Dr. Michael Bader

**Classification: **

- Hauptseminar in Informatik (Diplom/Master)
- Seminar in "Computational Science and Engineering (Master's Program)"
- Seminar für Studierende verwandter Fachrichtungen

**Time and Place:**

Preliminary session (Vorbesprechung) on
**Tuesday, January, 16th, 14:00**,
in room 02.07.023.

A quite common approach to represent continuous data in 2D, 3D, or even higher-dimensional domains is to approximate or interpolate this data on an appropriately generated computational grid. Applications exist in many fields of computational sciences; typical examples are finite difference or finite element methods in numerical simulation, the representation of geometrical objects in computer graphics or visualisation, and even general classification problems in data mining.

Algorithms and methods for grid generation are at least as diverse as their applications. It is the aim of this seminar to discuss several common approaches, for example:

- octree-based grids
- triangular or tetrahedral grids generated by bisection
- advancing-front methods
- Delauney/Voronoi methods
- sparse grids to represent high-dimensional data

The talks (approx. 45 minutes) in the seminar will be given in English. The ability to give presentations in English is nowadays a key qualification in many professions. Especially, for the students in Informatics, this seminar is intended to be a comparably stress-free opportunity to exercise these skills.

In addition to her or his talk, each student will have to prepare a short paper, which will be reviewed by two other seminar participants. The paper and the two reviews will, in addition to the talk, be considered to determine the final grade.

The following 13 topics from 6 rough categiories are available:

- Data structures to store object topologies

- Octree generation for simple objects and CSG (constructive solid geometry)
- Octrees meshes for changing/moving geometries

- Recursively structured triangular grid generation - a survey
- Data structures and algorithms for adaptive triangular grids - refinement trees, space-filling curves, stack- and stream-based processing.
- Tetrahedral (3D) meshes based on bisection

- Delauney Triangulation
- Advancing Front methods

- Hierarchical Basis representation and approximation of functions on sparse grids
- Classification/Data Mining on sparse grids

- amatos - an Adaptive Mesh generator for ATmospheric and Oceanic Simulation
- Unstructured grids in UG
- Grid generation in Diffpack

The seminar talks will be given in presumably 4-6 sessions on Thursday afternoons (starting from 15:00). Topics from the same category will be placed in the same session.

The following suggested session schedule is preliminary: sessions might start one week (or even a couple of weeks) earlier or later, and sessions might be swapped.

**Note that for the review process, the seminar papers have to
be submitted four weeks before the actual seminar talk!**

Session | Topic | student |
---|---|---|

Thu, May 24, 15:00Basics and Octrees |
Data structures to store object topologies |
N.N. |

Octree generation for simple objects and CSG |
N.N. | |

Octrees meshes for changing/moving geometries |
N.N. | |

Thu, May 31, 15:00Recursively Structured Triangular/Tetrahedral Grids |
Recursively structured triangular grid generation
- a survey |
N.N. |

Data structures and algorithms for adaptive triangular grids |
N.N. | |

Tetrahedral (3D) meshes based on bisection |
N.N. | |

Thu, Jun 14, 15:00Unstructured Meshes |
Delauney Triangulation |
N.N. |

Advancing Front methods |
N.N. | |

Thu, Jun 28, 15:00Sparse Grids |
Hierarchical Basis representation and approximation of
functions on sparse grids |
N.N. |

Classification/Data Mining on sparse grids |
N.N. | |

Thu, Jul 5, 15:00Grid Generation in Practice |
amatos - an Adaptive Mesh generator for ATmospheric and Oceanic
Simulation |
N.N. |

Unstructured grids in UG |
N.N. | |

Grid generation in Diffpack |
N.N. |

Michael Bader