Semester 2 UHH Numerics (OLD)

(to be discontinued - valid up to batch 2017)

Numerics @ UHH 30 ECTS credits

The second semester will be focused on Numerics and will be spent at UHH - University of Hamburg in Germany from April to August.

Below you can find information about the subjects for this semester.

ECTS credits 3
University University of Hamburg
Semester 2
Lecturer 1 Rodolfo Repetto
Objectives

Applications to the study of models in fluid dynamics.
Topics

Introduction to fluid dynamics. Continuum approach. Statics and kinematics of fluids. Mass conservation and balance laws. Constitutive laws: ideal fluids, Newtonian viscous fluids. The Navier-Stokes equations. Ideal fluids: Bernoulli's theorem and Kelvin theorem. Viscous fluids: unidirectional flows, the vorticity

ECTS credits 6
University University of Hamburg
Semester 2
Lecturer 1 Jörn BEHRENS
Objectives

- Students get to know the most important classes of modern machine learning algorithms. - They are going to develop an understanding why certain algorithms work well and others don't. - They learn how to evaluate and compare the results of different learning algorithms. - They learn how to model machine learning problems and what are common pitfalls.

ECTS credits 6
University University of Hamburg
Semester 2
Lecturer 1 Jens Struckmeier
Objectives

The overall emphasis is on studying the mathematical tools that are essential in developing, analyzing, and successfully using numerical methods for non-linear systems of conservation laws, particularly for problems involving shock waves.
Topics

Numerical methods for linear equations. Computing discontinuous solutions. Conservative methods for non-linear problems. Godunov's methods.
Approximate Riemann solvers. Nonlinear stability. High resolution methods.
Semi-discrete methods.

ECTS credits 6
University University of Hamburg
Semester 2
Lecturer 1 Christian KAHLE
Objectives

In this course the basic principles of the FE element method applied to the numerical treatment of elliptic PDEs are considered. Successful applicants will be able to use the FE method as analytic and numerical tool for the mathematical investigation of l
Topics

Topics include construction of FE spaces, derivation and numerical solution of the resulting linear algebra systems, error analysis in Sobolev spaces including interpolation estimates, basic principles of residual based a posteriori error analysis.

ECTS credits 6
University University of Hamburg
Semester 2
Lecturer 1 Thomas BERGER
Objectives

The objective of this lecture is first, to familiarize the participants with concepts for nonsmooth convex optimization in theory as well as in computation. Second, to give an understanding of the differences and similarities between smooth and nonsmooth
Topics

Fundamentals of convex analysis; subdifferential and epsilon-subdifferential; cutting palane algorithms; bundle methods; regularization.

ECTS credits 3
University University of Hamburg
Semester 2
Lecturer 1 Ingenuin Gasser
Lecturer 2 Elisabetta Felaco
Objectives

In this seminar we face the students with real world problems. We discuss the interface between the real world industrial problems and applied mathematics.
Topics

A series of 22 small real world industrial problems where mathematics has been applied successfully.