CIMNE researchers Santiago Badia, Jerrad Hampton and Javier Príncipe from the Large Scale Scientific Computing group have recently published the paper "Embedded multilevel monte carlo for uncertainty quantification in random domains" in the american scientific magazine International Journal for Uncertainty Quantification, edited by the Begell House.
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for uncertainty quantification (UQ) in partial differential equation (PDE) models. It combines approximations at different levels of accuracy using a hierarchy of meshes whose generation is only possible for simple geometries. On top of that, MLMC and Monte Carlo (MC) for random domains involve the generation of a mesh for every sample.
KEY WORDS: multilevel Monte Carlo, embedded methods, uncertainty quantification, topological uncertainty, geometric uncertainty, stochastic partial differential equations, random geometry