Course information, PhD course in simulation, 8 hp
Contents
 Introduction to simulation
 Simulation of ordinary differential equations, including stiff problems
 Simulation of differentialalgebraic equations
 Modelica and simulation of objectoriented models
Examination
 Hand in of mandatory exercises in exercises (20180105).
 For the DAEpart, mandatory participation in exercise solving classes, demonstrating your own solutions.
 Report of a mandatory miniproject in a topic related to the course. For examepl, choose a simulation model, possibly related to your research project, and demonstrate the correctness of the simulation.
 Oral examination: Exaplain and discuss theory and methods
 Extra work can merit extra credits
Course plan
Meeting 1  Introduction/simulation of ordinary differential equations
 Course meeting
 Responsible: Lars E
 Contents

Basic ODE:
Problem formulations (some classic problems from HairerNorsettWanner), existance and uniqueness.
Simple onestep methods, implicit and explicit.  Course material
 Material covering existance and uniqueness from Hairer, Norsett and Wanner and from Dahlqvist och Björk.
Meeting 2  Introduction/simulation of ordinary differential equations
 Course meeting
 Responsible: Lars E
 Contents

Concepts: Convergence, consistency, 0stability, absolute stability. Stiff decay.
Explicit one step methods: RungeKutta family.
Step length control, parameters för step length control.  Course material
 First 4 chapters in AscherPetzold until page 95.
Meeting 3  Introduction/simulation of ordinary differential equations
 Course meeting
 Responsible: Lars E
 Contents
 More on implicit and multistep methods.
Steplength control, parameters for steplength control. Zero detection.
Start implementation of an explicit (or implicit) method with steplength control.
Continued work on implementation and exercises in the course.  Course material

 Ascher och Petzold, remaining parts of Chapter 4 and Chapter 5.
 Deuflhard och Bornemann, "Scientific Comupting with Ordniary Differential Equations". Chapter 5 on step length control.
 John Mathews, "Computer Derivations of Numerical Differentiation Formulae (Classroom Notes)" Int. J. of Math. Education in Sci. and Tech., V 34, No 2 (MarchApril 2003), pp.280287.
Meeting 4  Introduction/simulation of ordinary differential equations
 Course meeting
 Responsible: Lars E
 Contents
 A little on BVP.
Continued work on implementation and exercises.
Survey/review and analysis of Matlab's solvers.
Traps and pitfalls.  Course material

 Chapter 68 in Ascher and Petzold, with emphasis on Chapters 67.
 More material on stiff differentialequations from Shampine och Gear A User's View of Solving Stiff Ordinary Differential Equations.
 Kjell Gustafsson, "Traps and Pitfalls in Simulantion".
Meeting 5  Introduction/simulation of ordinary differential equations
 Course meeting
 Responsible: Lars E
 Contents
 Discussion about results from hand in assignments.
 Course material
Meeting 6  Simulation of differentialalgebraic equations
Responsible: Erik Contents

 Motivating examples, some models
 Existence conditions for solutions to DAE:S, what do they look like?
 What separates an ODE from a DAER and when can an ODE solver be used to integrate DAE:s?
 Index, what is it and what does it mean? Complications and different definitions.
 Initial conditions.
 Why are index1 easy and index larger than 1 difficult to simulate?
 Course meeting
 Tuesday 31/10, 13.1515.00, Systemet, OH
 Course material

 C.W. Gear and L. Petzold, "ODE methods for the solution of differential/algebraic systems", SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 716728.
 Sid 372381 samt 452454 i Hairer del 2.
 L. Petzold, "Differential/Algebraic Equations are not ODE's", SIAM journal on scientific and statistical computing, vol. 3, no. 3, 367384, 1982.
 Exercises: 2.15, 2.7, 2.10a, 2.11
Meeting 7  Simulation of differentialalgebraic equations
Responsible: Erik Contents

 Introduction to method for semiexplicit index1 DAE:s
 statespace
 epsilonembedding + implicit RungeKutta
 BDF (DASSL)
 Pantelides algorithm for determination of consistent initial conditions
 Some methods for index reduction
 Problems with drift and possible solutions
 Baumgarte stabilization
 Projection methods
 Some about order and convergence with solvers, stiffly accurate methods
 ODE/DAE:er with invariants
 The unstructured problem F(y',y,x)=0 and overdetermined models
 Sensitivity analysis
 Introduction to method for semiexplicit index1 DAE:s
 Course meeting
 Wednesday 8/11, 13.1515.00, Systemet, OH
 Course material

 pages 455480 in Hairer part 2

C.C. pantelides "The
consistent initialization of differentialalgebraic
systems", SIAM Journal on scientific and statistical
computing, Vol. 9, No. 2, pp. 213231, March 1988.
the description of the graph theoretical algorith to find all MSS:s can be skipped  S. Mattson and G. Söderlind, "Index reduction in differentialalgebraic equations using dummy derivatives", SIAM Journal on Scientific Computing, vol. 14, No. 3, pp. 677692. 1993.
 If you want to known a lot on how DASSL/DASPK is implemented, then I recommend Chapter 5 in K.E. Brenan, S.L. Campbell and L.R. Petzold, "Numerical Solution of InitialValue Problems in Differential.Algebraic Equations", SIAM, 1996. Describes the solver in detail.
 Mattias Krysanders Matlabimplementation of Pantelides algoritm [zip, tar.gz]
 Exercises: 2.26, 2.1415, 2.18, 2.22, 2.24
Meeting 8  Modelica and simulation of objectoriented models
Responsible: Erik F Contents

 Introduction to equation based models
 How to go from a Modelica model to simulation code in C
 Structural index
 How can you, in the model, give clues to the solver for choice of states and initial conditions.
 How to automatically generate crossing/eventfunctions
 Course meeting
 Friday 17/11, 08.1510.00, Systemet, OH
 Course material

 Kapitel 17,18 i "Principles of ObjectOriented Modeling and Simulation with Modelica 2.1" av P. Fritzson. For those not familiar with Modelica, recommended reading in Chapter 2.
 G. Reissig, W.S. Martinson, P.I. Barton, " DifferentialAlgebraic Equations of Index 1 May Have an Arbitrarily High Structural Index", SIAM Journal on Scientific Computing, Volume 21, Number 6, pp. 19871990, 2000.
 H. Elmqvist and M. Otter, "Methods for tearing systems of equations in objectoriented modeling", Proceedings of the European Simulation Multiconference, pp. 326332, Barcelona, Spain, 1994.
 For the interested, a brief, somewhat incomplete, but still interesting description of how OpenModelica goes from model to C code. Adrian Pop, OpenModelica Compiler Phases, Open Source Modelica Consortium, 20080526.
 Exercises: 2.9, 2.10bd
Meeting 9  Modelica and simulation of objectoriented models
Responsible: Erik F Contents

 Pantelides algorithm
 Finding consistent initial conditions
 Computing structural index
 Indexreduktion using dummyderivatives
 Course meeting
 Thursday 23/11, 08.1510.00, Systemet, OH
 Course material

 Kapitel 17,18 i "Principles of ObjectOriented Modeling and Simulation with Modelica 2.1" av P. Fritzson. For those not familiar with Modelica, recommended reading in Chapter 2.
 C.C. pantelides "The consistent initialization of differentialalgebraic systems", SIAM Journal on scientific and statistical computing, Vol. 9, No. 2, pp. 213231, March 1988.
 S. Mattson and G. Söderlind, "Index reduction in differentialalgebraic equations using dummy derivatives", SIAM Journal on Scientific Computing, vol. 14, No. 3, pp. 677692. 1993.
 Exercises: 2.13, 2.29, 2.30
Meeting 10  DAE, exercise discussion 1
Responsible: Erik F Contents
 Presentations and discussion about mandatory exercises.
 Course meeting
 Monday, December 11, 13:1516:00
Meeting 11  DAE, exercise discussion 2
Responsible: Erik F Contents
 Presentations and discussion about mandatory exercises.
 Course meeting
Meeting 12  DAE, exercise discussion 2
Responsible: Erik F Contents
 Presentations and discussion about mandatory exercises.
 Course meeting
Course material
 Huvudbok för delen om ordinära differentialekvationer är "Computer Methods for Ordinary Differential Equations and DifferentialAlgebraic Equations" av U. Ascher och L. Petzold.
 För delen om differentialalgebraiska ekvationer kommer valda delar av "Solving Ordinary Differential Equations II  Stiff and DifferentialAlgebraic Problems" av E. Hairer och G. Wanner att användas. Avsnitt: VI.1, VII.1VII.2.
 För delen om simulering av objektorienterade modeller kommer kapitel ur "Principles of ObjectOriented Modeling and Simulation with Modelica 2.1" av P. Fritzson att kopieras upp.
 Deuflhard och Bornemann, "Scientific Comupting with Ordniary Differential Equations". Kapitel 5 om steglängdsreglering.
 Kjell Gustafsson, "Traps and Pitfalls in Simulation".
 L.F. Shampine and C.W. Gear (1979), "A User's View of Solving Stiff Ordinary Differential Equations", SIAM Review.
 T. Malya and L.R. Petzold, Numerical methods and software for sensitivity analysis of differentialalgebraic systems, Applied Numerical Mathematics Volume 20, Issues 12, Pages 5779, 1996.
 S.L. Campbell and C.W. Gear, "The index of general nonlinear DAEs", Numerische Mathematik, Vol 72, No. 2, 173196, 1995.
 L. Petzold, "Differential/Algebraic Equations are not ODE's", SIAM journal on scientific and statistical computing, vol. 3, no. 3, 367384, 1982.
 C.W. Gear and L. Petzold, "ODE methods for the solution of differential/algebraic systems", SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 716728.
 G. Reissig, W.S. Martinson, P.I. Barton, "DifferentialAlgebraic Equations of Index 1 May Have an Arbitrarily High Structural Index", SIAM Journal on Scientific Computing, Volume 21, Number 6, pp. 19871990, 2000.
 H. Elmqvist and M. Otter, "Methods for tearing systems of equations in objectoriented modeling", Proceedings of the European Simulation Multiconference, pp. 326332, Barcelona, Spain, 1994.
 C.C. pantelides "The consistent initialization of differentialalgebraic systems", SIAM Journal on scientific and statistical computing, Vol. 9, No. 2, pp. 213231, March 1988.
 S. Mattson and G. Söderlind, "Index reduction in
differentialalgebraic equations using dummy derivatives",
SIAM Journal on Scientific Computing, vol. 14, No. 3,
pp. 677692. 1993.
Ett konferensbidrag med liknande innehåll som ovan
S. Mattson and G. Söderlind, " A new technique for solving highindex differentialalgebraic equations using dummy derivatives", IEEE Symposium on ComputerAided Control System Design (CACSD). Napa, CA, USA. 218224, 1992.  K.E. Brenan, S.L. Campbell and L.R. Petzold, "Kapitel 5, Numerical Solution of InitialValue Problems in Differential.Algebraic Equations", SIAM, 1996.
 Adrian Pop, OpenModelica Compiler Phases, Open Source Modelica Consortium, 20080526.
 H. Elmqvist, M. Otter, and F.E. Cellier. "Inline Integration: A new mixed symbolic/numeric approach for solving differentialalgebraic equation systems", In Proceedings of ESM'95, European Simulation Multiconference, 1995.
Page responsible: Erik Frisk
Last updated: 20180105