Showing papers by "Leslie Greengard published in 2008"
TL;DR: This paper presents a simple and efficient method for the rapid evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin.
91 citations
TL;DR: In this article, a fast algorithm for the evaluation of exact, nonreflecting boundary conditions for the time-dependent Schrodinger equation in two dimensions on the unit circle is presented, where the exact outgoing condition for each Fourier mode contains a nonlocal term that is a convolution integral in time.
Abstract: We present a fast algorithm for the evaluation of exact, nonreflecting boundary conditions for the time-dependent Schrodinger equation in two dimensions on the unit circle. After separation of variables, the exact outgoing condition for each Fourier mode contains a nonlocal term that is a convolution integral in time. The kernel for that convolution is the inverse Laplace transform of the logarithmic derivative of a modified Bessel function, and the convolution integral can be split into two parts: a local part and a history part, which can be treated separately. The local part is easily handled by an appropriate quadrature. For the history part, we show that the convolution kernel can be well approximated by a sum of exponentials. Once such a representation is available, the convolution integrals can be evaluated recursively, reducing the cost from O(N2) work to O(N), where N is the number of time steps. The main technical development lies in the uniform rational approximation of the logarithmic derivative of the modified Bessel function Kν(√is). © 2007 Wiley Periodicals, Inc.
64 citations
New York University1, Oak Ridge National Laboratory2, California Institute of Technology3, Princeton Plasma Physics Laboratory4, Lawrence Berkeley National Laboratory5, Massachusetts Institute of Technology6, Columbia University7, University of Colorado Boulder8, Georgia Institute of Technology9, Lehigh University10, Rutgers University11, University of Utah12, University of California, Irvine13, North Carolina State University14, Auburn University15
TL;DR: Collaborative effort among physics, computer science, and applied mathematics within CPES has created the first working version of the End-to-end Framework for Fusion Integrated Simulation (EFFIS), which can be used to study the pedestal-ELM cycles.
Abstract: Performance of the ITER is anticipated to be highly sensitive to the edge plasma condition. The edge pedestal in ITER needs to be predicted from an integrated simulation of the necessary first-principles, multi-scale physics codes. The mission of the SciDAC Fusion Simulation Project (FSP) Prototype Center for Plasma Edge Simulation (CPES) is to deliver such a code integration framework by (1) building new kinetic codes XGC0 and XGC1, which can simulate the edge pedestal buildup; (2) using and improving the existing MHD codes ELITE, M3D-OMP, M3D-MPP and NIMROD, for study of large-scale edge instabilities called Edge Localized Modes (ELMs); and (3) integrating the codes into a framework using cutting-edge computer science technology. Collaborative effort among physics, computer science, and applied mathematics within CPES has created the first working version of the End-to-end Framework for Fusion Integrated Simulation (EFFIS), which can be used to study the pedestal-ELM cycles.
22 citations
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TL;DR: In this article, the authors developed a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3.
Abstract: In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a coupled system of Fredholm integral equations of the second kind for four scalar densities supported on the material interface. Like the classical Muller equation, it has no spurious resonances. Unlike the classical approach, however, the representation does not suffer from low frequency breakdown. We illustrate the performance of the method with numerical examples.
3 citations
3 citations