# Dresden 2017 – wissenschaftliches Programm

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# O: Fachverband Oberflächenphysik

## O 107: Heterogeneous Catalysis: Theory II

### O 107.8: Vortrag

### Freitag, 24. März 2017, 12:15–12:30, TRE Phy

**Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model** — •Patrick Gelß^{1}, Sebastian Matera^{1}, and Christof Schütte^{1,2} — ^{1}Freie Universität Berlin, Germany — ^{2}Zuse Institut Berlin, Germany

Kinetic Monte Carlo (kMC) simulations have become an important tool for modeling chemical kinetics on catalytic surfaces. Their appealing feature is the unbiased solution of the Markovian master equation, which results from a given microkinetic mechanism, while not being affected by the *curse of dimensionality*. However, the need to perform one reaction step after the other makes kMC ineffective for stiff problems, which are characterized by a large disparity in the values of the employed rate constants. We have developed an alternative approach with tunable accuracy, which directly solves the master equation by exploiting the Tensor Train Format[1]. Using a reduced model for the CO oxidation on RuO_{2}(110), we benchmark the approach against highly accurate kMC simulations. We demonstrate that numerical accuracy and linear scaling in the system size can be achieved for a large range of input parameters. The advantage over the kMC approach is illustrated for a problem with increasing stiffness, where our approach is hardly affected but the computational costs for kMC explode.

[1] P. Gelß, S. Matera, C. Schütte, J. Comput. Phys., 314, pp. 489–502 (2016)