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Identifier 000395369
Title Parallelization and uncertainty quantification of spatially extended kinetic Monte Carlo methods
Alternative Title Παραλληλοποίηση και ανάλυση ευαισθησίας για χωρικές μεθόδους Kinetic Monte Carlo
Author Αραμπατζής, Γεώργιος
Thesis advisor Κατσουλάκης Μάρκος
Reviewer Χαρμαντάρης, Ευάγγελος
Μακριδάκης, Χαράλαμπος
Κοσιόρης, Γεώργιος
Τσαγκαρογιάννης Δημήτριος
Τσόγκα, Χρυσούλα
Ζουράρης, Γεώργιος
Abstract In the first part of the thesis we present a mathematical framework for constructing and analyzing paral¬lel algorithms for lattice kinetic Monte Carlo (kMC) simulations. The resulting algorithms, Fractional Step kinetic Monte Carlo algorithms (FS-kMC), have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and trans¬port micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel kMC algorithms with exactly the same master equation as the serial one. We carry out a detailed benchmarking of the parallel kMC schemes using available exact solutions, for exam¬ple, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. In the second part we study from a numerical analysis perspective the algorithms proposed in the first part of the work. FS-kMC are fractional step algorithms with a time-stepping window At, and as such they are inherently partially asynchronous since there is no processor communication during the period At. In this contribution we primarily focus on the error analysis of FS-kMC algorithms as approximations of conventional, serial kinetic Monte Carlo. A key aspect of the presented analysis relies on emphasizing a goal-oriented approach for suitably defined macroscopic observables (e.g., density, energy, correlations, surface roughness), rather than focusing on strong topology estimates for individual trajectories. In the third part we propose a new class of coupling methods for the sensitivity analysis of high dimen¬sional stochastic systems and in particular for lattice kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g. coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. We demonstrate in several examples including adsorption, desorption and diffusion kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial kMC such as the Common Random Number approach Keywords. kinetic Monte Carlo, parallel, GPU, Fractional Step, goal-oriented, error analysis, sensitivity analysis, uncertainty quantification, variance reduction, stochastic coupling
Language English
Issue date 2014-06-11
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Doctoral theses
  Type of Work--Doctoral theses
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