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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, May 3, 2016 from 3:30PM to 5PM

POB 6.304

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Adaptive sparse grid reduced basis methods for Bayesian inverse problems

by Peng Chen

ICES, UT Austin

In this talk, we present a computational reduction strategy based on adaptive sparse grid and reduced basis methods for high-dimensional Bayesian inverse problems constrained by parametric PDE. We aim to evaluate some statistics, e.g. mean or variance, for a given quantity of interest (QoI) with respect to the posterior distribution of the parameter, which commonly faces the two computational challenges: the curse of dimensionality for the high-dimensional numerical integration, and the large-scale computation for the expansive forward PDE solution. To address the first challenge, we exploit the sparsity of the QoI w.r.t. parameter and construct a dimension-adaptive sparse grid quadrature, which is shown to achieve dimension-independent convergence rates of the quadrature errors w.r.t. the number of quadrature points, that is, the number of forward PDE solves. Moreover, when QoI is sufficiently sparse in the parameter indicated by the $\ell^p$-summability of its Fourier coefficient, the convergence with rate$N^{-s}$, where $s$ depends on $p$, becomes much faster than that of a statistical quadrature rule, e.g. Markov chain Monte Carlo quadrature with convergence rate at most $N^{-1/2}$. On the other hand, in harnessing the large-scale computation for the forward solve of the PDE at each of the quadrature points, we take advantage of the reducibility of its high-fidelity approximation in the physical space and propose an adaptive sparse grid reduced basis method. Moreover, for a given QoI, we employ a goal-oriented adaptation in order to further reduce the number of high-fidelity solves. We prove that the quadrature error converges with rate $N^{-2s}$ for affine-parametric and linear PDE w.r.t. the number of high-fidelity solves. Numerical examples will be presented to demonstrate this computational strategy. This is a joint work with Christoph Schwab.

Bio

Peng Chen obtained his Bachelor degree in Mathematics from Xi’an Jiaotong University in China in 2009. Afterwards, he continued his study at EPFL in Switzerland from 2009 to 2014, and obtained his PhD degree under the supervision of Prof. Alfio Quarteroni and Prof. Gianluigi Rozza. From 2014 to 2015, he conducted postdoctoral research with Prof. Christoph Schwab and lectured at ETH Zurich. Currently, he is working with Prof. Omar Ghattas as a research associate at ICES. His research interests include model order reduction, high-dimensional approximation, uncertainty quantification, inverse problems, and optimal control.

Hosted by Omar Ghattas

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**ICES Seminar-Computational Medicine Spring Seminar Series**

Thursday, May 5, 2016 from 3:30PM to 5PM

POB 6.304

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Combining Experiments with Computational Models to Understand and Manipulate Angiogenesis

by Shayn Peirce-Cottler

Professor, University of Virginia

Some of the most prevalent and devastating diseases of our time, such as diabetes, cancer, and cardiovascular disease, involve the body’s microvasculature. Treatments that have been developed to target aberrant microvessels (e.g. anti-VEGF therapies) are directed toward specific molecular pathways, yet some of the most damaging effects of these diseases (e.g. blood vessel insufficiency or overgrowth) manifest at the multi-cell, tissue-level scale. We study how dynamic, heterotypic cell interactions during angiogenesis give rise to new blood vessels by developing and utilizing agent-based computational modeling paired with experimental models that are amenable to dynamic, high-resolution, intravital imaging. The overarching goal of our work is to design new therapies that more effectively manipulate angiogenesis by targeting the multiple heterogeneous cell types (and their interactions) that are implicated in this process. We are specifically interested in the communication between endothelial cells and perivascular support cells in the context of diabetic retinopathy, and we are pursuing a cell-based therapy approach for treating retinal vasculopathy.

Bio:

Dr. Shayn Peirce-Cottler, Ph.D. is an Associate Professor with her primary appointment in the Department of Biomedical Engineering and secondary appointments in both the Department of Ophthalmology and Department of Plastic Surgery at the University of Virginia (UVa). She received her Bachelors of Science degrees in Biomedical Engineering and Engineering Mechanics from The Johns Hopkins University in 1997. She earned her Ph.D. in the Department of Biomedical Engineering at the UVa in 2002. A past recipient of the MIT Technology Review’s “TR100 Young Innovator Award” and the Biomedical Engineering Society’s “Rita Schaffer Young Investigator Award”, Dr. Peirce-Cottler researches how blood vessels grow and remodel in response to diseases, such as diabetes, peripheral arterial disease, and cancer. She and her research team combine experimental and computational modeling approaches to understand the complex web of molecular signals and cellular behaviors that contribute to vascular adaptations in tissues. Her lab also investigates the roles of circulating immune and progenitor cells in microvascular growth, which informs their translational investigation of adult stem cell therapies for tissue regeneration. Dr. Peirce-Cottler teaches courses to undergraduate students, graduate students, and medical students on the topics of computational systems bioengineering, cell and molecular physiology, and medical device design and commercialization. She was recently elected into the American Institute for Medical and Biological Engineering College of Fellows, and she is President-elect of the Microcirculatory Society.

Hosted by Michael Sacks

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**ICES Seminar - ICES Student Forum**

Friday, May 6, 2016 from 11AM to 12PM

POB 6.304

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A Large-Scale Ensemble Transform for Bayesian Inverse Problems Governed by PDEs

by Aaron Myers

ICES, The University of Texas at Austin

We present an ensemble-based method for prior samples to posterior ones. This method avoids Markov chain simulation and hence discards expensive work when a sample is rejected. The idea is to cast the problem of finding posterior samples into a large-scale linear programming problem for which efficient and scalable solver can be developed. Large-scale numerical results will be presented to demonstrate the capability of the method.

Hosted by Teresa Portone
and Travis Sanders

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**ICES Seminar**

Monday, May 9, 2016 from 2PM to 3:30PM

POB 6.304

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Designing functional materials from first principles: from databases to structural search

by Aldo Humberto Romero

Professor, West Virginia University

In recent years, computational materials science has been recognized for its materials prediction proficiency as well as the possibility of working together with experiments with a common goal: materials design. The prediction of low energy crystal structures only based on the knowledge of its chemical composition is a very complex optimization problem. Independently of the methodology used to describe the atomic interactions, which can go from parameterized classical potentials to the quantum nature of the electrons and ions, it is possible to develop methods that can search efficiently over the Born Oppenheimer surface, avoiding largely the exponentially complexity with respect to the number of atoms. This problem has been recognized within the "Materials Genome Project", where synergistic approaches from theory and experiment have proven to be very successful in addressing the materials design problem. In this direction, I will describe our efforts in creating a flexible computational package that, by using a large set of methods, will search over potential crystal structures (stable and metastable) based uniquely on the chemical composition. I will demonstrate its use by presenting different applications ranging from carbon based superconductors, lithium batteries to crystal topological materials.

Hosted by Robert Moser

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**ICES Seminar**

Thursday, May 19, 2016 from 11AM to 12PM

POB 6.304

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Adaptively Refined Multilevel Spline Spaces

by Ursuka Zore

MTU Aero Engines AG, Munchen, Germany

Motivated by the necessity to perform local refinement in geometric design and numerical simulations – especially in the context of Isogeometric Analysis – various approaches to extend the construction of tensor-product splines have been introduced: T-splines, locally-refined splines and (truncated) hierarchical (TH)B-splines. We will briefly review these approaches in the talk. Our research is based on THB-splines (and their generalizations) [1, 3, 4], as they possess advantageous properties, such as linear independence, the partition of unity property, preservation of coefficients and strong stability and sparsity properties, which make them highly useful in various applications [2].

The construction of THB-splines uses two essential ingredients: a nested sequence of subdomains (which describe the regions identified for further refinement), together with a nested sequence of spline spaces. The existing hierarchical framework currently does not allow for unrelated refinement, and is consequently not optimized for representing various types of features in the same geometrical model. In order to overcome this limitation, we discuss a possible generalization of THB-splines, where we consider a sequence of tensor-product spline spaces, which are only partially nested. We show how to define truncated B-splines for partially nested refinement by their local representations on patches, which partition the parameter domain. Under certain conditions, they are shown to be linearly independent, form a non-negative partition of unity, possess the preservation of coefficients property, and inherit the smoothness of the underlying splines spaces. Moreover, the construction results in the standard THB-splines, provided that the spaces form a nested sequence.

Joint work with Bert Juttler (Johannes Kepler University, Linz/Austria).

References

[1] C. Giannelli, B. Juttler, H. Speleers, 2012. THB-splines: The truncated basis for hierarchical splines. Comput. Aided Geom. Design, 29:485–498.

[2] C. Giannelli, B. Juttler, S. K. Kleiss, A. Mantzaflaris, B. Simeon, J. Speh, 2016. THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis. Comput. Methods Appl. Mech. Engrg., 299:337–365.

[3] R. Kraft, 1997. Adaptive and linearly independent multilevel B-Splines. In: A. Le Mehaute, C. Rabut, L. L. Schumaker (Eds.), Surface Fitting and Multiresolution Methods. Vanderbilt University Press, Nashville, 209–218.

[4] U. Zore, B. Juttler, 2014. Adaptively refined multilevel spline spaces from generating systems. Comput. Aided Geom. Design, 31:545–566.

Bio

Ursuka Zore is a PHD Candidate (Research Assistant) at the Institute of Applied Geometry at Johannes Kepler University

Hosted by Chandrajit Bajaj

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**ICES Seminar**

Thursday, May 19, 2016 from 3:30PM to 5PM

POB 6.304

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Using the Tensor-Product Structure in Isogeometric Analysis

by Bert Juettler

Professor, Mathematics, Institute of Applied Geometry, Johannes Kepler University of Linz, Austria

The novel methodology of Isogeometric Analysis (IgA) reconciles the representations used for describing the geometry of the computational domain, and for the unknown quantities considered in a numerical simulation [1]. This is achieved by adopting the NURBS (nonuniform rational spline) representation as an overarching framework for design and analysis. IgA aims at facilitating the data exchange between software tools used for Computer Aided Design (CAD) and for Numerical Simulation (typically based on the Finite Element (FE) Method). In addition it has been observed that using IgA may increase the robustness and improve the stability of FE simulations.

The task of matrix assembly in IgA is more challenging than in the case of traditional finite element methods. The additional difficulties associated with IgA are caused by the increased degree and the larger supports of the functions that occur in the integrals defining the matrix elements. Recently we introduced an interpolation-based approach that approximately transforms the integrands into piecewise polynomials and uses look-up tables to evaluate their integrals [2].

We briefly recall the main ideas of our earlier work and identify tensor methods as a promising mathematical technology for accelerating the assembly process even further [3]. More precisely, we show how to represent the matrices that occur in IgA as sums of a small number of Kronecker products of auxiliary matrices that are defined by univariate integrals. This representation, which is based on a low-rank tensor approximation of certain parts of the integrands, makes it possible to achieve a significant speedup of the assembly process without compromising the overall accuracy of the simulation.

We conclude with the observation that tensor methods provide a systematic way of exploiting the tensor-product structure of the representations for the functions used in IgA.

Joint work with Angelos Mantzaflaris, Ulrich Langer (both at RICAM, Linz/Austria) and Boris Khoromskij (MPI-MIS, Leipzig/Germany).

References

[1] J. A. Cottrell, T. J. R. Hughes, and Y. Bazilevs. Isogeometric Analysis: Toward Integration of CAD and FEA. John Wiley & Sons, 2009.

[2] A. Mantzaflaris and B. Juettler. Integration by interpolation and look-up for Galerkin-based isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 284:373–400, 2015.

[3] A. Mantzaflaris, B. Juettler, B.N. Khoromskij, and U. Langer. Matrix generation in isogeometric analysis by low rank tensor approximation. In J.-D. Boissonat et al., editors, Curves and Surfaces, LNCS, pages 321–340. Springer, 2015.

Bio

Bert Juettler is professor of Mathematics at Johannes Kepler University of Linz, Austria. He did his PhD studies (1992-94) at Darmstadt University of Technology under the supervision of the late Professor Josef Hoschek. His research interests include various branches of applied geometry, such as Computer Aided Geometric Design, Kinematics and Robotics. Bert Juettler is member of the Editorial Boards of Computer Aided Geometric Design (Elsevier) and the Int. J. of Shape Modeling (World Scientific) and serves on the program committees of various international conference (e.g., the SIAM conference on Geometric Design and Computing 2007).

Hosted by Chandrajit Bajaj