## Solving the master equation without kinetic Monte Carlo: tensor train approximations for a CO oxidation model

Please always quote using this URN: urn:nbn:de:0297-zib-55743
• In multiscale models of heterogeneous catalysis, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. This usually is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO_2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

Author: Patrick Gelß, Sebastian Matera, Christof Schütte ZIB-Report alternating linear scheme; heterogeneous catalysis; kinetic Monte Carlo; master equation; tensor decompositions; tensor train format 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A69 Multilinear algebra, tensor products 65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems 65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L15 Eigenvalue problems 80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A30 Chemical kinetics [See also 76V05, 92C45, 92E20] 2015/08/19 ZIB-Report (15-41) 1438-0064

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