# Mathematical Aspects of Object-Oriented Modeling and Simulation

FDA167, 2007HT

Status Archive National Graduate School in Computer Science (CUGS) PELAB Peter Fritzson

 Start: end of September 2007

## Course plan

#### Recommended for

Ph.D. students or practitioners in computer science or systems engineering.

#### Goals

The investigation of dynamical systems in mechanical, electrical or chemical
engineering usually requires a mathematical modeling of the system behavior.
This graduate course provides an understanding on the mathematical aspects
of object-oriented modeling and simulation based on Modelica. However it
differs from traditional numerical analysis courses in that it focuses on
the understanding of symbolic and numerical techniques necessary to build
simulation language compilers rather than on isolated detailed analyses on
them. Building simulation environments requires sometimes a different
approach compared to approaches used for traditional programming language
compilers. At the end of the course the participants should acquire the
necessary knowledge of the symbolic transformation and numerical algorithms
for building a simple prototype Modelica Compiler.

#### Prerequisites

Some elementary knowledge in numerical analyses and compiler construction.

#### Contents

1) OO Modeling and Simulation Environments.
a. The equation-based modeling and simulation paradigm
b. Principles of OO Modeling & Simulation with Modelica
c. Design of symbolic and numerical simulation engines.

2) Numerical methods for ordinary differential equations
with initial conditions:
a. single-step and multi-step algorithms.
convergence, discretization error, step size control
b. special methods for stiff systems
backward difference schemes
c. event handling, root -finding methods

3) Structural Analyses and symbolic manipulation
a. higher-index problems. index reduction,
assignment algorithms, dummy derivative methods
b. simple symbolic transformation.
eliminating trivial equations
c. Error handling and recovery. Structural and
numerical inconsistencies.

4)Solution of linear and nonlinear system of equations
a. Direct methods for small systems
LU (QR) - decomposition
b. iterative methods for large systems.
Jacobi- bzw. Gauß-Seidel methods
c. Newton-methods, quasi-Newton-methods

#### Organization

1st block: 24th-25th September (maybe 12 hours) 2nd block: 1st-2nd October
(maybe 12 hours) Between the two blocks the students can work on the
homework, which will be necessary for getting the credit points.

#### Lecturers

Prof. Bernhard Bachmann (University of Applied Sciences in Bielefeld,
Germany)

#### Examiner

Prof. Bernhard Bachmann/Prof Peter Fritzson

4.5 hp (3) p