Past Seminars- Applied and Computational Mathematics

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  • Pauline van den Driessche
    Mon Apr 18, 2016
    4:00 pm
    Spatial heterogeneity of both humans and water may influence the spread of cholera, which is an infectious disease caused by an aquatic bacterium. To incorporate spatial effects, two models of cholera spread are proposed that both include direct (rapid) and indirect (environmental/water) transmission. The first is a multi-group model and the...
  • Alex Townsend
    Mon Apr 11, 2016
    4:00 pm
    We synthesize the double Fourier sphere method and low rank function techniques to develop a collection of fast numerical algorithms for computing with functions based on the fast Fourier transform.  Furthermore, by imposing certain partial regularity conditions on the solutions of PDEs we derive optimal...
  • Albert Chern
    Mon Apr 4, 2016
    4:00 pm
    Simulation of incompressible fluids is widely used for studies of fluid mechanics and for visual effects in computer graphics. One major challenge is to capture dynamics of thin vortices in finite grid resolution. We describe a new approach to the simulation of incompressible fluids in 3D. In it, the fluid state is represented by complex-valued...
  • Shidong Jiang
    Mon Mar 28, 2016
    4:00 pm
    We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. The resulting numerical algorithm can handle optical waveguides with a large number of inclusions of  arbitrary irregular cross section. It is capable of finding the...
  • Cheng Wang
    Tue Mar 15, 2016
    3:00 pm
    A second order energy stable numerical scheme is presented for the two and three dimensional Cahn-Hilliard equation, with Fourier pseudo-spectral approximation in space. The convex splitting nature assures its unique solvability and unconditional energy stability. Meanwhile, the implicit treatment of the nonlinear term makes a direct nonlinear...
  • Richard Peng
    Mon Mar 14, 2016
    4:00 pm
    We introduce the sparsified Cholesky and sparsified multigrid algorithms for solving systems of linear equations. These algorithms accelerate Gaussian elimination by sparsifying the nonzero matrix entries created by the elimination process. We use these new algorithms to derive the first nearly linear time algorithms for solving systems of...
  • Oleg Igoshin
    Mon Feb 29, 2016
    4:00 pm
    Gene regulatory networks controlling cellular differentiation must sense changes in environmental conditions and coordinate gene expression with cell-division cycles. However, the mechanisms of sensing and integrating different signals remain elusive even for the best studied model systems. Here we uncover a simple solution to this complicated...