| Semester | Titel | Typ |
|---|---|---|
| Summer Semester 2013 | Geometric Numerical Integration | Lecture |
| Numerical methods in mathematical finance II | Lecture | |
| Winter Semester 2012/13 | Numerical methods in mathematical finance | Lecture |
| Seminar "Zeitintegration" | Seminar | |
| Winter Semester 2011/12 | Seminar | Seminar |
| Winter Semester 2010/11 | Seminar für Lehramtsstudierende: Mathematische Modelle | Seminar |
Research
My focus lies on the construction of numerical methods for stochastic reaction networks modeling the dynamics of biochemical processes.
A stochastic model uses randomness to describe hugely complex biophysical processes like regulation of gene expression or intracellular viral kinetics, with the mathematical formulation being provided by a Markov jump process. The corresponding probability distribution is the main object of interest in stochastic reaction kinetics and is obtained as the solution of the Chemical Master Equation (CME). However, the task of solving this equation is not trivial due to the curse of dimensionality: the computational effort grows exponentially with the number of species involved in the reaction network.
I work on mitigating the effects of the curse of dimensionality and make the CME and other high-dimensional problems computationally tractable.
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Research interests
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More information about my research area can be found here.
PhD Thesis
Tudor Udrescu. Numerical Methods for the Chemical Master Equation, PhD Thesis, online in Elektronischen Volltext-Archiv (EVA), Karlsruhe Institute of Technology (KIT), 2012.
Publications
Articles
- Tobias Jahnke and Tudor Udrescu. Solving chemical master equations by adaptive wavelet compression. Journal of Computational Physics, Volume 229, Issue 16, 5724-5741 (2010). As IWRMM 10/04 Preprint here.
- Gheorghe Juncu, Aurelian Nicola, Constantin Popa, Tudor Udrescu. Nonlinear multigrid methods for solving Richards’ equation in two space dimensions. Carpathian Journal of Mathematics, 25(1), 82-91 (2009).
- Constantin Popa and Tudor Udrescu. A fast solver for electrostatic field problems. Romanian Journal of Physics, Volume 52, Number 3-4, 237-249 (2007).
In proceedings
- Tudor Udrescu and Tobias Jahnke. An adaptive method for solving Chemical Master Equations using a sparse wavelet basis. AIP Conference Proceedings 1168, 1, 489-492 (2009).
- Constantin Popa and Tudor Udrescu. A fast approximation for discrete Laplacian, Proceedings of the 4th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, Constanta 2005, Publishing House of the Romanian Academy, 181-190 (2006).
Miscellaneous
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| Eugen Petac and Tudor Udrescu. Fundamente Java (Java Fundamentals, in Romanian), MatrixRom Publishing House, Bucharest 2005, 500 pag., ISBN 973-685-944-4 |
Selected Talks
- Numerical methods for the Chemical Master Equation, Promotionskolloquium, Karlsruher Institut für Technologie (KIT), 6 Juni 2012, Slides.
- Investigating the dynamics of metastable biochemical processes using adaptive wavelet methods, 3rd Annual meeting of SPP1324, Eisenach, November 2011.
- Approximating Chemical Master Equations with wavelet compression, 2nd Annual meeting of SPP1324, Eisenach, October 2010.
- Approximating Chemical Master Equations with wavelets, BIT 50 - Trends in Numerical Computing, Lund, Sweden, June 2010.
- An adaptive method for solving Chemical Master Equations using a sparse wavelet basis, ICNAAM, Rethymno, Greece, September 2009.
- Adaptive wavelet-based approximation for the solution of the chemical master equation, ENUMATH Conference, Uppsala University, Sweden, July 2009.
- Adaptive wavelet-based approximation of the Chemical Master Equation, Conference on Scientific Computing, Université de Genevé, Switzerland, June 2009.
- Multigrid-based preconditioning algorithms for diffusion-convection-reaction equations, Karlsruhe University, Germany, February 2008.
- Grid Portals: Providing an Access Point for Grid Services, SCCS-Kolloquium, TU München, Germany, December 2006, Slides.