Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries
For researchers in uncertainty quantification and PDEs, this work provides a practical approach to handle stochastic geometries, though the method is domain-specific and incremental.
This paper develops efficient Monte Carlo sampling and uncertainty quantification methods for elliptic PDEs on domains with stochastic boundaries, using domain transformations to achieve computational gains.
We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.