


ESSIM 2012



The Summer School — COURSES

[C1] 
Mathematical models and simulation of the human cardiovascular system.
Notification: Februar 10, 2012 by Dr. A. Noack
Teacher: Alexandra Moura (Technical University of Lisbon, Portugal)
The use of mathematical models and numerical simulations to study blood flow in the
circulatory system and related pathologies is an active interdisciplinary field of
research. It constitutes an inexpensive and non invasive tool, providing information
difficult to obtain in vivo and easily allowing the analysis of different scenarios, for
instance in surgery planning. Due to the complexity of the human cardiovascular system,
the use of computational models and simulation to study blood circulation in healthy and
pathological situations is a challenge to mathematicians and engineers. Nevertheless, the
enormous advances in this field in the last decade make it nowadays a reliable tool which is
increasingly used in clinical applications, such as the placement of stents in arteries with atherosclerotic
plaques, or the understanding of aneurysm growth and rupture.
In this course some of the fundamental aspects of mathematical modeling and numerical
analysis and simulation of blood flow in the human cardiovascular system will be
introduced and described. The main challenges, such as the use o patientspecific
geometrical models and accounting for the global circulation in local simulations, will
be addressed.
Course Script

[C2]

An Introduction to Algorithmic Differentiation.
Notification: March 12, 2012 by Dr. A. Noack
Teacher: Kshitij Kulshreshtha (Universität Paderborn, Germany)
Many applications like nonlinear optimisation and the solution of systems of nonlinear equations or the simulation of complex systems require the computation of derivatives.
In most applications not only the standard gradients and jacobian matrices are required but also directional derivatives and higher order derivatives.
Most often the functions that are to be differentiated are provided in the form of computer programs. Algorithmic Differentiation is a way to provide the required derivatives efficiently and accurately. In this course we shall derive methods of computing directional derivatives in forward mode, adjoints in reverse mode, and higher order derivatives (hessain matrices) in a mix of forward and reverse mode on the basis of the chain rule of
differentiation. We shall also examine the complexity of these calculations and discuss
various implementation issues and strategies.
Course Script
Exercises
Exercises
Exam with Solutions

[C3]

Environmental Modelling (Airborne Pollution studies).
Notification: April 10, 2012 by Dr. A. Noack
Teacher: Christopher Coles (University of Strathclyde, Glasgow, UK)
Increased Environmental, Health and Safety issues connected to airbourne particulates eminating from industrial plants have resulted in a requirement for a greater knowledge of the pollutant concentration. This course will examine a number of mathematical models and associated solution techniques in order to estimate the likely groundlevel particulate concentrations under various conditions.

[C4]

Introduction to Mathematical Biology.
Notification: April 24, 2012 by Dr. A. Noack
Teacher: Osvaldo Chara, Lutz Brusch (Technische Universität Dresden, Germany)
The life sciences are rapidly turning from qualitative into quantitative sciences. Integration of the increasing amount of biological data in a systematic way requires development and application of mathematical models.
The goal of Mathematical Biology is to gain a mechanistic understanding of biological problems through the analysis of appropriate mathematical models. During the course mathematical models (especially ordinary and partial differential equations, and cellular automata) are introduced and applied to biological key problems from developmental biology and tissue morphogenesis.
Script Monday
Script Tuesday
Script Wednesday
Script Thursday


Contact
Chair:
Prof. Dr. Stefan Siegmund
ECMIcoordinator
of Technische Universität Dresden
Contact Person
Dr. Antje Noack
Technische Universität Dresden
Dep. of Mathematics
Institute of Algebra
Phone: +49 351 46332149
Fax: +49 351 46334235
antje.noack@tudresden.de
Mail to:
TU Dresden
Institute of Algebra
01062 Dresden
Germany
Bulk mail to:
TU Dresden
Helmholtzstraße 10
01069 Dresden
Germany
