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, November 20th │ 4:00 PM │ 56-114

Online Adaptive Model Reduction for Nonlinear Systems
Benjamin Peherstorfer
MIT AeroAstro

This work presents a nonlinear model reduction approach for systems of equations stemming from the discretization of partial differential equations with nonlinear terms. Our approach constructs a reduced system with proper orthogonal decomposition and the discrete empirical interpolation method (DEIM); however, whereas classical DEIM derives a linear approximation of the nonlinear terms in a static DEIM space generated in an offline phase, our method adapts the DEIM space as the online calculation proceeds and thus provides a nonlinear approximation. The online adaptation uses new data to produce a reduced system that accurately approximates behavior not anticipated in the offline phase.
These online data are obtained by querying the full-order system during the online phase, but only at a few selected components to guarantee a computationally efficient adaptation. Compared to the classical static approach, our online adaptive and nonlinear model reduction approach achieves accuracy improvements of up to three orders of magnitude in our numerical experiments with time-dependent and steady-state nonlinear problems. The examples also demonstrate that through adaptivity, our reduced systems provide valid approximations of the full-order systems outside of the parameter domains for which they were initially built in the offline phase.

Thursday, December 4th │ 4:00 PM │ 56-114

Continuous analogues of matrix factorizations
Alex Townsend
MIT Applied Math

A fundamental idea in matrix linear algebra is the factorization of a matrix into simpler matrices, such as orthogonal, tridiagonal, and triangular. In this talk we extend this idea to a continuous setting, asking: "What are the continuous analogues of matrix factorizations?" The answer we develop involves functions of two variables, an iterative variant of Gaussian elimination, and sufficient conditions for convergence. This leads to a test for non-negative definite kernels, a continuous definition of a triangular quasimatrix (a matrix whose columns are functions), and a fresh perspective on a classic subject.

Thursday, December 11th │ 4:00 PM │ 56-114

MOOSE: An Open Source Platform For Rapid Development of Parallel Multiphysics Simulation Tools
Derek Gaston
MIT Computational Reactor Physics Group

Many physical phenomena can be modeled with systems of partial differential equations. Some examples include nuclear reactors, geothermal flow, microstructural evolution, and fluid-structure interaction. Solving systems of nonlinear equations has typically been achieved with custom software or by combining existing simulation tools. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE; employs a different approach: it provides a generic, common platform for solving multiphysics problems. This technique allows scientists and engineers to focus on the physics while the framework manages the task of parallel, nonlinear solver development. A discussion of the platform’s capabilities and software development model will be followed by several example applications in nuclear physics, geophysics, chemistry, and material science.