Past Seminars- Applied and Computational Mathematics

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  • Steven Wise
    Mon Apr 24, 2017
    4:00 pm
    I will describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth- order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural...
  • Lin Lin
    Mon Apr 17, 2017
    4:00 pm
    The Fock operator, which appears in the widely used Hartree-Fock theory and Kohn-Sham density functional theory with hybrid exchange-correlation functionals, plays a central role modern quantum chemistry and materials science.  The computational cost associated with the Fock exchange operator is however very high. In a simplified setting, the...
  • Yimin Zhong
    Mon Apr 10, 2017
    4:00 pm
    We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT solution by taking advantage of the isotropy of the scattering kernel, and solve the integral equation with a fast...
  • Stefan Llewellyn Smith
    Mon Apr 3, 2017
    4:00 pm
    A vortex in a straining field is a canonical situation describing vortices in an irrotational flow. Exact solutions to this problem have been found in the form of vortex patches and hollow vortices, both of which can be viewed as desingularizations of point vortices. After a review of the history of point vortices, we discuss hollow vortices,...
  • Sean Lawley
    Mon Mar 13, 2017
    4:00 pm
    A number of diverse biological systems involve diffusion in a randomly switching environment. For example, such processes arise in brain biochemistry, insect respiration, intracellular trafficking, and biochemical reaction kinetics. These processes present interesting mathematical subtleties as they combine two levels of randomness: Brownian...
  • Bernard Deconinck
    Mon Feb 13, 2017
    4:00 pm
    Integrable PDEs are a special class of PDEs for which many local and global properties are known. Perhaps the most famous of the solutions of an integrable PDE is its soliton solution, leading to these equations being referred to as soliton equations.  The importance of integrable equations derives from the understanding we gain from them...
  • Jianguo Huang
    Mon Jan 30, 2017
    4:00 pm
    Many problems arising in image processing and signal recovery with multi -regularization and constraints can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function and a nonsmooth function. In...