Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling

  title={Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling},
  author={Grigoris Katsiolides and Eike Hermann M{\"u}ller and Robert Scheichl and Tony Shardlow and Michael B. Giles and David J. Thomson},
  journal={J. Comput. Phys.},

Assessing erosion and flood risk in the coastal zone through the application of the multilevel Monte Carlo method

The risk from erosion and flooding in the coastal zone has the potential to increase in a changing climate. The development and use of coupled hydro-morphodynamic models is therefore becoming an ever

Multilevel Bayesian Quadrature

This paper proposes to further enhance multilevel Monte Carlo through Bayesian surrogate models of the integrand, focusing on Gaussian process models and the associated Bayesian quadrature estimators, and shows using both theory and numerical experiments that this approach can lead to improvements in accuracy.

Multilevel Monte Carlo Covariance Estimation for the Computation of Sobol' Indices

  • Paul MycekM. Lozzo
  • Computer Science, Mathematics
    SIAM/ASA J. Uncertain. Quantification
  • 2019
This paper derive and analyze multilevel covariance estimators and adapt the MLMC convergence theorem in terms of the corresponding covariances and fourth order moments, which are used in a sensitivity analysis context in order to derive a multileVEL estimation of Sobol' indices.

Higher-order adaptive methods for exit times of Itô diffusions

. We construct a higher-order adaptive method for strong approximations of exit times of Itˆo stochastic differential equations (SDE). The method employs a strong Itˆo–Taylor scheme for simulating SDE

Error Control of the Numerical Posterior with Bayes Factors in Bayesian Uncertainty Quantification

A bound on the absolute global error tolerated by the numerical solver of the FM in order to keep the BF of the numerical versus the theoretical posterior near one is introduced.



Lagrangian simulation of wind transport in the urban environment

Fluid element trajectories are computed in inhomogeneous urban‐like flows, the needed wind statistics being furnished by a Reynolds‐averaged Navier–Stokes (RANS) model that explicitly resolves

Flow Boundaries in Random-Flight Dispersion Models: Enforcing the Well-Mixed Condition

Abstract Lagrangian stochastic (LS) dispersion models often use trajectory reflection to limit the domain accessible to a particle. It is shown how the well-mixed condition (Thomson) can he expressed

Criteria for the selection of stochastic models of particle trajectories in turbulent flows

Many different random-walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed and several criteria have emerged to distinguish good models from bad. In this paper the

Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems

A rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo lattice rules for lognormal diffusion problems and shows that in practice theMultilevel QMC method consistently outperforms both the multileVEL MC method and the single-level variants even for non-smooth problems.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

It is shown that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

An Introduction to Computational Stochastic PDEs

This book offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis and theory is developed in tandem with state-of-the art computational methods through worked examples, exercises, theorems and proofs.

Adaptive Multilevel Monte Carlo Simulation

An adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithm introduced in AnnaDzougoutov et al.

Numerical Analysis of Multiscale Computations

This workshop proposed to address the following specialized aspects related to the multiscale computational approaches alluded to above, which are interested in developing direct numerical procedures to consistently drive the coarse scale evolution by using snapshots of fine scale solutions.

Multilevel Monte Carlo Path Simulation

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In

A continuation multilevel Monte Carlo algorithm

The asymptotic normality of the statistical error in the MLMC estimator is shown to justify in this way the error estimate that allows prescribing both required accuracy and confidence in the final result.