HYBRID- MONTE CARLO METHOD FOR SOLVING PDEs WITH RANDOM COEFFICIENTS

Abstract

This paper offers an application of the hybrid-Monte Carlo methods for solving
PDEs with random input data defined by the mean and correlation function. The Darcy
equation with random hydraulic conductivity coefficient is chosen to be solved in this way.
The comparison with Monte Carlo and quasi-Monte Carlo methods show a higher capacity
of the hybrid-Monte Carlo method to calculate Eulerian and Lagrangian velocity fields.