There is an in-person CAM seminar today @ 3:35pm (In 15 minutes)!

It will take place in

Ayres 112

Title + abstract are below.

Best,
Abner

Speaker: Stefan Schnake

Affiliation: ORNL

 

Title: Title Residual based rank adaptive algorithms for dynamic low-
rank approximation 

Abstract: Numerical discretizations of kinetic equations often suffer
from the curse of dimensionality which makes full resolution
computations intractable. A recent and popular technique to reduce the
order of complexity for these systems is Koch and Lubich’s Dynamic Low-
Rank Approximation (DLRA) which seeks to evolve the PDE on a low-rank
manifold. Numerical integrators utilizing DLRA accurately capture low-
rank features of kinetic systems by updating the global basis functions
in time, but few give indicators for when to adaptively increase the
rank of the solution. In this talk, we first present a formulation of
standard discontinuous Galerkin methods as a semi-discrete matrix-
valued ODE which is low memory, provides computationally efficient
evaluations of the discrete operator and easily fits the target
framework of DLRA. Second, we present residual-based indicators for
when to increase the rank of the DLRA solution and which basis vectors
should be added in order to optimally increase accuracy. These
residual-based estimators are also low memory and can be cheaply
computed. Low- and high-rank numerical examples are given at the end of
the talk.0



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