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.
Tuesday, Sep 6, 2016 from 3:30PM to 5PM
Probabilistic Numerics for Differential Equations
by Tim Sullivan
Free University of Berlin / Zuse Institute Berlin
Deterministic problems such as matrix inversion, quadrature, optimization, and the solution of ordinary and partial differential equations are ubiquitous in applied mathematics. With growing demand for uncertainty quantification throughout scientific computing applications, there has been a resurgence of interest in giving probabilistic solutions to such problems, in which the numerical tasks are interpreted as inference problems, and the role of stochasticity in the algorithm is to replace traditional error bounds as the carriers of epistemic uncertainty about the quality of the solution. Advantages offered by this viewpoint include better propagation of uncertainty through hierarchical systems than simple worst-case error bounds, and appropriate incorporation of numerical truncation and round-off error in inverse problems, so that the replicability of deterministic simulations is not confused with their accuracy, thereby yielding an inappropriately concentrated Bayesian posterior. This talk will describe recent work on probabilistic numerical solvers for ordinary and partial differential equations, including their theoretical construction, convergence rates, and applications to forward and inverse problems. It is joint work with Jon Cockayne and Mark Girolami (Warwick), Chris Oates (Sydney), and Andrew Stuart (Caltech).
Hosted by Tan Bui-Thanh
Tuesday, Sep 13, 2016 from 3:30PM to 5PM
Some New Ideas in the Numerical Analysis of Elastic Waves
by Thomas Hagstrom
Professor, Southern Methodist University
The focus of our research has been the development of reliable and efficient numerical methods for simulating waves in the time domain. In particular we are interested in:
• Robust, high-order volume discretizations applicable in complex geometry and capable of leveraging the efficiency of structured grids when feasible;
• Radiation boundary conditions which provide arbitrary accuracy at small cost (spectral convergence, weak dependence on the simulation time and wavelength).
For acoustic and electromagnetic waves, we believe we have methods which successfully meet these challenges. In particular we have arbitrary-order, energy-stable discontinuous Galerkin, Galerkin difference, and Hermite methods for both first and second order forms of the equations on hybrid grids and optimal local radiation boundary conditions for both exterior and wave guide geometries. In this talk we discuss our successes and failures in generalizing these methods to the elastic wave equation, as well as some promising new approaches to overcome the difficulties we have encountered.
Hosted by Tan Bui-Thanh
Thursday, Sep 22, 2016 from 3:30PM to 5PM
Isogeometric Analysis for Electromagnetic and Acoustic scattering
by Tahsin Khajah
University of Texas at Tyler
There is an emerging need for high-fidelity geometric modeling to obtain spatially realistic solutions in scattering analysis. In addition to accurate boundary representation, Isogeometric Analysis (IGA) offers many attractive properties which results in increased solution accuracy. I will talk about our research in two main areas: IGA for electromagnetic radiation, and IGA for acoustic scattering.
IGA can be used to generate a comprehensive computational framework, which integrates geometric modeling and mesh generation with analysis. It also has promising features such as control over continuity, and unique refinement possibilities. I will present IGA for electromagnetic radiation estimating electrical field inside a high-fidelity, image-based brain model. Due to the high dielectric constant and conductivity of biological tissue, the radiated electromagnetic field on the brain absorbs and attenuates exponentially inside the brain. Hence, delivering electromagnetic energy to deep seated tissue/tumor remains a difficult problem. In the second part of this talk, I will present the results of our study implementing IGA for exterior acoustic scattering. The performance of IGA in solving exterior Helmholtz problem and related pollution error will be discussed. This study shows that IGA is less prone to pollution error when compared with conventional Finite Element Analysis. The pollution error is considerably low when utilizing higher order basis functions even at very high frequencies.
The results of this research can be used both in evaluating the potential health and safety risks of electromagnetic and acoustic waves and development/optimization of medical devices used in non-invasive diagnostics and therapies. Other industrial applications include antenna design, computation of radar cross-section, and acoustic warfare.
Dr. Tahsin Khajah received a Master of Science in Mechanical Engineering degree from the Sharif University of Technology in Iran. He received the Doctor of Philosophy degree from Old Dominion University. He specialized in dynamics of structures and optimization for his Master's degree and in computational mechanics and Finite Elements, in particular Isogeometric Analysis, for his Ph.D. degree in mechanical engineering. He worked in Old Dominion University as an Adjunct Faculty and Visiting Lecturer prior to joining University of Texas at Tyler as an Assistant Professor in the fall semester of 2015. He has worked in industry for more than a decade as a design engineer.
Hosted by Leszek Demkowicz
ICES Seminar-Molecular Biophysics Series
Monday, Sep 26, 2016 from 2PM to 3PM
Hydrophobicity Versus Dipole Interactions in Self-assembly Processes
by Silvina Matysiak
University of Maryland
The delicate balance between hydrophobicity, hydrogen bonding and charge interactions determine the self-assembled structure of many biomolecular systems. In this presentation, a new coarse-grained model to study such delicate balance will be presented. By including polarization effects on a coarse-grained model for proteins and lipid membranes, we were able to achieve significant / secondary content , in model proteins, de novo without any added bias. In addition, this model allows us to simulate lipid domain formation, at the molecular level, in mixed bilayers driven by headgroup interactions for the first time. In the first part of the talk, a discussion on how the balance between hydrophobicity and dipole interactions change to drive folding and aggregation in aqueous solution and at interfaces will be presented. In the second part of the talk, a molecular mechanism behind the role of monovalent ion size driving lipid domain formation in mixed zwitterionic-anionic lipid bilayers will also be presented.
Hosted by Ron Elber
Thursday, Oct 13, 2016 from 3:30PM to 5PM
A Consistent Bayesian Approach for Stochastic Inverse Problems
by Tim M. Wildey
Computer Science Research Institute, Sandia National Laboratories
Uncertainty is ubiquitous in computational science and engineering. Often, parameters of interest cannot be measured directly and must be inferred from observable data. The mapping between these parameters and the measurable data is often referred to as the forward model and the goal is to use the forward model to gain knowledge about the parameters given the observations on the data. Statistical Bayesian inference is the most common approach for incorporating stochastic data into probabilistic descriptions of the input parameters. This particular approach uses data and an error model to inform posterior distributions of model inputs and model discrepancies. An explicit characterization of the posterior distribution is not necessary since certain sampling methods, such as Markov Chain Monte Carlo, can be used to draw samples from the posterior.
We have recently developed an alternative Bayesian solution to the stochastic inverse problem. We use measure-theoretic principles to prove that this approach produces a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior through the model will match the observed density on the data. Our approach requires approximating the push-forward of the prior through the computational model, which is fundamentally a forward propagation of uncertainty. We employ advanced approaches for forward propagation of uncertainty to reduce the cost of approximating the posterior density. Numerical results are presented to demonstrate the fact that our approach is consistent with the model and the data, and to compare our approach with the statistical Bayesian approach.
Tim Wildey is a Senior Member of the Technical Staff at the Computer Science Research Institute at Sandia National Laboratories in Albuquerque, NM. His research interests are finite element and finite volume methods, a posteriori error analysis and estimation, uncertainty quantification, adjoint methods, multiphysics and multiscale problems, operator splitting and decomposition, computational fluid dynamics, geomechanics, flow and transport in porous media, numerical linear algebra, domain decomposition, multilevel and multiscale preconditioners, and parallel computing.
Hosted by Tan Bui-Thanh