Computational PDEs

Tim Haubold

Institut für Numerische und Angewandte Mathematik
Lotzestraße 16-18
D-37083 Göttingen
Room 0.125
email: t.haubold@math.uni-goettingen.de
At the moment I am a Postdoc in the CPDE-group and working on Unfitted methods for interface problems for time-harmonic Maxwells equation. I am also researching dual functions for high order vectorial basis functions as a mean of fast computational interpolation or embedding operators.

Fields of interest

  • (Unfitted) Finite Element methods for Maxwells equations
  • High order finite element methods and especially high order basis functions
  • Orthogonal polynomials and special functions
  • Application of computer algebra to high order FEM
  • (Finite volume methods)

Research

'Recursion Formulas for Integrated Products of Jacobi Polynomials'

Joint work with 'Sven Beuchler' and 'Veronika Pillwein'

It is well known that high order basis functions based on Jacobi polynomials have many beneficial properties. We were able to use some of this properties to establish recursive relations between the entries of high order element matrices, which yield in assembly routines in optimal complexity.

'Recurrences for Quadrilateral High-Order Finite Elements'

Joint work with Sven Beuchler and Veronika Pillwein.

Similar to the paper above, but specialized on quadrilateral or hexahedral elements. Also included in this paper are recursive relations for the efficient computation of hanging nodes.

'High order biorthogonal functions in H(Curl)'

Joint work with Sven Beuchler and 'Joachim Schöberl'.

We were able to derive high order biorthogonal functions for the special case of H(Curl) basis functions. A followup regarding H(div) functions is in preparation.

Upcoming Conferences

You can find me at the following upcoming conferences:

  • 03.-07.03.25 SIAM Conference on Computational Science and Engineering (CSE25), Fort Worth, Texas, U.S.

Past Conferences

  • 18-22.03.24 GAMM Annual Meeting, Magdeburg
  • 3.-7.06.24 Eccomas, Lisbon, Portugal
  • 17-19.06.24 NGSolve User Meeting, Vienna, Austria
  • 21-26.06.24 WCCM, Vancouver, Canada
  • ...

Thesis

My 'Phd-thesis' Applications of Special Functions in High Order Finite Element Methods was written under the supervision of Prof. Sven Beuchler at the Leibniz University of Hannover.

My Master-thesis Hydrostatic reconstructed FORCE scheme and application to the non-unique Riemann solutions for the shallow water equations was written under the subervision of Dr. Ee Han and 'Prof. Alfred Schmidt' at the University of Bremen.

Teaching

  • WS 24/25 Lecture and exercises: Numerics of partial differential equations III (Together with Prof. Christoph Lehrenfeld)

  • SS 24 Exercises: Numerics of partial differential equations II

  • WS 23/24 Exercises: Numerics of partial differential equations I (with Fabian Heimann)

  • SS 22 Lecture and exercises: Interaktive algorithmische Einführung in die Finiten Elemente (with Prof. Sven Beuchler)

  • SS 23 and prior: Exercises for Numerics I, Numerics II, Numerics of partial differential equations (german and english), Numerical methods for continuum mechanics, and some more. (at the Leibniz University Hannover)