UQ benchmark problems for multiphysics modeling

Multiphysics problems are found in numerous areas of science and engineering.
They can take the form of a single equation that tightly couples different types of physical behavior or the form of a system of equations wherein the solution to certain equations is passed to other equations to determine physical properties or loadings or both. Further, there are multiphysics problems that couple different types of physical behavior with fundamentally different descriptions at different scales, as well as multiphysics problems that couple physical behavior in different regions of space through a shared interface.

Uncertainty quantification for multiphysics problems raises various conceptual, mathematical, and numerical challenges. Modeling challenges arise in the characterization of parametric uncertainties and modeling errors that may exist either within subsidiary components or at their interfaces. Further, once these parametric uncertainties and modeling errors are modeled, mathematical challenges arise in the analysis of the local and global existence, uniqueness, regularity, and stability of solutions. Finally, both the use of monolithic solution methods and the use of partitioned solution methods raise numerical challenges relevant to error analysis, stability, convergence, and computational efficiency.

This presentation will report on interactions with the USACM community to set up one or more benchmark problems for multiphysics modeling. The ultimate goal of uncertainty quantification in these benchmark problems will be discussed, and the conceptual, mathematical, and numerical challenges in addressing these benchmark problems will be described.