WS, Björn Engquist: Numerical Methodologies for Multiscale Limits, homogenization and interfaces

Speaker
Björn Engquist,The University of Texas at Austin

Abstract
The computational challenge from multiscale differential equations where the smallest scales cannot be practically resolved on the computational mesh has inspired development of a variety of methodologies. We will consider two settings. One where the smaller scales are all over the computational domain and the analytic limit is homogenization and another where the small scales are localized and the analytic limit is an interface. Many of the numerical techniques require scale separation but there are also efforts to reduce the dependence on substantial scale gaps. These, so called, seamless methods mimic the limiting process by rescaling. There is similarity to turbulence modeling, artificial compressibility for incompressible flow and the Car-Parinello technique for molecular dynamics. We will introduce the methodology, present some analysis and numerical examples.