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The results of a parallel implementation of a randomized vector algorithm for solving systems of linear equations are presented in the paper. The solution is represented in the form of a Neumann series. The stochastic method computes this series by sampling only random columns, avoiding multiplication of matrix by matrix and matrix by vector. We consider the case when the matrix is too large to fit in random-access memory (RAM). We use two approaches to solve this problem. In the first approach, the matrix is divided into parts that are distributed among MPI processes and stored in the available RAM of the cluster nodes. In the second approach, the entire matrix is stored on each node's hard drive, loaded into RAM, and processed in parts. Independent Monte Carlo experiments for random column indices are distributed among MPI processes or OpenMP threads for both approaches to matrix storage. The efficiency of parallel implementations is analyzed. Results are given for a system governed by dense matrices of size 10 4 and 10 5 . [ABSTRACT FROM AUTHOR]

We suggest in this paper a parallel implementation of cellular automation and global random walk algorithms for solving drift–diffusion–recombination problems which in contrast to the classical random walk on spheres (RWS) methods calculate the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is based on the adjoint symmetry property of the Green function and a double randomization approach. The synchronous multi-particle cellular automaton model of drift–diffusion–recombination is based on known cellular automata. The global RWS and cellular automaton models are tested against the exact solutions of the equation. The accuracy and computer time of both algorithms is analyzed. Parallel codes for the Monte Carlo and cellular automaton algorithms are implemented. The domain decomposition method is employed for the cellular automaton parallel implementation. The global random walk algorithm is parallelized by the Monte Carlo trajectories distribution among the cluster cores. The efficiency of the parallel codes is studied. [ABSTRACT FROM AUTHOR]

Stochastic models and simulation algorithms for spatially separated reactants in the vicinity of traps were developed. The methods were applied to simulate electron-hole recombination in inhomogeneous semiconductors. Continuous kinetic Monte Carlo methods were compared with a discrete cellular automata algorithm. Recombination kinetics for pure diffusion and diffusion in the vicinity of tunneling regimes were investigated. A difference in the electron-hole spatial correlations simulated by the discrete and continuous models and the relevant segregation phenomena in two-dimensional (2D) and three-dimensional (3D) semiconductors was discovered. This results in different spatial patterns during segregation of electron and hole clusters. Comparative analysis of different statistical characteristics evaluated by the two studied methods was performed. In addition, the execution time of codes implementing the two models was studied versus the number of electron-hole pairs simulated and the size of the semiconductor domain. [ABSTRACT FROM AUTHOR]