Meshfree Methods (MA 5324)

Meshfree methods are a comparatively new approach for the (numerical) interpolation or approximation of some unknown function. In contrast to more traditional techniques - like finite differences, finite elements, spectral methods or wavelets - they do not require a mesh of the underlying computational domain (where the unknown function lives) to be generated first. These methods are very flexible with respect to the geometry of the domain, work in higher space dimensions and their basic implementation is strikingly simple.

This lecture will cover the basics of meshfree methods with an emphasis on approximation by radial basis functions. The lecture will be intertwined with programming exercises in MATLAB.

News

• There will be no lecture on June 7th.

Lecture notes

Di 12-14, MI 02.08.011

• Lecture notes (online) 
  
• Chapter 1
  • Problem 1.3, Problem 1.4, Problem 1.5, Problem 1.7
• Chapter 2
  • Problem 2.13
• Chapter 3
  • Problem 3.5, Problem 3.6, Problem 3.7, Problem 3.8
• Chapter 4
• Chapter 5
  • Problem 5.1
• Chapter 6
  • Problem 6.1
• Chapter 7

Tutorials

Every second We 12-14, MI 03.10.011, see tumonline

Exercise Sheets

• Sheet 01
  • Tutorial 01, exercise 1.3
• Sheet 02
  • Tutorial 02
• Sheet 03
  • Tutorial 03, exercise 3.4, beet.mat
• Sheet 04
  • Tutorial 04,
• Sheet 05
  • Tutorial 05, exercise 5.3,
• Sheet 06
  • Tutorial 06, exercise 6.3, exercise 6.4,
• Sheet 07
  • Tutorial 07

Software

• kdtree, sdistm.m, points.m

Klausur

• Die Klausur findet am Montag, den 01. August um 10:00 im Raum 02.08.011 statt.
• Bringen Sie Ihren gültigen Studentenausweis, sowie einen amtlichen Lichtbildausweis mit.
• Zur Klausur sind keine Hilfsmittel zugelassen, außer einem Spickzettel, der aus einem beschriebenen oder bedruckten DIN A4 Blatt besteht, wenn notwendig, beidseitig beschrieben.
• Die Einsicht findet am Mittwoch, den 03.08.2016 zwischen 11:00 und 12:00 Uhr statt.

References

• Gregory E. Fasshauer: Meshfree approximation methods with MATLAB. World Scientific Publishing, 2007.
• Holger Wendland: Scattered data approximation. Cambridge University Press, 2005.