# Legacy display Course

This is an archived course. The content might be broken.

#### Vorlesung im Sommersemester 2014:

# V4E2 – Numerical Simulation

### Prof. Dr. Carsten Burstedde

#### Assistent: Philipp Morgenstern

#### Requirements: Wissenschaftliches Rechnen I (V3E1/F4E1).

We will discuss optimization and inverse problems with PDEs. If we define the forward problem by computing the solution of a PDE given its right hand side and system coefficients, optimization and inverse problems refer to computing right hand sides or coefficients given a certain target solution. Such problems are particularly challenging for the following reasons:1. | Even for a linear forward problem, the inverse problem can be (strongly) nonlinear. |

2. | The inverse problem may be ill-posed: its solution may not depend continuously on the input data, and there may be none or multiple exact solutions. |

3. | We may want to restrict the unknown coefficients to certain subspaces (for example, they should be non-negative if they enter the bilinear form of an elliptic operator). |

4. | Computationally, we solve a minimization problem where the PDE is a constraint. We will introduce Lagrange multipliers in certain function spaces. Each step of the inverse solver involves one or more solves of the PDE. |

#### Date & time

Lectures: | Tue, | 10:15–11:45 am, | Wegelerstraße 6, Room 6.020 |

Thu, | 8:30–10:00 am, | Wegelerstraße 6, Room 6.020 | |

First lecture: | Tue, | 8.4.2014 | |

Tutorial: | Wed, | 4:30–6:00 pm, | Wegelerstraße 6, Room 6.020 |

#### Exercise sheets

Exercises are handed out on tuesdays, and are to be handed in one week later.- Exercise Sheet 1
- Exercise Sheet 2
- Exercise Sheet 3
- Exercise Sheet 4
- Exercise Sheet 5
- Exercise Sheet 6
- Exercise Sheet 7
- Exercise Sheet 8
- Exercise Sheet 9
- Exercise Sheet 10

#### Requirements for the exam

Students need to achieve 50% of all points, separately for theory and programming exercises.Date of the examinations will be **21.–23.7.**

#### Literature

[1] | L. Biegler, G. Biros, O. Ghattas, Y. Marzouk, M. Heinkenschloss, D. Keyes, B. Mallick, , L. Tenorio, B. van Bloemen Waanders, and K. Willcox, eds., Large-scale Inverse Problems and Quantification of Uncertainty, Wiley, 2011. |

[2] | A. Borzì and V. Schulz, Computational Optimization of Systems Governed by Partial Differential Equations, SIAM, 2012. |

[3] | F. Troltzsch, Optimale Steuerung partieller Differentialgleichungen, Vieweg, Wiesbaden, Germany, 2005. |

[4] | F. Troltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications, vol. 112 of Graduate Studies in Mathematics, American Mathematical Society, 2010. |