Numerical Analysis Research Club

The Numerical Analysis Research Club (NARC) at the University of Washington meets once a week for a combination of seminars, student presentations and research discussions. Anyone interested in numerical analysis or scientific computing is welcome to attend.

June 11, 2015

Speaker: Deep Ray
Title: A sign preserving WENO reconstruction

(1:30-2:30 in Lewis 208)

Abstract: A third-order WENO reconstruction is proposed, which satisfies the sign property required for constructing high resolution entropy stable finite difference scheme for conservation laws. The reconstruction technique, which is termed as SP-WENO, is endowed with additional properties making it a more robust option compared to ENO schemes of the same order. The performance of the proposed reconstruction is demonstrated via a series of numerical experiments for linear and nonlinear scalar conservation laws. This work was done jointly with Ulrik S. Fjordholm.

June 4, 2015

Speaker: Trevor Caldwell
Title: Near-normal dilations of nonnormal operators

(1:30-2:30 in Lewis 208)

A dilation of an operator on a Hilbert space is an operator on a larger Hilbert space whose restriction to composed with the orthogonal projection onto is . Using results from operator theory, one can show that every square matrix has a near-normal dilation, a dilation similar to a normal matrix via a similarity transformation with small condition number whose spectrum lies on the boundary of the numerical range of . Using this perspective, we can think of a nonnormal matrix as an orthogonal projection of a near-normal operator with spectrum on the boundary of the numerical range of . In this talk, we numerically compute these near-normal dilations for a variety of matrices, and illustrate their use in understanding bounds on functions of matrices.

May 14, 2015

Speaker: Scott Moe
Title: The Differential Transform Method for Hyperbolic PDEs

(1:30-2:30 in Lewis 208)

The Lax-Wendroff method is a single-step second order (in space and time) discretization of hyperbolic PDE. It works by first computing a time Taylor series of your solution, and then using the PDE to convert time-derivatives into space derivatives. It is possible to extend this methodology to compute higher order Taylor series, however this can be prohibitively expensive and also extremely messy. Recently so called Differential Transform techniques originating in automatic differentiation have been adapted to computing the time Taylor series necessary for Lax-Wendroff style time stepping. During this talk Scott will introduce these methods and go through some numerical examples.

About NARC

The goals of the Numerical Analysis Research Club are to:

  • Provide a forum to discuss recent journal articles and pre-prints on interesting topics in numerical analysis or scientific computing, especially on topics related to our research. Students not yet actively involved in their own research projects can consider leading such discussions as a way to learn about interesting problems and explore some possibilities. Looking through the contents of recent issues of journals in this area may provide ideas for topics, e.g. those listed here.
  • Provide an informal atmosphere for students, postdocs, and faculty to practice talking about their research, get feedback and suggestions, and keep others informed about what they are doing.
  • Provide a forum for researchers from around campus or elsewhere to present interesting computational results or get advice on the algorithms they are using.

You are encouraged to subscribe to NA-Digest for weekly news on numerical analysis.

Some journals containing papers suitable for discussion.

UWNARC Google group: Sign up here for email or to view recent discussions.

Calendar for NARC

For a list of previous NARC events, please see UW NARC Archive.