Seminar Series

 

The Householder Seminar Series is sponsored jointly by the Computational and Applied Mathematics Group at Oak Ridge National Laboratory and the Department of Mathematics at the University of Tennessee, Knoxville. The purpose of the seminar is to have distinguished mathematicians present research on various topics in computational and applied mathematics. The series began in 2014 and is held twice per year, alternating each time between the two institutions.

The seminar series honors Dr. Alton S. Householder, who spent the majority of his career in the Mathematics Division at Oak Ridge National Laboratory (now the Computational Science and Mathematics Division), serving as the director for much of that time, before joining the Department of Mathematics at the University of Tennessee. Householder specialized in mathematical biology and numerical analysis. He is best known as the inventor of the Householder transformation in linear algebra and the root-finding algorithm known as Householder's method, as the founding organizer of the Gatlinburg Symposium on Numerical Linear Algebra (now called the Householder symposium), and as the author of the textbook The Theory of Matrices in Numerical Analysis (1961). Householder also published the monograph Mathematical Biophysics of the Central Nervous System (1946) and the book Principles of Numerical Analysis (1953). He served as president of the Association for Computing Machinery (1954-1956) and the Society for Industrial and Applied Mathematics (1963-1964).

Thomas J.R. Hughes
Isogeometric Analysis: Past, Present, and Future
March 8 and 9, 2016

Abstract: October 1, 2015 marked the tenth anniversary of the appearance of the first paper [1] describing my vision of how to address a major problem in Computer Aided Engineering (CAE). The motivation was as follows: Designs are encapsulated in Computer Aided Design (CAD) systems. Simulation is performed in Finite Element Analysis (FEA) programs.  FEA requires the conversions of CAD descriptions to analysis-suitable formats form which finite element meshes can be developed.  The conversion process involves many steps, is tedious and labor intensive, and is the major bottleneck in the engineering design-through-analysis process, accounting for more than 80% of overall analysis time, which remains an enormous impediment to the efficiency of the overall engineering product development cycle. 

The approach taken in [1] was given the pithy name Isogeometric Analysis. Since its inception it has become a focus of research within both the fields of FEA and CAD and is rapidly becoming a mainstream analysis methodology and a new paradigm for geometric design [2].  The key concept utilized in the technical approach is the development of a new and expanded framework for FEA, based on rich geometric descriptions originating in CAD, resulting in a single geometric model that serves as a basis for both design and analysis. 

In these talks I will describe areas in which progress has been made in developing improved Computational Mechanics methodologies to efficiently solve vexing problems that have been at the very least difficult, if not impossible, within traditional FEA.  I will also present what is known mathematically about IGA, and discuss areas of intense current activity, in which problems remain open, representing both challenges and opportunities for future research (see, e.g., [3]).

[1]  T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis:  CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135-4195.
[2]  J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, U.K., 2009.
[3] Isogeometric Analysis Special Issue (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 284, (1 February 2015), 1-1182.

Biography: Thomas J.R. Hughes holds B.E. and M.E. degrees in Mechanical Engineering from Pratt Institute and an M.S. in Mathematics and Ph.D. in Engineering Science from the University of California at Berkeley. He taught at Berkeley, Caltech and Stanford before joining the University of Texas at Austin in 2002. He is an elected member of the US National Academy of Sciences, the US National Academy of Engineering, the American Academy of Arts and Sciences, the Academy of Medicine, Engineering and Science of Texas, and a Foreign Member of the Royal Society of London, the Austrian Academy of Sciences, and the Istituto Lombardo Accademia di Scienze e Lettere. Dr. Hughes has received honorary doctorates from the universities of Louvain, Pavia, Padua, Trondheim, Northwestern, and A Coruña.

Dr. Hughes is one of the most widely cited authors in Engineering Science. He has received the Huber Prize and Von Karman Medal from ASCE, the Timoshenko, Worcester Reed Warner, and Melville Medals from ASME, the Von Neumann Medal from USACM, the Gauss-Newton Medal from IACM, the Computational Mechanics Award of the Japan Society of Mechanical Engineers, the Grand Prize from the Japanese Society of Computational Engineering and Sciences, the Computational Mechanics Award of the Japanese Association for Computational Mechanics, the Humboldt Research Award for Senior Scientists from the Alexander von Humboldt Foundation, the AMCA Award for an International Scientific Career from the Argentinian Association for Computational Mechanics, and the Wilhem Exner Medal from the Austrian Association für SME (Öesterreichischer Gewerbeverein, OGV). The Special Achievement Award for Young Investigators in Applied Mechanics is an award given annually by the Applied Mechanics Division of ASME. In 2008 this award was renamed the Thomas J.R. Hughes Young Investigator Award. In 2012 the Computational Fluid Mechanics Award of the United States Association of Computational Mechanics was renamed the Thomas J.R. Hughes Medal.

Quiang Du
Application of Householder transform to transition state search
October 30, 2015

Abstract: Finding transition states on a complex energy landscape is an
interesting computational problem that appears in many applications.
This lecture will discuss how Householder transform plays a useful
role in the design of robust algorithms for effective transition
state search. Rigorous mathematical analysis of such algorithms
will be presented along with some discussion on various applications.

Biography: Dr. Du earned Ph.D. in Mathematics (1988) from Carnegie Mellon University, after which he has held faculty positions at University of Chicago, Michigan State University, Iowa State University, and Hong Kong University of Science and Technology. Dr. Du was most recently the Verne M. Willaman Professor of Mathematics and Professor of Materials Science and Engineering at Penn State University. Recognitions for Dr. Du's work include the Frame Faculty Teaching Award (1992) at Michigan State University, the Liberal Arts and Sciences Award for outreach/extension (2000), the Feng Kang prize in scientific computing (2005), the Eberly College of Science Medal (2007) from Penn State University, and his selection as a 2013 SIAM Fellow for contributions to applied and computational ma-thematics with applications in materials science, computational geometry, and biology.

Dr. Du's research interests are in numerical analysis, mathematical modeling and scientific computation with selected applications in physical, biological, materials, data and information sciences.

Stanley Osher
What Sparsity and ℓ₁ Optimization Can Do For You
September 30, 2015

Abstract: Sparsity and compressive sensing have had a tremendous impact in science, technology, medicine, imaging, machine learning and now, in solving multiscale problems in applied partial differential equations, developing sparse bases for Elliptic eigenspaces. ℓ₁ and related optimization solvers are a key tool in this area. The special nature of this functional allows for very fast solvers: ℓ₁ actually forgives and forgets errors in Bregman iterative methods. I will describe simple, fast algorithms and new applications ranging from sparse dynamics for PDE, new regularization paths for logistic regression and support vector machine to optimal data collection and hyperspectral image processing.

Biography: Stanley Osher is a Professor of Mathematics, Computer Science, Chemical Engineering and Electrical Engineering at UCLA. He is also an Associate Director of the NSF-funded Institute for Pure and Applied Mathematics at UCLA. He received his MS and PhD degrees in Mathematics from the Courant Institute of NYU. Before joining the faculty at UCLA in 1977, he taught at SUNY Stony Brook, becoming professor in 1975. He has received numerous academic honors and co-founded three successful companies, each based largely on his own (joint) research. He has co-invented and/or co-developed the following widely used algorithms: 1.) Essentially nonoscillatory (ENO), weighted essentially nonoscillatory (WENO) and other shock capturing schemes for hyperbolic systems of conservation laws and their analogues for Hamilton-Jacobi equations; 2.) The level set method for capturing dynamic surface evolution; 3.) Total variation and other partial differential based methods for image processing; 4.) Bregman iterative methods for L1 and related regularized problems which arise in compressive sensing, matrix completion, imaging and elsewhere; 5.) Diffusion generated motion by mean curvature and other threshold dynamics methods. Osher has been elected to the US National Academy of Science and the American Academy of Arts and Sciences. He was awarded the SIAM Pioneer Prize at the 2003 ICIAM conference and the Ralph E. Kleinman Prize in 2005. He was awarded honorary doctoral degrees by ENS Cachan, France, in 2006 and by Hong Kong Baptist University in 2009. He is a SIAM and AMS Fellow. He gave a plenary address at the 2010 International Conference of Mathematicians and the John von Neumann Lecture at the SIAM 2013 annual meeting. He is a Thomson-Reuters highly cited researcher--among the top 1% from 2002-2012 in both Mathematics and Computer Science. In 2014 he received the Carl Friedrich Gauss Prize from the International Mathematics Union, which is regarded as the highest prize in applied mathematics. His current interests involve information science which includes optimization, image processing, compressed sensing and machine learning and applications of these techniques to the equations of physics, engineering and elsewhere.