Adaptive load balancing for massively parallel multi-level Monte Carlo solvers

Abstract

The Multi-Level Monte Carlo algorithm was shown to be a robust solver for uncertainty quantification in the solutions of multi-dimensional systems of stochastic conservation laws. For random fluxes or random initial data with large variances, the time step of the explicit time stepping scheme becomes random due to the random CFL stability restriction. Such sample path dependent complexity of the underlying deterministic solver renders our static load balancing of the MLMC algorithm very inefficient. We introduce an adaptive load balancing procedure based on two key ingredients: (1) pre-computation of the time step size for each draw of random inputs (realization), (2) distribution of the samples using the greedy algorithm to "workers" with heterogeneous speeds of execution. Numerical experiments showing strong scaling are presented. © 2014 Springer-Verlag.