CEE 7710 - [Stochastic Problems in Science and Engineering]

Fall. 3 credits.

Permission of instructor required.

M. D. Grigoriu.

Review of probability theory, random functions, and Monte Carlo simulation. Representation of material properties at various scales by probabilistic models that are consistent with physics and observations. Solutions of stochastic algebraic and differential equations by Monte Carlo simulation, collocation, Galerkin, and reduced order models. Applications include construction of probabilistic models for a broad range of material microstructures, estimates for properties of response fields, for example, potential and stress/strain fields, and bounds on the discrepancy between continuum mechanics solutions and solutions based on high resolution probabilistic models for microstructures.