Seminars are held Tuesdays and Thursdays in POB 6.304 from 3:30-5:00 pm, unless otherwise noted. Speakers include scientists, researchers, visiting scholars, potential faculty, and ICES/UT Faculty or staff. Everyone is welcome to attend. Refreshments are served at 3:15 pm.
Thursday, Apr 30, 2015 from 3:30PM to 5PM
Cubature formulae, flat extensions and convex relaxation
by Bernard Mourrain
INRIA Sophia Antipolis
Cubature formulae are important ingredients in scientific computing, used to compute efficiently numerical approximation of integrals. Since the work of Radon, their construction has received a lot of attention, including many case studies and specific dedicated methods. In this talk, we present a new general algorithmic approach which allows to generate automatically such cubature formulae.
The problem is transformed into the computation of truncated Hankel operators with flat extension. We analyse the algebraic properties associated to flat extensions and show how to recover the cubature points and weights by eigenvector computation. To compute cubature formula with a minimal number of points, we describe a relaxation hierarchy of convex optimization problems, which minimizes the nuclear norm of the Hankel operators. We show that, when the order of relaxation is high enough, a minimizer of the convex optimization problem
corresponds to a cubature formula. Moreover, the cubature formulae with a minimal number of points are associated to a face of the corresponding convex set. This new method is illustrated on some examples, for which we obtain new minimal cubature formulae.
(joint work with M.A. Bucero and C. Bajaj)
Hosted by Chandrajit Bajaj
ICES Seminar - Center for Cardiovascular Simulation
Monday, May 4, 2015 from 10:30AM to 11:30AM
"Cardiovascular Mathematics - From the Computer Lab to the Bedside: Perspectives and Challenges"
by Alessandro Veneziani
Mathematical and numerical modelling of cardiovascular problems has experienced a terrific progress in the last years, evolving into a unique tool for patient-specific analysis. However, the extensive introduction of numerical procedures as a part of an established clinical routine and more in general of a consolidated support to the decision making process of physicians still requires some steps both in terms of methods and infrastructures (to bring computational tools to the operating room or to the bedside). The quality of the numerical results needs to be carefully assessed and certified. An important research line - quite established in other fields - is the integration of numerical simulations and measurements in what is usually called Data Assimilation. A rigorous merging of available data (images, measures) and mathematical models is expected to reduce the uncertainty intrinsic in mathematical models featuring parameters that would require a patient-specific quantification; and to improve the overall quality of information provided by measures. However, computational costs of assimilation procedures - and in particular variational approaches - may be quite high, as typically we need to solve inverse problems, dual and possibly backward-in-time equations. For this reason, appropriate model reduction techniques are required, to fit assimilation procedures within the timelines and the size of patient cohorts usually needed by medical doctors. In this talk, we will consider some applications of variational data assimilation in vascular and cardiac problems and associated model reduction techniques currently investigated to bring numerical simulations into the clinical routine. For solving incompressible flows in network of pipes we will address hierarchical modeling (HiMod) of the solution of partial differential equations in domains featuring a prevalent mainstream, like arteries. The HiMod approach consists of approximating the main direction of each vessel with finite elements, coupled with spectral approximation of the transverse dynamics. The rationale is that a few modes are enough to a reliable approximation of secondary motion. In addition, modal adaptivity allows to tune the local accuracy of the model. This results in a "psychologically" 1D modeling to be compared with classical approaches based on the Euler equations. Finally, we will address some more advanced applications of geometrical processing for (a) investigating patient-specific bioresorbable stents; (b) supporting decision making of neurosurgeons in deploying flow diverters for cerebral aneurysms.
Professional Preparation: Politecnico di Milano (Italy), Laurea degree in Electronic Engineering, 1994; University of Milano, Ph.D. in Applied Mathematics (Numerical Analysis), 1998.
Appointments: Department of Mathematics and Computer Science, Emory University, Associate Professor (since 2007); Biomedical Engineering Program External Faculty, Wallace H. Coulter Biomedical Engineering Department, Georgia Tech & Emory University (since 2009); Politecnico di Milano, Department of Mathematics, Italy, Associate Professor (2002-2007);
Politecnico di Milano, Department of Mathematics, Assistant Professor (2000-2002); University of Verona, Department of Science and Technology, Assistant Professor (1997-2000)
Products: Author of a text book, Co-editor of two books, author of 63 papers on peer-reviewed journals, 21 proceedings, 10 chapters of books.
Honors: 2004 SIAM Outstanding Paper Prize (with A. Quarteroni and P. Zunino); 2007 International Prize “G. Sacchi Landiani” Young numerical analyst;2010 The 4th Annual Research Grant Award for Excellence in Brain Aneurysm Research
Editorial work: Member of the Editorial Board of 3 International Journals
Hosted by Michael Sacks
ICES Seminar-Numerical Analysis Series
Tuesday, May 5, 2015 from 11AM to 11:59PM
Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime
by Jianliang Qian
Professor, Department of Mathematics, Michigan State University
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian computational geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green’s functions of the Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the new method is that the Huygens-Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic
solution so that caustics associated with the usual geometrical- optics ansatz can be treated automatically. The second novelty is that a butterfly algorithm is adapted to carry out the matrix-vector products induced by the Huygens-Kirchhoff integration in O(N log N ) operations, where N is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green’s functions of the Helmholtz equation for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green’s function in nearly optimal complexity in terms of the total number of mesh points, where the prefactor of the complexity only depends on the specified accuracy and is independent of the frequency parameter. Both two-dimensional (2-D) and three-dimensional (3-D) numerical experiments are presented to demonstrate the performance and accuracy of the new method. This is a joint work with Songting Luo and Robert Burridge.
Hosted by Sergey Fomel
Thursday, May 7, 2015 from 3:30PM to 5PM
Key challenges for computational plasma physics and applied math in light of ITER
by Frank Jenko
"Bio: See www.physics.ucla.edu/~jenko/about.html"
University of California, Los Angeles
The ITER experiment in Southern France will be the most complex machine ever built. It is part of a plan to create a new type of energy source based on fusion. A central problem in this context is to reliably predict the turbulent transport processes inside the hot, magnetically confined plasmas. An alliance between computational plasma physics and applied math will be needed to tackle this grand challenge. This is a great opportunity for both of these research fields to join forces and make a big difference in an area of great societal concern. Some key challenges will be outlined, together with initial progress and future perspectives.
ICES Seminar-Numerical Analysis Series
Thursday, May 7, 2015 from 11AM to 11:59AM
Digital Filters in Multigrid
by Gustaf Soderlind
Professor, Center for Mathematical Sciences, Lund University
Abstract: Multigrid methods are based on a separate iterative treatment of high frequency (HF) and low frequency (LF) errors. HF is suppressed by a smoother, and LF is taken care of by “coarse grid correction”. Mapping fine grid residuals to the coarse grid is fraught with aliasing, and in this talk we examine special restriction operators based on anti-aliasing digital filters used in down-sampling in signal and image processing. Without anti-aliasing, the coarse grid correction is not sufficiently accurate, but with dedicated high order anti-aliasing filters, in combination with corresponding reconstruction filters, there is a possibility to use “aggressive” coarsening, bypassing intermediate grids. We demonstrate proof of concept for two-point boundary value problems and outline a two-grid (two-scale) method, with broadband smoothing and up to 16:1 coarsening with fast convergence.
Hosted by Bjorn Engquist
ICES/BME Joint Seminar - CCS Series
Monday, May 11, 2015 from 10:30AM to 11:30AM
Bioengineering of Extracellular Matrix
by Narendra Vyavahare
The extracellular matrix (ECM) is a collection of extracellular molecules secreted by cells that provide structural and biochemical support to the surrounding cells. It not only provides physical structure to tissues but also provides important cues for intercellular signaling. Cell survival and function depends on the healthy ECM surrounding the cells. Under various disease conditions ECM is either improperly assembled or degraded due to inflammation. Such alteration in ECM can be devastating for tissue and organ function and can cause significant morbidity and mortality. Regenerative approaches for tissues need to provide correct content and 3D architecture of ECM molecules for creating functional tissues.
One of the major extracellular matrix proteins is elastin. Elastic fiber degradation causes loss of elastic recoil in tissues and can be fatal in aortic aneurysms or in COPD. Unfortunately, our body cannot regenerate degraded elastic fibers. There are no therapies to stop degradation of elastin or allow cells to regenerate lost elastin. Research in our laboratory will be highlighted in this area where we have found out ways to stop degradation and regeneration of elastic fibers. The talk will discuss recent advances in targeted therapies. He will provide some specific examples of advances from his own research.
Dr. Naren Vyavahare is a Hunter Endowed Chair and Professor of Bioengineering at Clemson University, Clemson, SC, USA. Dr. Vyavahare research and teaching interests are in the area of heart valve biomaterials, site-specific therapies, and extracellular matrix remodeling in tissue regeneration. Dr. Vyavahare is a Director of NIH funded South Carolina Bioengineering Center of Regeneration and Formation of Tissues (SC BioCRAFT). Dr. Vyavahare’s research is published in over 150 journal publications and conference proceedings, and 6 book chapters; additionally Dr. Vyavahare holds 13 International and US Patents. Some of the patents are now licensed to companies to develop products. He has graduated 10 PhD students and 20 MS students as a major advisor. Dr. Vyavahare is the recipient of many awards including; McQueen Quattlebaum Faculty Excellence Award, Clemson University and Alumni award for outstanding achievement in research, Clemson University. He is a Fellow of American Institute of Medical and Biological Engineering (AIMBE), Dr. Vyavahare is an active participant in several scientific societies and conference series; he chaired Cardiovascular Biomaterials special interest group in the Society for Biomaterials, he was chair of the North American Vascular Biology workshop in 2013. Prior to joining Clemson, Dr. Vyavahare served as a Research Assistant Professor at the University of Pennsylvania School of Medicine (1996-1999), and University of Michigan (1993-1996). He finished his PhD at National Chemical Laboratory, in India (1990). His current research includes targeted treatments to restore extracellular matrix and tissue function in heart valves, aortic aneurysms, vascular calcification, chronic obstructive pulmonary disease (COPD), and skin disorders.
Hosted by Michael Sacks
Tuesday, May 26, 2015 from 3:30PM to 5PM
Equation-Oriented Flowsheet Simulation and Optimization Using Pseudo-Transient Models
by MIchael Baldea
Assistant Professor, Chemical Engineering, UT Austin (and ICES Affiliated Faculty)
In this presentation, we introduce a new process modeling and simulation framework that relies on pseudo-transient continuation to improve the convergence properties of chemical process flow-sheet models. The steady-state models of unit operations are reformulated as differential-algebraic equation (DAE) systems that have the same steady-state solution as the original model. We present a generic model reformulation algorithm and a library of pseudo-transient models for the most widely-used unit operations. We then develop a flow-sheet optimization strategy by seamlessly integrating these models with a time-relaxation optimization algorithm implemented in gPROMS. Several industrial case studies will be discussed to illustrate the theoretical ideas.
Hosted by Robert Moser