Un of Tenn | Math Department

Seminars and Colloquiums
for week of November 21, 2011

Speaker:

Prof. Luis Finotti, Monday
Prof. Jan Rosinski, Monday
Clayton Webster, Computer Science and Mathematics Division, ORNL, Monday

If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Judy Day.

Monday, November 21

ALGEBRA SEMINAR
TIME: 2:30 -- 3:20 p.m.
ROOM: Ayres B004
SPEAKER: Prof. Luis Finotti
TITLE: Construction of Witt Vectors (Part 2)
ABSTRACT: We will continue with the construction of Witt vectors.

PROBABILITY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 122
SPEAKER: Prof. Jan Rosinski
TITLE: Ito-Nisio Theorem in Skorohod space. Part 3: Applications to stable processes
ABSTRACT: We illustrate applications of the theorem considering cadlag symmetric stable processes. The Ito-Nisio Theorem in Skorohod space allows to strengthen LePage representation of such processes and derive explicit representations of their jumps, and of the related functionals in non-Markovian setting.The talk is based on a joint work with Andreas Basse-O'Connor.

DE/APPLIED and COMPUTATIONAL MATH SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 113
SPEAKER: Clayton Webster, Computer Science and Mathematics Division, ORNL
TITLE: Adaptive sparse grid generalized stochastic collocation methods for PDEs with random input data
ABSTRACT: Our modern treatment of predicting the behavior of physical and engineering problems often relies on approximating solutions in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. The goal of the mathematical and computational analysis becomes the prediction of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of some responses of the system (quantities of physical interest), given the probability distribution of the input random data. For higher accuracy, the computer simulation must increase the number of random variables (stochastic dimensions), and expend more effort approximating the quantity of interest within each individual dimension. The resulting explosion in computational effort is a symptom of the curse of dimensionality. Adaptive sparse grid generalized stochastic collocation (gSC) techniques yield non-intrusive methods to discretize and approximate these higher dimensional problems with a feasible amount of unknowns leading to usable methods.

It is the aim of this talk to survey the fundamentals and analysis of an adaptive sparse grid gSC method utilizing both local and global polynomial approximation theory. We will present both a priori and a posteriori approaches to adapt the anisotropy of the sparse grids to applications of both linear and nonlinear stochastic PDEs. Rigorously derived error estimates, for the fully discrete problem, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical results and are used to show that, for moderately large dimensional problems, the adaptive sparse grid gSC approach is extremely efficient and superior to all examined methods, including Monte Carlo.

Past notices: