Fall '14 Distinguished Seminar Series in Computational Science and Engineering

September 18: Professor Andy Philpott,University of Auckland
September 25: Professor Christoph Schwab, ETH Zurich
October 16: Professor Lexing Ying, Stanford University
October 30: Professor Stephen Wright, University of Wisconsin

Thursday September 25, 2014 | 4:00 PM | 56-114

Infinite-Dimensional Numerical Analysis
Christoph Schwab
Seminar for Applied Mathematics
ETH Zurich

Spurred by the emerging engineering discipline of Uncertainty Quantification and the `big-data, sparse information' issue, engineering and life-sciences have seen an explosive development in numerics of direct-, inverse- and optimization problems for (deterministic or stochastic) differential equations on high- or even infinite-dimensional state- and parameter-spaces, and for statistical inference on these spaces, conditional on given (possibly large) data.

One objective of this talk is a (biased...) survey of several emerging computational methodologies that allow efficient treatment of high- or infinite-dimensional inputs to partial differential equations in engineering, and to illustrate their performance by computational examples.

We address in particular Multilevel Monte-Carlo (MLMC) and Multilevel Quasi-Monte-Carlo (MLQMC) Methods, adaptive Smolyak and generalized polynomial chaos (gpc), of Galerkin and collocation type, and tensor compression techniques.

A second objective is to indicate elements of a mathematical basis for these methods that has emerged in recent years that has allowed to prove dimension-independent rates of convergence. The reates are shown to be limited only by the order of the method and by certain sparsity measures for the uncertain inputs' KL, gpc or ANOVA decompositions.

Examples include stochastic elliptic and parabolic PDE, their Bayesian inversion, control and optimization, reaction rate models in biological systems engineering, shape inversion in acoustic and electromagnetic scattering, and nonlinear hyperbolic conservation laws.

Despite favourable scaling, massively parallel computation is, as a rule, required for online simulations of realistic problems. Scalability and Fault Tolerance in an exascale compute environment become crucial issues in their practical deployment.

Grant support by Swiss National Science Foundation (SNF), ETH High Performance Computing Grant, and the European Research Council (ERC).

Thursday October 16, 2014 | 4:00 PM | 56-114

Inverting high frequency wave equations
Lexing Ying
Department of Mathematics and Institute for Computational and Mathematical Engineering
Stanford University

Wave is ubiquitous as we see it everywhere around us. The numerical solution of high frequency wave propagation has been a longstanding challenge in computational science and engineering. This talk addresses this problem in the time-harmonic regime. We consider a sequence of examples with important applications, and for each we construct an efficient preconditioner (approximate inverse) that allows one to solve the system with a small number of iterations. From these examples emerges a new framework, where sparsity, geometry of wave phenomenon, and highly accurate discretizations are combined together to address this challenging topic.

Thursday October 30, 2014 | 12:00 PM | 37-212

Optimimization in Electrical Power Grid Monitoring and Analysis
Stephen Wright
Computer Science Department
University of Wisconsin-Madison

In quasi-steady state, the electrical power grid is well modeled by a system of algebraic equations that relate the supplies and demands at nodes of the grid to (complex) voltages at the nodes and currents on the lines. This "AC model" can be used to formulate nonlinear optimization problems to study various issues related to monitoring and security of the grid. We discuss three such issues here. The first is restoration of feasible operation of the grid following a disruption, with minimal shedding of demand loads. The second issue is vulnerability analysis, in which we seek the attack that causes maximum disruption to the grid, as measured by the amount of load that must be shed to return it to feasibility. The third issue is the use of streaming data from phasor measurement units (PMUs) to detect single-line outages rapidly, and optimal placement of these units to maximize reliability of detection. In each case we discuss the optimization models and algoithms that are used to formulate and solve these problems.