# Mathematics Department Seminar

## Computational and Applied Mathematics Seminar

Fall 2017

Mondays at 4:10 p.m. in 401 Carver

The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.

Archive of earlier seminars

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12/04

Stochastic Homogenisation of Free-Discontinuity Problems

Filippo Cagnetti

Abstract: Free-discontinuity problems were introduced by Ennio De Giorgi and Luigi Ambrosio in 1988. These are variational problems where the energy to be minimised involves both volume and surface terms. The expression "Free-Discontinuity" refers to the fact that the set where the surface energy is concentrated is not a priori fixed, and can be described as the discontinuity set of a function. We will discuss the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised functional, whose volume and surface integrands are characterised by asymptotic formulas involving minimisation problems on larger and larger cubes with special boundary conditions. In the proof we combine a recent deterministic Gamma-convergence result for free-discontinuityfunctionals with the Subadditive Ergodic Theorem by Akcoglu and Krengel.

This is a joint work in collaboration with Gianni Dal Maso (SISSA), Lucia Scardia (University of Bath), and Caterina Zeppieri (University of Münster).

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8/28 Organization meeting

9/04 Labor Day

9/11

Magnetohydrodynamic (MHD) flow in closed channels.

Monalisa Muns

Iowa State University

Abstract: Channel flow of electrically charged fluid in presence of an external magnetic field is known as MHD flow. This has applications in metallurgy (liquid metal flow), MRI study of blood flow through vessels, microfluidic devices and so on. I shall be talking about how an external magnetic field affects the channel flow with wall constrictions/dilations of length Re^(1/7) and its properties.

9/20 Wednesday 2:10--3:00pm, Carver 401

Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations

David Herzog
Iowa State University

Abstract: We discuss scaling methods which can be used to solve low mode control problems for nonlinear partial differential equations. These methods lead naturally to a infinite-dimensional generalization of the notion of saturation, originally due to Jurdjevic and Kupka in the finite-dimensional setting of ODEs. The methods will be highlighted by applying them to specific equations, including reaction-diffusion equations, the 2d/3d Euler/Navier-Stokes equations and the 2d Boussinesq equations. Applications to support properties of the laws solving randomly-forced versions of each of these equations will be noted.

9/25

Multiscale simulation of wave-matter interactions

Stongting Luo

Iowa State Universtiy

Abstract: I will discuss some multiscale problems rising from wave-matter interactions. Depending on the wavelength and size of the matter, different models are used, and appropriate schemes must be designed to capture the interactions faithfully. I will briefly talk about some problems and numerical methods for high-frequency wave propagation, kinetic models and nano optics.

10/02 No meeting

10/09

The two membranes problem for fully nonlinear operators

Luis Duque

The University of Texas at Austin.

Abstract: This double membrane problem consists on studying the position
of equilibrium of two elastic membranes in contact to each other and was
initially explored by Vergara-Caffarelli in 1971. After this, more general
scenarios involving multiple elastic membranes (Chipot, Vergara
Caffarelli, 1983) and non linear operators (Silvestre, 2005) have been
considered. In this talk we will explain a probabilistic version of this
problem and sketch the existence and optimal regularity of solutions in
this new scenario. Joint work with Luis Caffarelli and Hernan Vivas.

10/16

Dynamic Resource Control and Optimization for Stochastic Network Systems

Jia (Kevin) Liu
Dept. of Computer Science
Iowa State University

Abstract: Due to the proliferation of smart mobile devices and Internet-of-Things (IoT), recent years have witnessed an explosive growth of mobile data demands. As a result, today's data network infrastructures are being stretched to their capacity limits. The quest for an ever-increasing network capacity has attracted tremendous research interests to develop new data-intensive networking technologies, which is envisioned to be the backbone of future IoT. However, the emerging IoT applications also introduce much more stringent performance requirements on throughput, latency, and convergence speed in controlling data network infrastructure.

To this end, in this talk, we introduce a new momentum-based network congestion control and scheduling optimization approach to address the above challenges. Based on this momentum-based approach, we develop a cross-layer optimization framework that offers throughput-optimality, fast-convergence, and significant delay reduction. Further, we show that the proposed momentum-based approach offers an elegant three-way trade-off in throughput, delay, and convergence, which is achieved under a near index-type simple policy with two control degrees of freedom. Our work opens the door to an unexplored network congestion control and scheduling optimization paradigm that leverages advanced techniques based on "memory/momentum" information for data-intensive networking.

Short Bio: Jia (Kevin) Liu is currently an Assistant Professor in the Dept. of Computer Science at Iowa State University, where he joined in Aug. 2017. He received his Ph.D. degree from the Bradley Dept. of Electrical and Computer Engineering at Virginia Tech in 2010. He was a Postdoctoral Researcher from Feb. 2010 to Nov. 2014, and subsequently a Research Assistant Professor from Nov. 2014 to Jul. 2017, both in the Dept. of Electrical and Computer Engineering at The Ohio State University. His research areas include theoretical foundations of control and optimization for stochastic networked systems, distributed algorithms design, optimization of cyber-physical systems, Internet-of-things, data analytics infrastructure, and machine learning. Dr. Liu is a senior member of IEEE and a member of ACM. His work has received numerous awards at top venues, including IEEE INFOCOM'16 Best Paper Award, IEEE INFOCOM'13 Best Paper Runner-up Award, IEEE INFOCOM'11 Best Paper Runner-up Award, and IEEE ICC'08 Best Paper Award. He is a recipient of Bell Labs President Gold Award in 2001 and China National Award for Outstanding Ph.D. Students Abroad in 2008. His research has been supported by NSF, AFOSR, AFRL, and ONR.

10/23

Shape Optimization for the first non trivial Steklov Eigenvalue among nonsimply connected planar domains with two boundary components.

Leoncio Rodriguez Quiñones
Dept. of Mathematics
Iowa State University

Abstract: We introduce some results in isoperimetric inequalities for the Steklov eigenvalue problem obtained by A. Girouard and I. Polterovich. We also describe a shape derivative approach to provide a candidate for an optimal domain among non-simply connected plannar domains with two boundary components. This approach is an adaptation of the work on the extremal eigenvalue problem for the Wentzell-Laplace operator developed by Dambrine, Kateb and Lamboley. In this talk all domains are assumed to be smooth enough.

10/30

Invariant-Region-Preserving high order DG schemes for hyperbolic conservation law systems

Yi Jiang

Dept. of Mathematics
Iowa State University

Abstract: In this talk, we'll introduce our recent work on high order invariant-region-preserving (IRP) schemes solving hyperbolic conservation law systems. Some general results for multi-dimensional cases will be discussed. Numerical tests on compressible Euler equations will be provided to illustrate the properties of the IRP schemes.

11/06

Fast High Order Nystrom Method for Elastic Wave Scattering and Applications in Nondestructive Evaluation

Jiming Song

Electrical and Computer Engineering
Iowa State University
Ames, Iowa, USA
jisong@iastate.edu

Abstract: A fast high order Nystrom method is developed for 3D elastic wave scattering. The high order Nystrom method features a simple local correction scheme resulting from a careful choice of the basis function, a simple and efficient singularity subtraction scheme, and an effective near singularity subtraction scheme. The approach has higher accuracy and faster convergence compared with low order method. The proposed near singularity treatment also makes it robust and accurate for extreme geometries like penny-shape voids of high aspect ratios by just solving the conventional boundary integral equation (CBIE). The multilevel fast multipole algorithm (MLFMA) is employed as the accelerator of the high order algorithm to handle large scale problems. Numerical examples are given to demonstrate the accuracy and efficiency of the approach.

Short Bio: Jiming Song received Ph.D. degree in Electrical Engineering from Michigan State University in 1993. From 1993 to 2000, he worked as a Postdoctoral Research Associate, a Research Scientist and Visiting Assistant Professor at the University of Illinois at Urbana-Champaign. From 1996 to 2000, he worked part-time as a Research Scientist at SAIC-DEMACO. Dr. Song was the principal author of the Fast Illinois Solver Code (FISC).  He was a Principal Staff Engineer/Scientist at Semiconductor Products Sector of Motorola in Tempe, Arizona before he joined Department of Electrical and Computer Engineering at Iowa State University as an Assistant Professor in 2002.
Dr. Song currently is a Professor at Iowa State University’s Department of Electrical and Computer Engineering. His research has dealt with modeling and simulations of interconnects on lossy silicon and RF components, electromagnetic wave scattering using fast algorithms, the wave propagation in metamaterials, acoustic and elastic wave propagation and non-destructive evaluation, and transient electromagnetic field. He received the NSF Career Award in 2006 and is an IEEE Fellow.

11/13

Fast Numerical Methods for Uncertainty Quantification in High Dimensional Problems

Xueyu Zhu
Assistant Professor, PhD
Department of Mathematics
University of Iowa
B1D, MacLean Hall, Iowa City, 52242
office phone: 319-335-0763

Abstract: Development of efficient numerical methods for the solution of problems with high-dimensional stochastic inputs has been a subject of active research in computational sciences and engineering. This is motivated by the need to reduce the computational cost of Uncertainty Quantification (UQ). In this talk, I will discuss several recently developed UQ algorithms that are particularly suitable for high dimensional large-scale simulations. More specifically, we present multi-fidelity stochastic collocation methods. The methods combine the computational efficiency of low-fidelity models with the high accuracy of expensive high-fidelity models. The methods can be useful when the computational resources are limited. And they are non-intrusive and applicable to black-box simulation tools.

12/04

Stochastic Homogenisation of Free-Discontinuity Problems

Filippo Cagnetti

Abstract: Free-discontinuity problems were introduced by Ennio De Giorgi and Luigi Ambrosio in 1988. These are variational problems where the energy to be minimised involves both volume and surface terms. The expression "Free-Discontinuity" refers to the fact that the set where the surface energy is concentrated is not a priori fixed, and can be described as the discontinuity set of a function. We will discuss the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised functional, whose volume and surface integrands are characterised by asymptotic formulas involving minimisation problems on larger and larger cubes with special boundary conditions. In the proof we combine a recent deterministic Gamma-convergence result for free-discontinuityfunctionals with the Subadditive Ergodic Theorem by Akcoglu and Krengel.

This is a joint work in collaboration with Gianni Dal Maso (SISSA), Lucia Scardia (University of Bath), and Caterina Zeppieri (University of Münster).

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