Numerical Analysis Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

09/11 3:00pm 
BLOC 628 
Winnifried Wollner TU Darmstadt 
Optimization of PhaseField Damage Evolution
Within this talk, we will address optimization problems governed by timediscrete phasefield damage processes. The presence of an irreversibility of the fracture growth gives rise to a nonsmooth system of equations. To derive optimality conditions we introduce an additional regularization and show that the resulting optimization problem is wellposed. To tackle discretization errors, as well as convergence in the limit of the irreversibility penalty, an improved differentiability result is shown for the time discrete regularized damage process. Based upon this, we can show that certain local minimizers of the optimization problem can be approximated by the proposed penalty approach. Further, we will give a short discussion of resulting discretization error estimates.


11/06 3:00pm 
BLOC 628 
Simon Pun TAMU 
Computational multiscale methods for firstorder wave equation
In this talk, we present a pressurevelocity formulation of the heterogeneous wave equation and employ the constraint energy minimizing generalized multiscale finite element method to solve this problem. The proposed method provides a flexible framework to construct crucial multiscale basis functions for approximating the pressure and velocity. These basis functions are constructed by solving a class of local auxiliary optimization problems over the eigenspaces that contain local information on the heterogeneity. Techniques of oversampling are adapted to enhance the computational performance. The firstorder convergence of the proposed method is proved and illustrated by several numerical tests. 

11/20 3:00pm 
BLOC 628 
Gunnar Martinsson UT Austin 
Randomized algorithms for large scale linear algebra
The task of solving large scale linear algebraic problems such as factorizing matrices or solving linear systems is of central importance in many areas of scientific computing, as well as in data analysis and computational statistics. The talk will describe how randomization can be used to design algorithms that in many environments have both better asymptotic complexities and better practical speed than standard deterministic methods. 
The organizer for this seminar is
Bojan Popov.