Speaker: Michael Eldred  

Title: Multilevel-Multifidelity Approaches for Uncertainty Quantification and Design

 

Abstract:

In the simulation of complex physics, multiple model forms of varying fidelity and resolution are commonly available.  In computational fluid dynamics, for example, common model fidelities include potential flow, Reynolds-averaged Navier-Stokes, and large eddy simulation, which are further augmented by a variety of subgrid-scale turbulence models and spatio-temporal discretizations.  In this presentation, we focus on novel algorithms that simultaneously exploit multiple model forms and multiple resolutions, both for uncertainty quantification (UQ) and for optimization under uncertainty (OUU).  These hybrid methods exploit multifidelity methods across the model form hierarchy in combination with multilevel accelerators across an associated discretization hierarchy, manifesting as multilevel control variate and polynomial expansion methods in the UQ case and trust-region multigrid optimization in the OUU case.  These techniques will be demonstrated for both model problems and engineered systems, and will be placed within the broader context of algorithm research and development within the Dakota project at Sandia.