We then study the one dimensional case where the particles undergo a random walk on a lattice, next to a continuum region. As the atomistic region is random, this technique yields a fixed point iteration of distributions. We run numerical tests to study the long term behavior of such an iteration, and compare the results with the deterministic case. We also discuss a probability transition matrix approach, in which we assume that the boundary conditions at each iterations follow a Markov chain.Next, since w(l) = 0 and ua#39;(0) = h, we have aha(0)w(0)+ / aua#39;wa#39;dx a / fwdx. Jo Jo The finite element formulation to find u Ap VT such that w) = (/, io) + hA(0) w(0) for all u; Ap Vw, (3.1.4) where B(u, v) = J^aua#39;va#39;dx and = J^uvdz. Equation (3.1.4) isanbsp;...

Title | : | An Adaptive Algorithm for an Elliptic Optimization Problem, and Stochastic-deterministic Coupling: A Mathematical Framework |

Author | : | Sheldon Lee |

Publisher | : | ProQuest - 2008 |

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