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Archive : Numerical Analysis and PDE

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Charles Epstein, University of Pennsylvania Charles Epstein, University of Pennsylvania Ewing 336Title. The stability of time-domain integral equations for acoustic wave propagation <br></br> Abstract. We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain. This is joint work with Leslie Greengard and Tom Hagstrom 11/16/2017 4:30:00 PM11/16/2017 5:30:00 PMFalse
Lise-Marie Imbert Gerard, New York University and University of Maryland College Park Lise-Marie Imbert Gerard, New York University and University of Maryland College Park Ewing 336Title: Pseudo-spectral methods on surfaces of genus one Abstract: We will discuss a numerical method for elliptic partial differential equations on manifolds. In this framework the geometry of the manifold introduces variable coefficients. Fast, high order, pseudo-spectral algorithms were developed for inverting the Laplace-Beltrami operator and computing the Hodge decomposition of a tangential vector field on closed surfaces of genus one in a three dimensional space. Robust, well-conditioned solvers for the Maxwell equations will rely on these algorithms.11/9/2017 4:00:00 PM11/9/2017 5:00:00 PMFalse
Wei Guo, Texas Tech University Wei Guo, Texas Tech University Ewing 336Title: A Sparse Grid Discontinuous Galerkin Method for High-Dimensional Transport Equations with Application to Kinetic Simulations <br></br> Abstract: In this talk, we present a sparse grid discontinuous Galerkin (DG) scheme for transport equations with application to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG schemes for hyperbolic problems and is proven to be L^2 stable and convergent. A major advantage of the scheme lies in its low computational and storage cost due to the employed sparse finite element approximation space. This attractive feature is explored in simulating linear and nonlinear transport problems including Vlasov-Maxwell/Poisson system. Good performance in accuracy and conservation is verified by numerical tests in up to four dimensions. This is joint work with Dr. Yingda Cheng and Dr. Zhanjing Tao from Michigan State University. 11/2/2017 3:00:00 PM11/2/2017 4:00:00 PMFalse
Lian-Ping Wang, Department of Mechanical Engineering, University of Delaware Lian-Ping Wang, Department of Mechanical Engineering, University of Delaware Ewing 336Title: Mesoscopic simulation methods of multiphase and turbulent flows: An overview and recent developments <br></br> <p>Abstract: Since the 1980s, direct numerical simulations have served as a vital research tool to probe flow structures and nonlinear dynamics in complex flows such as multiphase flows and turbulent flows. Most of these simulations were performed based on the continuum (conventional or macroscopic) Navier-Stokes equation. In recent years, mesoscopic methods based on the Boltzmann equation, such as the lattice Boltzmann method and gas kinetic schemes, have been developed and applied to these complex flows. In this talk, I will discuss some recent advances in applying mesoscopic methods for rigorous simulations of such complex flows. Three specific examples will be considered: (a) turbulent channel flow laden with finite-size moving particles, (b) hydrodynamic interactions of cloud droplets, and (c) compressible turbulent flow. A few implementation issues in these simulations will be discussed. The purpose is to expose the capabilities of these mesoscopic methods, open research issues, and their potentials for various complex flow problems. I will also comment on the physical accuracy and computational efficiency of mesoscopic methods relative to conventional simulation methods such as pseudo-spectral and finite-volume methods. </p>10/12/2017 3:00:00 PM10/12/2017 4:00:00 PMFalse

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