# Fast solvers for nonsmooth PDEs

## News

- The solution (matlab programs) for exercise 7 are now online (see below).
- Starting with 2014-11-27 the tutorial and the lecture will swap its time slots and room.

## Dates

Lecture | Thu, 10:15 - 11:45 | Takustraße 9, SR 049 |

Tutorial | Thu, 12:15 - 13:45 | Arnimallee 3, SR 210 |

Oral examinations | tba | Arnimallee 6, R 121 |

## General information

### Description

Nonsmooth partial differential equations arise as mathematical models for many physical processes, e.g., as mathematical descriptions of the separation of alloys, fluids in porous media, multi phase flow, contact problems for elastic bodies, and many more. The lack of smoothness makes the numerical solution of such problems challenging because classical nonlinear schemes are in general not applicable.

During the lecture we will introduce problems arising from several applications and present robust and efficient numerical methods for their numerical solution. To this end we will use techniques from convex analysis, nonsmooth optimization, and multigrid and domain decomposition ideas.

### Target Audience

Students of Bachelor and Master courses in Mathematics and of BMS

### Requirements

- Basics of calculus (Analysis I,II)
- Linear algebra (Lineare Algebra I,II)
- Numerical analysis (Numerik I)
- Numerical methods for partial differential equations (Numerik 3)

## Registration

All participants should register at the KVV, so that we know who is participating. The overall number of participants is also necessary to justify the equipment of the course. In addition, depending on your program of study, you have to register in the Campus Management. Please be aware of the deadlines for binding registration in the Campus Management.

## Exercises and Criteria for a Certificate

### Tutorial

The tutorial offers the possibility to discuss and better understand the presented material and exercises. Furthermore solutions of exercises are presented by the students.

### Exercises

- A sheet with exercises will be handed out each Thursday during the lecture. These exercises are also available electronically on this web page (see below).
- The exercises are intended to be solved by teams of 2-3 members.
- The exercises consist of theoretical and programming problems. The latter should be solved using Matlab (available at the students computer pool at the institute). Both types of exercises are rated separately.
- The solutions have to be finished before the tutorial two weeks after they were handed out.
- The solutions of the programming exercises should be delivered by email
to graeser@mi.fu-berlin.de. Note that a complete solution consists of
a well documented and running Matlab code including matlab scripts named
`run_x_y.m`

that execute the required test runs for exercise`y`

on sheed`x`

without having to pass any parameters. Please also add protocols of the execution of these test runs. Delivering a correct and running code without knowing what is going on in the code will be regarded and rated as attempt of deception. - The solutions of the theoretical problems have to be presented in the tutorial on request (without regard to preference and presence) by a member of a given group.

### Exams

There will be oral examinations in the last week of the lecture time. The schedule for the examination will be announced in the lecture.

### Criteria for the Certificate

- Passing the oral exam
- Active participation: 50% of the maximal number of points for both, theoretical and programming problems
- Constant participation: 85% attendance in the tutorial (not checked)

Certificates are graded according to the result of the oral exam.

### Exercise sheets

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5 (test program and solutions)
- Exercise 7 (test programs and solution)
- Exercise 8 (test programs)
- Exercise 9 (test programs)

## Accompanying Material

There will be a list of topics and important results for each lecture available here

## Literature

Will be added soon.

## Contact

Prof. Dr. Carsten Gräser | graeser@mi.fu-berlin.de | Arnimallee 6, Raum 121 Office hour: Tue 14:00-15:00 |