistic Computing, 9:39‚Äď47, 1988.
E. Griepentrog and R. M√§rz. Differential-Algebraic Equations and Their Numerical Treatment, volume 88 of Teubner-Texte zur Mathematik. BSB B.G.Teubner Verlagsgesellschaft, Leipzig, 1986.
E. Hairer and G. Wanner. Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin, Germany, 2nd edition, 1996.
D.J. Higham and N.J. Higham. MATLAB Guide. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition, 2005. ISBN 0-89871-578-4.
C. H√∂ger. Operational semantics for a modular equation language. AVICPS 2013, page 5, 2013.
C. H√∂ger. Dynamic structural analysis for daes. In Proceedings of the 2014 Summer Simulation Multiconference, page 12. Society for Computer Simulation International, 2014.
P. Kunkel and V. Mehrmann. Index reduction for differentialalgebraic equations by minimal extension. Zeitschrift f√ľr Angewandte Mathematik und Mechanik, 84(9):579‚Äď597, 2004.
P. Kunkel and V. Mehrmann. Differential-Algebraic Equations. Analysis and Numerical Solution. EMS Publishing House, Z√ľrich, Switzerland, 2006.
S. Mattsson and G. S√∂derlind. Index reduction in differentialalgebraic equations using dummy derivatives. SIAM Journal on Scientific and Statistic Computing, 14:677‚Äď692, 1993.
C.C. Pantelides. The consistent initialization of differentialalgebraic systems. SIAM Journal on Scientific and Statistic Computing, 9:213‚Äď231, 1988.
P. Pepper, A. Mehlhase, Ch. H√∂ger, and L. Scholz. A compositional semantics for Modelica-style variable-structure modeling. In P. Fritzson F.E. Cellier, D. Broman and E.A. Lee, editors, 4th International Workshop on Equation-Based Object-oriented Modeling Languages and Tools (EOOLT 2011), number 56 in Link√∂ping Electronic Conference Proceedings, pages 45‚Äď54, Zurich, Switzerland, 2011. September 5, 2011.
J. Pryce. A simple structural analysis method for DAEs. BIT Numerical Mathematics, 41:364‚Äď394, 2001.
L. Scholz and A. Steinbrecher. A combined structuralalgebraic approach for the regularization of coupled systems of DAEs. Preprint 30-2013, Institut f√ľr Mathematik, TU Berlin, 2013.
L. Scholz and A. Steinbrecher. Efficient numerical integration of dynamical systems based on structural-algebraic regularization avoiding state selection. In K.-E. Arzen H. Tummescheit, editor, Proceedings of the 10th International Modelica Conference, March 10-12, 2014, Lund, Sweden, number 96 in Link√∂ping Electronic Conference Proceedings, pages 1171‚Äď1178. Modelica Association and Link√∂ping University Electronic Press, 2014.
A. Steinbrecher. Numerical Solution of Quasi-Linear Differential-Algebraic Equations and Industrial Simulation of Multibody Systems. PhD thesis, Technische Universit√§t Berlin, 2006.