Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems.

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discretizations of the eigenvalue problem on a hierarchy of increasingly finer meshes. For the discretized, algebraic eigenproblems we use both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi (IRA), providing an analysis of the cost in each case.

Separating internal and externally forced contributions to global temperature variability using a Bayesian stochastic energy balance framework.

Earth's temperature variability can be partitioned into internal and externally forced components. Yet, underlying mechanisms and their relative contributions remain insufficiently understood, especially on decadal to centennial timescales. Important reasons for this are difficulties in isolating internal and externally forced variability.

Multilevel simulation of hard-sphere mixtures.

We present a multilevel Monte Carlo simulation method for analyzing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously studied two-level version.

Critical point for demixing of binary hard spheres.

We use a two-level simulation method to analyze the critical point associated with demixing of binary hard-sphere mixtures. The method exploits an accurate coarse-grained model with two- and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture.

Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model.

We present a method that exploits self-consistent simulation of coarse-grained and fine-grained models in order to analyze properties of physical systems. The method uses the coarse-grained model to obtain a first estimate of the quantity of interest, before computing a correction by analyzing properties of the fine system. We illustrate the method by applying it to the Asakura-Oosawa model of colloid-polymer mixtures.