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Mathematics Department

Applied Math Seminar

Fall 2018

All talks are from 12:00-1:00 p.m. in the Seminar Room CH351, unless otherwise specified.

  • Oct
    26
  • Least square discretization and preconditioning for mixed variational formulations
    Constantin Bacuta
    University of Delaware

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    We consider a least squares method for discretizing boundary value problems written as mixed variational formulations with different types of trial and test spaces. At the continuous level the only assumptions we require are LBB and data compatibility conditions. For the proposed discretization method a discrete $\inf-\sup$ condition is automatically satisfied by the natural choices of test spaces (first) and the corresponding trial spaces (second). The discretization and the iterative approach does not require nodal bases for the trial space. We present a multilevel conjugate gradient preconditioning approach that could take into considerations discontinuous coefficients and coupled physics of the problem to be solved. Applications of the method include discretizations of second order PDEs with variable coefficients, interface problems, and first order systems of parametric PDEs, such as the time-harmonic Maxwell equations.
  • Oct
    12
  • The impacts of 3D radiative transfer effect on cloud radiative property simulations and retrievals
    Scott Hottovy
    USNA, Mathematics Department

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    In this talk I will give a brief overview on the CyberTraining Class I participated in under the NSF Grant for Big Data + High-Performance Computing + Atmospheric Sciences (http://cybertraining.umbc.edu/). This course was 16 weeks and included studying parallel computing, atmospheric physics, and techniques in information sciences and big data. The course culminated in a 4 week research project. I will describe the research project and my contributions to it. Research Project: Satellite observations provide good opportunities to evaluate global cloud properties, but the 3D effects induced by the horizontal inhomogeneity of the medium cause possible uncertainties in the cloud remote sensing products. In this work, we we developed a method to generated synthetic cloud fields based on the inverse 2D Fourier transform and used it investigate the impacts of 3D effects on MODIS cloud property retrieval. Both the 3D and 1D radiative transfer simulation studies are conducted in order to understand the impacts of the 3D effects. We retrieve the cloud optical thickness(COT) and cloud effective radius(CER) from the simulated reflectance at 0.86\mum and 2.1\mum bands and compare between the retrieval and true values. The liquid water path (LWP) was obtained via CER and COT. The impacts in the cloud liquid water path retrieval are further studied and we find that the bias in the COT and CER will cause the over estimation of LWP estimations for both the illuminating and shadowy pixels.
  • Oct
    05
  • On the emergence of a turbulence model: Navier-Stokes-alpha model
    Jing Tian
    Towson University

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    Turbulence is a pervasive, complex family of phenomena observed in nature, and has been a great challenge to mathematicians, physicists, engineers and computational scientists. It is widely accepted by the scientific community that turbulent flows are governed by the Navier-Stokes equations, for large values of the Reynolds numbers. In this talk, we will begin with a brief introduction to turbulence, Navier-Stokes equations and the existence and smoothness problem. We then discuss a turbulence modelling method, the Navier-Stokes-alpha model. With the hypothesis that the turbulence described by the Navier-Stokes-alpha model partly due to the roughness of the walls, we present the transition from the Navier-Stokes equations into the Navier-Stokes-alpha model by introducing a Reynolds type averaging.
  • Sep
    21
  • Radial Basis Functions (RBFs) for Numerical Simulation of High Energy Lasers and Interfacial Fluid Dynamics
    Jonah Reeger
    USNA, Math Department
  • Sep
    14
  • PDE Constrained Optimization
    Harbir Antil
    George Mason University
    Time: 12:00 PM

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    Optimization problems with partial differential equations (PDEs) as constraints is known as PDE Constrained Optimization. In this talk, I will start with several applications of PDE constrained optimization, including, free boundary problems, magnetic drug targeting, and fractional nonlocal PDEs. I will focus on optimization problems under uncertainty. I will describe risk-measures and their role in such optimization problems. Several illustrative numerical examples will be discussed.
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