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# Upcoming Seminars

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.

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**ICES Seminar**

Tuesday, Mar 28, 2017 from 3:30PM to 5PM

POB 6.304

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Analysis of the DG method applied to an elliptic problem with nonlinear Newton boundary conditions

by Miloslav Feistauer

Professor, Charles University, Faculty of Mathematics and Physics Prague, Czech Republic

Details

The lecture will be devoted to the analysis of the discontinuous Galerkin method (DGM) for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. Problems of this type appear in the modeling of electrolysis of aluminium, radiation heat transfer problems or in nonlinear elasticity. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate DG solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown that due to the singular boundary points, the solution looses regularity in a vicinity of these points. It comes out that the error estimation depends essentially on the opening angle of the corner points and the nonlinearity in the boundary term. It also depends on the parameter defining the nonlinear behaviour of the Newton boundary condition. Important tools in the analysis are the results of A. Buffa and C. Ortner on compact embeddings of broken Sobolev spaces. Theoretical results are accompanied by numerical experiments showing nonstandard behaviour of the error in the L2-norm and the H1-seminorm.

The results were obtained in cooperation with Filip Roskovec and Anna-Margarete Sandig.

Bio

Prof. Dr. Miloslav Feistauer, DrSc., Dr.h.c., professor of mathematics at Charles University in Prague, was born in Náchod into a family of teachers. From an early age he was interested in mathematics and physics, and also devoted himself to music. After eleven years at high school in 1960, wondering whether to study violin or mathematics, he decided to study at the Faculty of Mathematics and Physics, Charles University. There he has spent all his professional life. After graduating in Applied Mathematics in 1965, he joined the Department of Applied Mathematics. After three years he was appointed lecturer and in the following year received the degree of Doctor of Natural Sciences (RNDr.). In 1972 he defended the scientific degree of Candidate of Sciences (Ph.D.) and in 1982 took a habilitation in mathematics. However, since Prof. Feistauer had From Pokroky Mat. Fyz. Astronom. 58 (2013), 73–75. Translated by Miluša Bubeníková 489 never been politically active, his appointment to the position of associate professor was held up till 1988. In 1990 he was awarded the degree of Doctor of Sciences (DrSc.) and shortly thereafter in 1991 was appointed full professor of mathematics in the field of approximate and numerical methods. In this position he has worked up to now. In the period of 1986–1994 he worked at the Mathematical Institute of Charles University and in 1994 he gained the post of the head of the Department of Numerical Mathematics at Charles University in open competition. In this position he served till 2006. Professionally, Prof. Feistauer's scientific activity has been in the areas of partial differential equations, numerical and computational mathematics and mathematical methods in fluid dynamics. More than 200 papers, 3 monographs, more than 130 invited lectures at universities, more than 180 lectures at conferences (including 68 invited main or plenary lectures and 15 lectures in Oberwolfach), organizing conferences in the Czech Republic and abroad (e.g., member of the Program Committee of the series of the conferences ENUMATH). Teaching activities of Prof. Feistauer are in accord with his successful research activities. In addition to courses on numerical mathematics he presents lectures on mathematical methods in fluid mechanics and mathematical modelling and supervises seminars on continuum mechanics and numerical mathematics. He has significantly contributed to the development of numerical analysis and mathematical modelling at the Faculty of Mathematics and Physics. His lectures are highly evaluated by students. He has trained a number of graduate and doctoral students who were awarded in various national and international competitions. Many of his former students became prominent experts, associate professors and full professors at universities in the Czech Republic and abroad where they continue his work and fulfil his aims and objectives. In the years 1994–2012 Prof. Feistauer was member of the Scientific Council of the Faculty of Mathematics and Physics. He has worked in various committees and bodies of the faculty, but also beyond. He is member of the committee for doctoral studies F11 and M6 at Charles University, he was member of the Scientific Council of the Faculty of Mechanical Engineering, currently he is member of the Scientific Council of the Faculty of Chemical Engineering at the Institute of Chemistry and Technology in Prague and for many years he worked in an advisory commission of the Grant Agency of the Czech Republic. He is member of numerous scientific

societies (GAMM, ISIM, AMS, EUROMECH, ECMI and others) and member of the editorial boards of five international journals. His research and teaching activities were awarded by the medal of the Faculty of Mathematics and Physics and by the silver medal of Charles University. In 2004 he was elected member of the Learned Society of the Czech Republic. In 2006, Prof. Feistauer received another prestigious award, the title of Honorary Doctor of the Technical University of Dresden. Among his more recent awards, Feistauer received the 2008 Memorial Medal of the Charles University and the 2013 Memorial Medal of the Czech Mathematical Society. His nonprofessional interests include the history of art, music: painting, playing violin, viola, and music composition.

Hosted by Ivo Babuska

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**ICES Seminar - Computational Medicine Series**

Tuesday, Mar 28, 2017 from 10AM to 11AM

POB 6.304

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Abdominal Aortic Aneurysm Risk Assessment: Biomechanics or Geometry-based Criterion?

by Ender Finol

Associate Professor, The University of Texas at San Antonio

Details

The rupture of an abdominal aortic aneurysm (AAA) is believed to represent the culmination of a complex vascular mechanism partially driven by the forces exerted on the arterial wall. To prevent rupture, a diagnosed AAA is differentiated by its suitability for surgical or endovascular repair based on its maximum diameter or expansion rate measured over time during patient follow-up. At nearly all major hospitals in the U.S., subjects with aneurysms smaller than 5.5 cm (on average) are placed under clinical surveillance while those greater or equal than 5.5 cm or growing at a rate 3 0.5 cm/year are recommended for elective repair. Since AAA is a largely asymptomatic condition, the screening necessary to measure growth rate over time often cannot be completed. It is a known fact, however, that basing the clinical management of this disease on expansion rate and/or maximum diameter is not a reliable measure of individual rupture risk. This is evident by the number of small aneu

rysms that rupture prior to reaching the critical diameter of 5.5 cm and the many more that are diagnosed at an advanced stage of expansion having exceeded the threshold size for intervention and yet did not rupture. This inability to predict accurately the individual at-risk status of an AAA has led to extensive research into other potential indicators of rupture or equivalent evaluation criteria for assessing the need for repair. Our laboratory is using a combination of image processing and numerical methods to model the geometry and the biomechanical environment of patient-specific AAAs. In this talk, I will describe our efforts in accurately modeling these aneurysms at the organ and tissue scales and the useful quantitative information we can predict from clinical images. This research represents a contribution to the ultimate goal of developing a computational tool that can be used in a clinical setting to assess the individual aneurysm rupture potential on the same day

of AAA diagnosis.

Bio:

Dr. Finol received his B.E. degree in Mechanical Engineering from Universidad de Carabobo, Venezuela (1994), M.S. degree in Mechanical Engineering from University of Massachusetts Lowell (1997) and Ph.D. degree with a dual major in Mechanical and Biomedical Engineering (2002) from Carnegie Mellon University. He is currently an Associate Professor in the Department of Mechanical Engineering at University of Texas at San Antonio and previously a research faculty at Carnegie Mellon Universitys Institute for Complex Engineered Systems (ICES). Dr. Finol operates the Vascular Biomechanics and Biofluids Laboratory and has research interests that include non-destructive tissue mechanics, fluid and solid mechanics modeling of blood vessels, design and optimization of intravascular medical devices, and medical image analysis.

Hosted by Michael Sacks

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**ICES Seminar**

Wednesday, Mar 29, 2017 from 2PM to 3PM

POB 4.304

#### Event Update Notification: NOTE: different day/time/room

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Ab initio computations in many-electron systems

by Shiwei Zhang

Professor of Physics, William & Mary College

Details

One of the grand challenges in materials physics and chemistry is the accurate treatment of interacting many-electron systems. Computational methods need to reach beyond the incredible success afforded by the Kohn-Sham density functional theory (KS-DFT), and its independent-electron and perturbative extensions. This is difficult because of the combinatorial growth of the dimension of the Hilbert space involved, along with the high degree of entanglement produced by the combination of Fermi statistics and electron-electron interactions. We have formulated a computational framework to tackle this challenge, by combining field-theory and Monte Carlo simulations. The framework can be viewed as a superposition of KS-DFT systems evolving in fluctuating auxiliary fields, which are treated by stochastic sampling. We discuss the approach with examples in condensed matter physics and quantum chemistry, and comment on opportunities for its optimization and general application from a mathematical and computational perspective.

Hosted by James Chelikowsky and Graeme Henkelman

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**ICES Seminar**

Thursday, Mar 30, 2017 from 3:30PM to 5PM

POB 4.304

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Recent splitting schemes for the incompressible Navier–Stokes equations

by Peter Minev

Professor, Mathematical & Statistical Sciences, University Of Alberta, Canada

Details

The presentation will be focused on two classes of recently developed splitting schemes for the Navier-Stokes equations. The first class is based on the classical artificial compressibility (AC) method. The original method proposed by J. Shen in 1995 reduces the solution of the incompressible Navier-Stokes equations to a set of two or three parabolic problems in 2D and 3D correspondingly. Unfortunately, its accuracy is limited to first order in time and can be extended further only if the resulting scheme involves an elliptic problem for the velocity vector. Recently, together with J.L. Guermond (Texas A&M University) we proposed a scheme that extends the AC method to any order in time using a bootstrapping approach to the incompressibility constraint that essentially requires to solve only a set of parabolic equations for the velocity. The conditioning of the corresponding linear systems is therefore much better than the one resulting from an elliptic problem for the velocity. The second class of methods is based on a novel approach to the Navier-Stokes equations that reformulates them in terms of stress variables. It was developed in a recent paper together with P. Vabishchevich (Russian Academy of Sciences). The main advantage of such an approach becomes clear when it is applied to fluid-structure interaction problems since in such case the problems for the fluid and the structure, both written in terms of stress variables, become very similar. Although at first glance the resulting tensorial problem is more difficult, if it is combined with a proper splitting, it yields locally one dimensional schemes with attractive properties, that are very competitive to the most widely used schemes for the formulation in primitive variables. Several schemes for discretization of this formulation will be presented together with their stability analysis. Finally, numerical results for a problem with a manufactured solution will be presented.

Hosted by Mary Wheeler

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**ICES Seminar-Student Forum Series**

Friday, Mar 31, 2017 from 10AM to 11AM

POB 6.304

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A Stochastic Operator Approach to Model Inadequacy with Applications to Contaminant Transport

by Teresa Portone

ICES, UT Austin

Details

We present recent developments on the uncertainty quantification of models. Models are imperfect representations of complex physical processes, hence exploring representations of the model inadequacies is crucial. We introduce an inadequacy model in the form of a linear operator acting on the model solution and explore methods for incorporating knowledge of model shortcomings and relevant physics. This representation is developed in the context of scalar dispersion in porous media, but the methods presented are applicable for other models.

Hosted by Gopal Yalla

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**ICES Seminar-Numerical Analysis Series**

Thursday, Apr 6, 2017 from 3:30PM to 5PM

POB 6.304

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Schrödinger’s Smoke

by Albert Chern

Applied and Computational Mathematics, Caltech.

Details

Nearly inviscid incompressible fluids has been a challenging study in analysis and numerical simulation. We introduce a new framework for describing incompressible fluids. In it, the fluid state is represented by a wavefunction evolving under the Schrödinger equation subject to incompressibility constraints. The underlying dynamics satisfies the Euler equation modified with a Landau-Lifshitz force. The latter not only regularizes the singular nature of the Euler equation, but also ensures that dynamics due to thin vortical structures are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. The numerical algorithms for time evolution are exceedingly simple. In the talk I will also discuss the underlying theory which reveals fascinating relations between the Clebsch variables in classical fluids, spins in quantum mechanics, Landau-Lifshitz theory of ferromagnetic material, and the geometry of the 3-sphere.

This is a joint work with Peter Schröder from Caltech, and Felix Knöppel, Steffen Weißmann, Ulrich Pinkall from TU Berlin.

Bio:

Albert Chern is PhD candidate in Applied and Computational Mathematics at Caltech. Research interest: Fluid Dynamics, Computational Math, Discrete Differential Geometry, Computer Graphics.

Hosted by Richard Tsai

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**ICES Seminar-Babuska Forum Series**

Friday, Apr 7, 2017 from 10AM to 11AM

POB 6.304

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Optimal power plant operation

by Sergey Kolos

BP America

Details

The talk is designed to show an example problem that quantitative analysts work on in energy markets. We describe a popular contract in power markets - power plant tolling agreement. First we discuss how power plant constraints are reflected in the contract specification, what are the methods and challenges in pricing such contracts. Then we will review the contribution by BP's last year intern to techniques in accelerating this contract valuation.

Bio:

Sergey Kolos received his PhD in Computational and Applied Mathematics at The University of Texas at Austin in 2005. His mentor was Ehud Ronn and the dissertation topic was “Risk Management in Energy Markets”. Upon completion of the PhD program he started as a quantitative analyst in Citigroup’s Global Commodities unit where he developed various models for pricing and risk management of vanilla and complex energy contracts. In 2015 he joined BP as a senior quantitative analyst. His current research focus is developing algorithms for optimal hedging of complex energy contracts in illiquid markets.

Hosted by Amir Gholaminejad

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**ICES Seminar-Numerical Analysis Series**

Friday, Apr 7, 2017 from 1PM to 2PM

POB 6.304

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Inverse Source Problems for Wave Propagation

by Peijun Li

Professor, Purdue University

Details

The inverse source problems, as an important research subject in inverse scattering theory, have significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, optical tomography, and fluorescence microscopy. Although they have been extensively studied by many researchers, some of the fundamental questions, such as uniqueness, stability, and uncertainty quantification, still remain to be answered. In this talk, our recent progress will be discussed on the inverse source problems for acoustic, elastic, and electromagnetic waves. I will present a new approach to solve the stochastic inverse source problem. The source is assumed to be a random function driven by the additive white noise. The inverse problem is to determine the statistical properties of the random source. The stability will be addressed for the deterministic counterparts of the inverse source problems. We show that the increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies. I will also highlight ongoing projects in random medium and time-domain inverse problems.

Hosted by Kui Ren

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**ICES Seminar**

Tuesday, Apr 11, 2017 from 3:30PM to 5PM

POB 6.304

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TBA

by Ioannis Kevrekidis

TBA

Details

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**ICES Seminar**

Thursday, Apr 13, 2017 from 3:30PM to 5PM

POB 6.304

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Computational Nanoscale Hydrodynamics

by N. R. Aluru

Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign

Details

Many applications in biology, engineering and science rely on efficient hydrodynamic transport through nanometer scale pores and channels. For example, channels and pores in cellular membranes regulate the functionality of the cell by selectively and efficiently exchanging water and ions between extra and intra cellular environments. Selective pores in ultrathin membranes have been shown to be highly efficient for water desalination and power generation. Classical theories often fail to describe fluid physics at nanometer scale. For example, density layering, size dependent fluid properties, restricted translational and rotational motions, charge inversion, flow reversal and several other important phenomena have been observed at nanometer scale. The focus of this talk is to develop efficient theories and computational approaches to accurately describe fluid physics at nanometer scales. First, we will introduce an empirical potential-based quasi-continuum theory (EQT) to accurately predict the structure of confined fluids. We show that the density layering from EQT matches well with molecular dynamics (MD) and EQT is many orders of magnitude faster compared to MD. Next, we show that the EQT framework can be combined with the generalized Langevin theory to compute diffusion of confined fluids and with the classical Navier-Stokes equations to compute the transport of confined fluids. We will show several examples to demonstrate the accuracy and efficiency of the quasi-continuum theory for confined fluids.

Bio

N. R. Aluru received the B.E. degree from the Birla Institute of Technology and Science (BITS), Pilani, India, in 1989, the M.S. degree from Rensselaer Polytechnic Institute, Troy, NY, in 1991, and the Ph.D. degree from Stanford University, Stanford, CA, in 1995. He was a Postdoctoral Associate at the Massachusetts Institute of Technology (MIT), Cambridge, from 1995 to 1997 and he joined the University of Illinois at Urbana-Champaign as an Assistant Professor in 1998.

He is currently the Richard W. Kritzer Professor in the Department of Mechanical Science and Engineering and Director of the Computational Science and Engineering Program at the University of Illinois at Urbana-Champaign (UIUC). He is also affiliated with the Beckman Institute for Advanced Science and Technology, the National Center for Supercomputing Applications (NCSA), the Department of Electrical and Computer Engineering, and the Bioengineering Department at UIUC.

He is a recipient of several honors and awards including the NSF CAREER award in 1999, the NCSA faculty fellowship in 1999, 2006 and 2014, the 2001 CMES Distinguished Young Author Award, the Xerox Award for Faculty Research in 2002, the ASME Gustus L. Larson Memorial Award in 2006, the USACM Gallagher Young Investigator Award in 2007, was named a Willett Faculty Scholar in 2002 and University Scholar in 2010. He held a William Mong Visiting Research Professorship from the University of Hong Kong and is a Fellow of both the U.S. Association for Computational Mechanics (USACM) and the American Society of Mechanical Engineers (ASME). He currently serves as the Associate Editor of the journal Microfluidics and Nanofluidics and has in the past served as the Associate Editor of IEEE/ASME Journal of Microelectromechanical Systems. He also serves on the editorial board of a number of other journals.

Hosted by Omar Ghattas