October 26, 2009 (Monday)
Speaker: John C. Butcher, University of Auckland, New Zealand
Title of talk: A Beginner's Guide to Numerical ODEs
Room: Group I - 218 Computer Lab
Time: 4:00 - 5:15 pm
Abstract
Ordinary differential equations are at the heart of applied mathematics and arise in models of almost every scientific phenomenon. An analytical solution is not usually available and numerical approximations therefore become necessary. This beginners guide starts with the classical numerical method associated with the name of Euler and shows how this can be generalized to obtain more accurate and efficient numerical procedures. It is hoped to demonstrate that this is not only a useful subject but that it is also a subject which contains some beautiful mathematics.
November 9, 2009 (Monday)
Speaker: Donald T. Poole, Outermost Land Survey, Inc
Title of talk: Land Surveying
Room: Group I - 218 Computer Lab
Time: 4:00 - 5:00 pm
Abstract
My talk will be about the history of land surveying, with an emphasis on the trig aspects of developing accurate measurements and spatial relations. I would like to review the careers available thorough Land Surveying, and finish with a discussion of GPS use in the Land Surveying world. I expect to review, in a general manner, the theory and practice of survey quality gps, the brief history it has enjoyed and the development of more precise geoids. I will discuss the history of the geoids used in the USA up to the most recent 2008 geoid.
November 12, 2009 (Thursday)
Speaker: Misha Kilmer, Tufts University
Title of talk: Linear Algebra meets Image Processing
Room: Group I - 218 Computer Lab
Time: 4:00 - 5:00 pm
Abstract
We consider two types of problems in this talk: image deblurring and image reconstruction for Magnetic Resonance (MR) Imaging. In each case, the discrete forward model consists of a set of linear equations which must be approximately solved in order to obtain the desired image. These problems are ill-posed in the sense that noise in the data (due to modeling, discretization or measurement errors) will contaminate the solution if we use traditional methods to solve the corresponding system of equations. Using the matrix singular value decomposition (SVD), we show that it is possible to ``filter" the noise under certain conditions to achieve reasonable restorations/reconstructions. However, in practice, we cannot compute the SVD for the matrices in either of these applications. Clever alternative algorithms will be *briefly* discussed. This talk will be accessible to anyone with a linear algebra background, and will be complete with plenty of pictures.
November 20, 2009 (Friday)
Speaker: Steven Wise, University of Tennessee at Knoxville
Title of talk: Numerical Methods for Bistable Gradient Systems
Room: Group I - 218 Computer Lab
Time: 4:00 - 5:00 pm
Abstract
I will discuss a very general class of bistable gradient PDE's, giving some well know examples, including the Allen-Cahn and Cahn-Hilliard equations, as motivation. I will then touch upon the main difficulties associated with solving such equations numerically, including issues of efficiency, stability, solvability, and convergence. I present a relatively simple nonlinear numerical scheme based on first order convex splittings. I show how the idea can be generalized to obtain second-order convex splitting schemes. In both cases I demonstrate that solutions to schemes can be efficiently obtained using nonlinear multigrid and conjugate gradient methods. I will give applications of the schemes in problems of tumor growth, two-phase flow, crystal growth, and epitaxial thin films.