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January 29, 2021
Thi-Thao-Phuong Hoang
Auburn University
Location and Time: Zoom, 2pm-3pm
Title: Global-in-time domain decomposition methods for the coupled Stokes and Darcy flows
Abstract: We study decoupling iterative algorithms based on domain decomposition for the time-dependent Stokes-Darcy model, in which different time step sizes can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on either physical interface conditions or equivalent Robin-Robin interface conditions. Such an interface problem is solved iteratively by a Krylov subspace method (e.g. GMRES) which involves at each iteration parallel solution of time-dependent Stokes and Darcy problems. Consequently, local discretizations in both space and time can be used to efficiently handle multiphysics systems with discontinuous parameters. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed methods.
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February 5, 2021
Matthias Maier
Texas A&M University
Location and Time: Zoom, 2pm-3pm
Title: Optical Phenomena and Resonances in the Homogenization of Layered Heterostructures
Abstract: An important class of metamaterials consists of plasmonic crystals that are made of stacked metallic or semi-metallic 2D material structures arranged periodically with subwavelength spacing and embedded in a dielectric host. They offer a level of control of the path and dispersion of light that is of fundamental interest and leads to exciting new optical devices and applications. A particularly important building block in creating such a plasmonic crystal are atomically thick 2D metallic sheets, for example graphene, or black phosphorus.
In this talk we present analytical and computational approaches to simulate resonant effects of surface plasmon polaritons (SPPs) on 2D material interfaces and layered heterostructures. The computational approach is based on a homogenization theory for layered heterostructures and an adaptive finite-element simulation framework. We present a spectral analysis of the cell problem that quantitatively describes resonances in the effective material parameters of plasmonic crystals.
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February 12, 2021
Martina Bukac
University of Notre Dame
Location and Time: Zoom, 2pm-3pm
Title: Numerical methods for fluid-poroelastic structure interaction
Abstract: Poroelastic materials can be found in nature (e.g., tissues, rocks, soils, sand beds) as well as in engineering systems (e.g., foams, concretes and polymer composites). To describe poroelastic structures, a commonly used model is the Biot model, which consists of the mechanics equation describing the elastic phase and Darcy's law describing the fluid phase. The two phases are mutually coupled. In many instances, the poroelastic materials are in contact with a free-flowing fluid and their interaction forms a two-way coupled problem. Due to their many applications, the development of numerical methods for fluid-poroelastic structure interaction (FPSI) has been an area of active research. This talk will focus on the development of partitioned numerical methods for FPSI problems. The challenges in the design of such methods will be discussed, and several different algorithms will be presented. We will also discuss the stability and accuracy of the proposed methods, as well as their performance on numerical examples.
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February 19, 2021
Wuchen Li
University of South Carolina
Location and Time: Zoom, 2pm-3pm
Title: Learning via transport information geometry
Abstract: Recently optimal transport has many applications in machine learning. In this talk, we introduce dynamical optimal transport on machine learning models. We proposed to study these model as a Riemannian manifold with a Wasserstein metric. We call it transport information geometry. Various developments, especially the Fokker-Planck equation and mean field games on learning models, will be introduced. The entropy production of Shannon entropy in AI models will be established. Many numerical examples, including restricted Boltzmann machine and generative adversary network, will be presented.
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March 5, 2021
Haizhao Yang
Purdue University
Location and Time: Zoom, 2pm-3pm
Title: Reproducing Activation Functions for Deep Learning
Abstract: Deep learning is a powerful tool not only in computer science and data science but also in scientific computing. It has led to numerous breakthroughs in science and engineering. This talk introduces newly developed reproducing activation functions as a simple but very efficient technique to boost the performance of deep learning. Both theoretical insights and numerical evidence are provided to demonstrate the effectiveness of reproducing activation functions in terms of approximation theory and optimization analysis.
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March 12, 2021
Songting Luo
Iowa State University
Location and Time: Zoom, 2pm-3pm
Title: TBD
Abstract: TBD
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March 26, 2021
Hoa Nguyen
Trinity University
Location and Time: Zoom, 2pm-3pm
Title: TBD
Abstract: TBD
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April 2, 2021
Jiaqi Cheng
Auburn University
Location and Time: Zoom, 2pm-3pm
Title: TBD
Abstract: TBD
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April 9, 2021
John Schotland
Yale University
Location and Time: Zoom, 2pm-3pm
Title: TBD
Abstract: TBD
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April 16, 2021
Shuwen Xue
Auburn University
Location and Time: Zoom, 2pm-3pm
Title: TBD
Abstract: TBD
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April 23, 2021
Weiwei Hu
University of Georgia
Location and Time: Zoom, 2pm-3pm
Title: TBD
Abstract: TBD
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