# Seminars - 2007

## Algorithm Stabilization and Acceleration in Computational Fluid Dynamics: Exploiting Recursive Properties of Fixed-Point Algorithms

By Dr. Aleksandar Jemcov (Fluent Inc.)

Monday, June 4

Abstract: The current trend in applied computational science is the increase of the size and physical complexity of the problems that are being solved. This is evident in Computational Fluid Dynamics (CFD), where the steady increase of the size of the problems leads to computational simulations with several hundred millions of unknowns. In addition, new physical models that incorporate increasingly complex terms in the basic set of the Navier-Stokes equations also contribute to increased stiffness of the problems. Another source of difficulties is the inherent nonlinear nature of the Navier-Stokes system of equations. Modern CFD codes must be capable of handling these difficulties in an efficient manner. In this seminar, a stabilization and acceleration method based on recursive properties of fixed-point algorithms is described that is capable of handling various problems in CFD simulations. The method is equally applicable to iterative solvers used for the solution of systems of linear equations, as well as to nonlinear CFD algorithms. Examples of the use of these stabilization and acceleration algorithms will be demonstrated for 2D and 3D flows with various levels of difficulty.

## A Computational Study of the Travelling Salesman Problem

By Dr. William Cook (Georgie Tech)

Monday, March 19

Abstract: The traveling salesman problem asks for the cheapest tour passing through each of a finite set of cities and returning to the point of departure. We give a brief survey of the history and applications of the TSP, including work on genome sequencing, and report on the solution of the full set of TSPLIB challenge problems, the largest instance having 85,900 cities arising in a VLSI application. We also discuss the solution of geometric TSP instances with exact (real) Euclidean travel costs and make an estimation of the Beardwood, Halton, and Hammersley TSP constant. To treat very large instances of the TSP we describe decomposition techniques for computing tight upper and lower bounds on optimal tour values. Finally, we consider the use of Gomory mixed-integer cutting planes for improving TSP relaxations.

The talk is based on joint work with D. Applegate, R. Bixby, V. Chvatal, S. Dash, D. Espinoza, R. Fukasawa, M. Goycoolea, and K. Helsgaun.

## Real-time Non-Rigid Registration for IGNS: Mesh Generation

By Dr. Nikos Chrisochoides (The College of William and Mary)

Monday, March 5

Abstract: Image Guided Neurosurgery (IGNS) is an important tool for neurosurgical resection, which is a common therapeutic intervention in the treatment of cerebral gliomas (tumours). However, during the course of intervention the areas of interest may dislocate due to brain shift/deformation, making rigid body registration inadequate. Research underway at Brigham and Women's Hospital (Boston) and the College of William and Mary, attempts to use intra-operative MRI to track brain deformation and align (register) preoperative data accord ingly. The challenges of the non-rigid registration methods and software for IGNS are: (1)accuracy, (2) validation, (3) speed (4) fault-tolerance, and (5) ease-of-use. In this talk, we will present a FEM-based method for non-rigid registration in order to motivate our work on real-time mesh generation which we believe can improve the accuracy of the intra-operative imaging where it matters most, i.e., near by the tumor.

Existing parallel mesh generation codes are based on the parallelization of well known sequential mesh generation methods. In this talk we discuss performance of COTS (commercial of-the-shelf) based approaches to real-time (parallel) mesh generation. We will discuss our experience from different parallel meshing methods that are using state-of-the-art sequential software. In addition we will present research on extensions to meet our new requirements like conforming the mesh to the boundary between different tissues.

Joint Centre for Computational Mathematics in Industry and Commerce and Waterloo Institute for Health Informatics Research

## Central Path & Edge Path: Curvature & Diameter

By Dr. Tamas Terlaky (McMaster University)

Monday, February 19

Abstract: It was shown recently that the central path can be bent along the simplex path of Klee-Minty cubes. This lead to tightening the iteration complexity bound of central path following interior point methods. Further, intriguing analogs between edge-paths and central paths arise. We conjecture that the order of the largest total curvature of the central path is the number of inequalities, and that the average diameter of a bounded cell of an arrangement is less than the dimension. We substantiate these conjectures and prove a continuous analog of the $d$-step conjecture.

Joint work with: A. Deza, E. Nematollahi and Y. Zinchenko

## Recent Advances in Bound Constrained Optimization

By Bill Hager (University of Florida)

Monday, February 5

Abstract: This talk focuses on large-scale optimization problems with bound constraints. Such problems arise in many applications including optimal control, variational inequalities, and multiplier methods. In this talk an overview of recent developments in computational techniques is given. A new active set algorithm with strong local and global convergence properties is introduced. An implementation based on the recent conjugate gradient algorithm CG_DESCENT and a cyclic Barzilai-Borwein algorithm is given. Numerical experiments are presented using box constrained problems in the CUTEr and MINPACK-2 test problem libraries.

## The Ontario Centres of Excellence's New Program Portfolio: An Overview/Question and Answer Session

By Gary Brock (Ontario Centres of Exellence)

Thursday, January 25

Abstract: This talk will be of interest to University faculty/researchers interested in hearing about OCE's New Program Portfolio. It will also be a useful opportunity to ask questions regarding the potential applicability of these programs to their own research activities.

Background: The Ontario Centres of Excellence were founded in 1987 and consist of five Centres: Collectively, the Centres promote the economic development of Ontario through directed research, commercialization of technology and training for highly qualified personnel. The Centres are among the few publicly funded institutions that systematically integrate and manage connections from university to marketplace to ensure the successful application of innovative science and technology to profitable new businesses. OCE's new program portfolio is structured in three core areas: Research, Commercialization and Talent. These programs focus on outcomes that address Ontario's competitiveness and economic prosperity. Underpinning these programs are 12 targeted initiatives and one page descriptions of each are posted on our website at http://www.oce-ontario.org/pages/program/programs.php.

The bottom line is to strengthen the connections between Ontario researchers, industry, entrepreneurs and the investment community and accelerate the movement of new knowledge and innovations to the marketplace.

• Centre for Energy
• Centre for Communications and Information Technology
• Centre for Earth and Environmental
• Technologies
• Centre for Materials and Manufacturing
• Centre for Photonics

## SAGE: Software for Algebra and Geometry Experimentation

By Dr. William Stein (University of Washington)

Monday, January 22

Abstract: The goal of SAGE is to create an optimal software environment for research and experimentation in algebra, geometry, number theory, cryptography, and related areas. The speaker started SAGE in 2005 by combining together the very best of existing free software (e.g., Singular, PARI, GAP, Macaulay2, Maxima, gfan, etc), creating interfaces to non-free software (e.g., MAGMA, Maple, Mathematica), and beginning to fill in the gaps with new code. Now many developers have joined him in working on filling these gaps and making SAGE a polished and efficient piece of software. This talk will demo SAGE, and explain how it works.

## Data Mining Research on Networks

By Shirley Mills (Carleton University)

Monday, January 22

Abstract: This talk will be in two parts. The first will discuss general types of problems that offer a rich area for research in computational mathematics; these problems will generally involve high dimensional data and massive data sets but, additionally, the complexities of the datasets present special challenges Applications generally involve networks (static or dynamic) and may involve risk analysis, intrusion detection, analysis for crime, and terrorist behaviour. The second part of the talk will provide some examples of visualization for dynamic networks (e.g. email, weblogs) and attempts to conduct analyses on these networks.