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, Oct 8, 2015 from 3:30PM to 5PM
Non-uniform Grid Based Acceleration of Iterative and Direct Integral Equation Solvers
by Amir Boag
Professor, Physical Electronics Department, School of Electrical Engineering, Tel Aviv University
In this presentation we describe the Non-uniform Grid (NG) approach and demonstrate that it can be employed to accelerate both iterative and direct integral equation-based solvers. The NG approach stems from the observation that, locally, phase and amplitude compensated field radiated by a finite size source is an essentially bandlimited function of the angular and radial coordinates of the source centered spherical coordinate system. Therefore, the radiated field can be sampled on a non-uniform spatial grid (NG) and subsequently evaluated at any point by phase and amplitude compensated interpolation. Using such NG field representation and conventional hierarchical domain decomposition, the multilevel non-uniform grid (MLNG) algorithm reduces the complexity of field evaluation from O(N^2) to O(NlogN) (N being the number of unknowns), thus facilitating fast iterative solution of electromagnetic and acoustic problems. Furthermore, we developed a direct solver using NG-based matrix compression for scattering from quasi-planar objects. In this context, we show that approximately O(N^1.5) complexity is attained for the matrix compression, and the computational cost of the solution for each right-hand-side is approximately of O(N).
Bio: Prof. Amir Boag received the B.Sc. degree in electrical engineering and the B.A. degree in physics in 1983, both Summa Cum Laude, the M.Sc. degree in electrical engineering in 1985, and the Ph.D. degree in electrical engineering in 1991, all from Technion - Israel Institute of Technology, Haifa, Israel. From 1991 to 1992 he was on the Faculty of the Department of Electrical Engineering at the Technion. From 1992 to 1994 he was a Visiting Assistant Professor with the Electromagnetic Communication Laboratory of the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign. In 1994, he joined Israel Aircraft Industries as a research engineer and became a manager of the Electromagnetics Department in 1997. Since 1999, he has been with the Physical Electronics Department of the School of Electrical Engineering at Tel Aviv University, where he is currently a Professor. Dr. Boag's interests are in computational electromagnetics, wave scattering, imaging, and design of antennas and optical devices. He has published over 95 journal articles and presented more than 200 conference papers on electromagnetics and acoustics. In 2008, Amir Boag was named a Fellow of the IEEE for his contributions to integral equation based analysis, design, and imaging techniques.
Hosted by Ali Yilmaz
Tuesday, Oct 13, 2015 from 3:30PM to 5PM
Fast solvers for 3D elastodynamic Boundary Element Methods
by Stephanie Chaillat
Professor, CNRS and Paris Tech
The main advantage of the Boundary Element Method (BEM) is that only the boundaries of the domain are discretized. This leads to a drastic reduction of the total number of degrees of freedom. However, the dimensional advantage with respect to domain discretization methods is offset by the fully-populated nature of the BEM matrix. This presentation will provide an overview of recent works on improving the efficiency of the method both on memory requirements and CPU time. Several numerical validations related to elastic wave propagation problems for large-scale domains will be given.
I will first show the principle of the Fast Multipole Method (FM-BEM) in 3D elastodynamics and visco-elastodynamics,to speed up the solution of the BEM. I will present a new FMM for the elastic half-space Green's functions and discuss on the numerical difficulties related to an efficient implementation.
The FM-BEM is intrinsically based on an iterative solver as we used a matrix-free matrix-vector product to converge to solution. In 3D elastodynamics, the number of iterations can significantly hinder the overall efficiency. To overcome this issue, I will present an analytic preconditioner. It is based on a clever integral representation of the scattered field which naturally incorporates a regularizing operator. When considering Dirichlet boundary value problems, the regularizing operator is a high-frequency approximation to the Dirichlet-to-Neumann operator, and is constructed in the framework of the On-Surface Radiation Condition (OSRC) method.
Finally, I will show an alternative to the FM-BEM. Using the H-matrix arithmetic and low-rank approximations (performed with Adaptive Cross Approximation), we derive a fast direct solver. I will assess the numerical efficiency and accuracy on the basis of numerical results obtained for problems having analytical solutions.
Stéphanie Chaillat-Loseille is a Junior Scientist (CR1 CNRS), POEMS, ENSTA, Palaiseau, France. In 2008, she earned her PhD in Computational Mechanics from the École Nationale des Ponts et Chaussées, France under the direction of Prof. M. Bonnet and Prof. JF. Semblat. Her research interests are primarily in Numerical Methods (Inverse problems, Fast Singular Value Decomposition, Boundary integral equations and boundary element method, Fast multipole method, Hierarchical Matrices, Iterative and direct solvers and Preconditioning ), Mechanics (Acoustics in frequency domain, Elastodynamics in frequency domain, Viscoelastocity, and Wave propagation), and Seismology (Seismic wave propagation and Site effects-seismic wave amplification in alluvial valleys).
Hosted by George Biros
ICES Seminar - CCS Seminar Series
Friday, Oct 16, 2015 from 10AM to 11AM
Elasticity and the Shapes of Tumors
by Krishna Garikipati
Professor, University of Michigan
It is well established that the mechanical environment influences cell functions in health and disease. In this talk, I will address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we have found that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurred when the tumors were grown in hydrogels that were stiffer than the tumors, but when they were grown in more compliant hydrogels they remained closer to spherical in shape. Using large scale, nonlinear elasticity computations we showed that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesized that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. Such studies result may hold significance for explaining the shape progression of early solid tumors in vivo and could be an important step in understanding the processes underlying solid tumor growth.
Krishna Garikipati obtained his PhD from Stanford University in 1996, and joined the faculty at University of Michigan in 2000, where he is now a professor of Mechanical Engineering, and Mathematics. He works on mathematical models of coupled, continuum phenomena in biophysics and materials physics. He and his group specialize in large scale, high performance codes for problems in these areas. Among his awards are the Presidential Early Career Award for Scientists and Engineers, and the Research Fellowship of the Alexander von Humboldt Foundation. He also serves as Associate Director for Research of the Michigan Institute for Computational Discovery & Engineering.
Hosted by Michael Sacks
Tuesday, Oct 20, 2015 from 3:30PM to 5PM
On the Problem of Singular Limit of the Navier - Stokes- Fourier System with Radiation
by Sarka Necas
Institute of Mathematics, Academy of Sciences of the Czech Republic
We consider relativistic and ”semi-relativistic” models of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in  and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number case we prove the convergence toward the incompressible Navier - Stokes - Fourier system coupled to a system of two stationary transport equations. In the diffusion case we prove the convergence toward the compressible Navier - Stokes - Fourier system with modified state functions (equilibrium case) or toward the compressible Navier - Stokes - Fourier system coupled to a diffusion equation (non equilibrium case). Moreover, the coupling with magnetic field and singular limit will be described. It is a joint work with B. Ducomet.
 B. Ducomet, E. Feireisl, S. Necasova: On a model of radiation hydrodynamics. Ann. I. H. Poincare-AN 28 (2011) 797–812.
Hosted by Ivo Babuska
Thursday, Oct 22, 2015 from 3:30PM to 5PM
Biomechanical Imaging: Shall We See How You Feel
by Assad A. Oberai
Professor, Mechanical, Aerospace, and Nuclear Engineering, Scientific Computation Research Center, Rensselaer Polytechnic Institute
Certain types of diseases lead to changes in the microstructural organization of tissue. Altered microstructure in turn leads to altered macroscopic tissue properties, which are often easier to image than the microstructure itself. Thus the measurement of macroscopic properties offers a window into tissue microstructure and health. In Biomechanical Imaging (BMI) we aim to utilize this association between the macroscopic mechanical properties of tissue and its health by generating images of the mechanical properties and using these to infer tissue microstructure and health. At the heart of BMI lies the solution of an inverse problem in continuum mechanics: given the deformation of the medium (tissue) and a constitutive model, determine the spatial distribution of the material properties. In this talk, I will discuss the well-posedness of this inverse problem and describe efficient and robust algorithms for solving it. I will also describe the development of new constitutive models that are motivated by tissue microstructure. I will end with applications of BMI that include improved in-vivo diagnosis of breast cancer, and imaging elastic properties of tissue at the cellular, and sub-cellular levels.
Assad Oberai is a Professor in the Department of Mechanical Aerospace and Nuclear Engineering at Rensselaer Polytechnic Institute (RPI). He is also the Associate Dean for Research and Graduate Studies in the School of Engineering, and the Associate Director of the Scientific Computation Research Center (SCOREC). Assad started his academic career at Boston University, where he was an Assistant Professor of Aerospace and Mechanical Engineering from 2001 to 2005. He joined the Rensselaer faculty in 2006 as an Assistant Professor, was promoted to Associate Professor in 2007, and to Professor in 2011. Assad received his Bachelors degree in Mechanical Engineering from Osmania University in 1992, an MS in Mechanical Engineering from the University of Colorado in 1994, and a PhD in Mechanical Engineering from Stanford University in 1998. Assad is a recipient of the National Science Foundation Career award in 2005 and the Department of Energy Early Career award in 2004. He was awarded the Thomas J.R. Hughes Young Investigator Award by the American Society of Mechanical Engineers in 2007. He received the Humboldt Foundation Award for experienced researchers in 2009, and the Erasmus Mundus Master Course Lectureship at Universidad Politécnica de Cataluña, Barcelona in 2010. In 2015, he was awarded the Research Excellence Award by the School of Engineering at RPI, and was elected as a Fellow of the United States Association of Computational Mechanics. He is on the board of academic editors for the journal PlosOne.
Hosted by Tom Hughes
ICES Seminar - CCS Series
Friday, Oct 23, 2015 from 1:30PM to 2:30PM
From the Computer Lab to the Bedside: Perspectives and Challenges of Translational Cardiovascular Mathematics
by Alessandro Veneziani
Professor, Departments of Mathematics and Computer Science, Emory University
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; (c) analyzing patients suffering from aortic diseases like dissection and cardiac insufficiency.
Alessandro Veneziani is Full Professor of Mathematics and Computer Science at Emory University Atlanta (GA), USA since September 2015. He graduated in Electronic Eng at the Politecnico di Milano, Italy in 1994 and got his PhD in Applied Math from University of Milan, Italy in 1998. He was previously appointed as Assistant Professor at the University of Verona, Italy (1997-2000) and at the Politecnico di Milano (2000-2002), as Associate Professor at the Politecnico di Milano (2002-2007) and at Emory University (2007-2015). He is also external program faculty at the Department of Biomedical Engineering at GA Tech and Emory. His interests cover mathematical and numerical modeling of problems of fluid dynamics specifically related to hemodynamics, cardiology and the associated computational aspects. He is author of one textbook, co-editor of two research books of around 65 peer-review papers and 20 conference proceedings papers. He is recipient of the 2004 SIAM Outstanding Paper Prize and of the 2007 G. Sacchi-Landriani International Prize. Recently, one of his paper has been listed as one of the most notable paper 2014 by ACM. He is currently PI of 2 NSF Grants, 1 Emory Grant and coPI of 2 Industrial Grants. He has been adviser of 18 PhD students, 10 Undergraduate students and 34 Master Students.
Hosted by Michael Sacks
Thursday, Oct 29, 2015 from 3:30PM to 5PM
The Variational Approach to Fracture for Ductile Materials
by Mike Borden
Professor, Department of Civil, Construction, and Environmental Engineering, North Carolina State University
The determination of complex three-dimensional failure processes has been difficult, if not impossible, with traditional computational approaches.
Traditional finite element methods have achieved some success in two dimensions, but a satisfactory methodology for full three-dimensional configurations has never been achieved. In this presentation I will describe my work to develop a methodology for simulating three-dimensional crack propagation in both brittle and ductile materials. This methodology is based on a phase-field formulation and has several unique attributes: First, all calculations can be performed with reference to the initial mesh, and are independent of the topology of the fractured domain. Second, cracks spontaneously nucleate, bifurcate, trifurcate, etc., without any ad hoc devices determining where these events occur. Third, crack formation is not restricted or related in any way to the structure of the mesh. Fourth, the computer implementation of the formulation is remarkably simple and is exactly the same in three dimensions as it is in two dimensions.
I will describe the work that is being performed in my group to apply phase-field models to dynamic fracture of brittle and ductile materials. As part of this work we have extended existing quasi-static models to dynamic fracture, and introduced a higher-order phase-field model that has shown the potential to provide higher-order accurate results for fracture. I will also discuss our current efforts to develop and quantify the constitutive theory of phase-field models for ductile fracture. Numerical results, which demonstrate that the phase-field approach is able to model complex crack behavior in both two and three dimensions, will be presented.
Dr. Michael Borden is an Assistant Professor in the Department of Civil, Construction, and Environmental Engineering at North Carolina State University. Mike began his academic career at Brigham Young University in Provo, Utah where he earned both a BS and MS in Civil Engineering. He then worked as a member of the technical staff at Sandia National Laboratories where he developed computational geometry methods to support Sandia’s finite element codes. After five years at Sandia, Mike went on to earn a Ph.D. in Computational Science, Engineering, and Mathematics from The University of Texas at Austin. Mike joined the faculty at NC State in 2014.
Hosted by Tom Hughes
Tuesday, Nov 24, 2015 from 3:30PM to 5PM
The Time Dimension, “iIntegrators” and Next Generation State-of-the-Art for First/Second Order ODE/DAE Systems
by Kumar K. Tamma
Professor, Department of Mechanical Engineering; University of Minnesota
Each computational science and engineering simulation, whether it is the analysis of a single discipline or a multi-physics application involving, first or second order system or combination thereof, has its own emphasis and analysis requirements; wishful thinking is that a “wish list” of desired attributes by the analyst to meet certain required analysis needs is desirable. Optimal design developments of algorithms are not trivial; and alternately, how to foster, select, and determine such optimal designs for a targeted application if such an optimal algorithm does not readily exist, is a desirable goal and a challenging and daunting task; not to mention the added complexity of additionally designing a general purpose unified framework – a one size fits all philosophy. Under the notion of Algorithms by Design and the theoretical basis emanating from a generalized time weighted residual philosophy, we have developed under the umbrella of "isochronous time integrators [iIntegrators]" representing the use of the "same time integration framework/architecture", novel designs for first/second order ODE /DAE transient/dynamic systems for the general class of LMS methods . The framework not only encompasses most of the research to-date developed over the past 50 years or so, but additionally encompasses more new and novel schemes and solution procedures with improved physics such as energy-momentum or symplectic-momentum conservation and other optimal attributes with/without controllable numerical dissipation. All formulations within the "iIntegration framework of individual or mixed algorithms and designs" yield the much coveted second-order time accuracy in all kinematic and algebraic variables for ODE’s and DAE’s of any index. Under the umbrella of a single unified architecture, the iIntegration framework is envisioned as the next generation toolkit; and illustrative examples are highlighted as well for computational science and engineering.
Dr. Kumar K. Tamma, is currently - Professor in the Dept. of Mechanical Engineering, College of Science and Engineering at the University of Minnesota. He has published over 200 research papers in archival journals and book chapters; and over 300 in refereed conference proceedings, and conference abstracts. His primary areas of research encompass: Computational mechanics with emphasis on multi-scale/multi-physics and fluid-thermal-structural interactions; structural dynamics and contact-impact-penetration; computational aspects of microscale/nanoscale heat transfer; composites and manufacturing processes and solidification; computational development of finite element technology and time dependent algorithms by design; and development of techniques for applications to large-scale problems and high performance parallel computing environments; and virtual surgery applications in medicine. He serves on the editorial boards for over 20 archival national/international journals, Editor-in-Chief (co-shared) of an online journal, and is the Fellow of IACM, USACM, and the Minnesota Supercomputing Institute. He is the recipient of numerous research awards including the “ICCES Outstanding Research Medal for Contributions to Computational Structural Dynamics, June 2014”; and the "George Taylor Research Award" and selected for the University of Minnesota/Institute of Technology Award for Significant and Exceptional Contributions to Research. He is also the recipient of numerous Outstanding Teaching and other national and university awards. His recent book is titled “Advances in Computational Dynamics of Particles, Materials and Structures”, John Wiley & Sons publication.
Hosted by Leszek Demkowicz
ICES Seminar - ICES Student Forum
Wednesday, Dec 9, 2015 from 9AM to 10AM
A Randomized Misfit Approach for Data Reduction in Large-Scale Inverse Problems. --> NOTE: Different day/time
by Ellen Le and Aaron Myers
"The ICES Student Forums are presentations given by current students in the CSEM program to their peers. The aim of the forums is to expose students to each other's research and encourage collaboration. Seminar credit will be given to first and second year CSEM students."
ICES, The University of Texas at Austin
We present a randomized misfit approach (RMA) for efficient data reduction in large-scale inverse problems. The method is a random transformation approach that generates a reduced data set via random combinations of the original data. The main idea is to first randomize the misfit and then use the sample average approximation to solve the resulting stochastic optimization problem. At the heart of our approach is the blending of the stochastic programming and the random projection theories, which brings together advances from both areas and exploits opportunities at their interfaces. This permits a more complete analysis of the RMA method that is unlikely possible using theory from either area alone. One of the main results builds upon the interplay between the Johnson-Lindenstrauss lemma and large deviation theory. In particular, the former provides sharp bounds on the reduced data dimensions for a large class of sparse random transformations, while the latter introduces a new interpretation and proof of the former. To justify the RMA approach, a detailed theoretical analysis is carried out for both linear and nonlinear inverse problems. A tight connection between the Morozov’s discrepancy principle and the Johnson-Lindenstrauss lemma is presented. This accounts for the efficacy of the RMA method in significantly reducing observation data with acceptable accuracy loss for the solution of inverse problems. Various numerical results to motivate and to verify our theoretical findings are presented for inverse problems governed by elliptic partial differential equations in one, two, and three dimensions.