General descriptionThe behavior of many physical systems can be mathematically modeled by deterministic partial differential equations (PDEs). These models however differ from reality for two main reasons: (1) our inability to accurately characterize all parameters of the mathematical model; and/or (2) an intrinsic variability of the physical system. Uncertainty is therefore a fundamental feature of physical systems and needs to be takin into account when building a mathematical model. Examples appear in the description of flows in porous media, behavior of living tissues, combustion problems, deformation of composite materials, earthquake motions, etc. In order to understand the uncertainties inherent in the model, and often represented in a probabilistic setting, we need a process called uncertainty quantification (UQ).
In this course we consider different types of PDEs (elliptic, parabolic, and hyperbolic) with stochastic input parameters (coefficients, forcing terms, boundary conditions, shape of the physical domain, etc.) and study varios numerical techniques for solving the stochastic problems.
Office hoursW 14:30-16:00 SMLC 216
Projects schedule and report due: Schedule