Numerical Analysis Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

01/23 1:00pm 
Mitchell Institu 
A. Cohen, E. Tadmor and W. Dahmen minisymposium 
``Challenges in Computational Mathematics’'
Albert Cohen, Optimal nonintrusive methods in high dimension;
Wolfgang Dahmen, Error controlled Computation  the merit of residuals;
Eitan Tadmor, Emergent behavior in collective dynamics.
More information can be found at
http://gain.math.tamu.edu/Compmath2019.html
Abstract 

03/06 4:00pm 
BLOC 628 
Uwe Kocher HelmutSchmidtUniversity, Hamburg 
Numerical simulation of coupled flow and deformation in porous media with spacetime methods
The efficient and accurate simulation of coupled flow and deformation in porous media in space and time is of fundamental importance in many engineering fields. The quasistatic and dynamic poroelastic models appear for instance in simulation studies to support the development of nextgeneration batteries. Such must support fastcharging and fastdraining with currents of a factor of at least 100 or more compared to nowadays cuttingedge technologies. Future generation numerical simulation tools must incorporate multiphysics phenomena in which sharp concentration and pressure gradients, high mechanical stresses, elastic wave propagation, memoryeffects on the media parameters, multiphase behavior, crack propagation as well as electrochemical reactions occur. In this contribution highorder spacetime discretisations, including mixed finite elements (MFEM) for the flow variables and interiorpenalty discontinuous Galerkin finite elements (IPDG) for the displacement and velocity variables, are presented. The arising linear block systems are solved with a sophisticated monolithic solver technology with flexible multistep fixedstress physical preconditioning. Inside the preconditioner highly optimized system solvers for low order approximations can be used. Additionally, our solver technology allows for parallelintime application. The performance properties of the solver and for further applications are illustrated by numerical experiments. 

03/08 12:45pm 
BLOC 628 
Sara Pollock University of Florida 
Anderson acceleration improves the convergence rate in linearly converging fixed point methods
The extrapolation method known as Anderson acceleration has been used for decades to speed up nonlinear solvers in many applications, however a mathematical justification of the improved convergence rate has remained elusive. Here, we provide theory to establish the improved convergence rate. The key ideas of the analysis are relating the difference of consecutive iterates to residuals based on performing the inneroptimization in a Hilbert space setting, and explicitly defining the gain in the optimization stage to be the ratio of improvement over a step of the unaccelerated fixed point iteration. The main result we prove is that this method of acceleration improves the convergence rate of a fixed point iteration to first order by a factor of the gain at each step. 

03/20 4:00pm 
BLOC 220 
Antoine Mellet UMD 
Anomalous Diffusion Phenomena: A Kinetic Approach
The derivation of diffusion or driftdiffusion equations from transport equations (such as VlasovFokkerPlanck or Boltzmann equations) is a classical problem. In this talk, we will discuss situations in which the usual derivation fails because the mean squared displacement of the particles does not grow linearly with
time. We will show that such "anomalous diffusion" regimes typically lead to fractional diffusion equations. We will present results in both bounded and unbounded domain and we will discuss some applications to the description of anomalous energy transport in chains of nonharmonic oscillators (FPUalpha and FPUbeta chains).


03/27 3:00pm 
BLOC 628 
Serge Prudhomme Polytechnique Montreal 
TBA 

04/24 3:00pm 
BLOC 628 
Soeren Bartels AlbertLudwigsUniversity Freiburg 
TBA 
The organizer for this seminar is
Bojan Popov.