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9 papers · 2 filters
A fast direct solver for structured linear systems by recursive skeletonization
Kenneth L. Ho, Leslie Greengard
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix…
On the efficient representation of the half-space impedance Green's function for the Helmholtz equation
Michael O'Neil, Leslie Greengard, Andras Pataki
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions…
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Colin B. Macdonald, Jeremy Brandman, Steven J. Ruuth
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on ra…
Fast multi-particle scattering: a hybrid solver for the Maxwell equations in microstructured materials
Zydrunas Gimbutas, Leslie Greengard
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accura…
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
Andreas Klöckner, Tim Warburton, Jan S. Hesthaven
We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate w…
Variational integrators for electric circuits
Sina Ober-Blöbaum, Molei Tao, Mulin Cheng +2
In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electrical circui…