Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation

By B. Alpert, Leslie Greengard, Thomas M. Hagstrom. 2002

163 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Geophysics

View Paper: https://www.semanticscholar.org/paper/bde9ca679b9240b8d31e36a899cfc714fbdc3fe8

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

In Geophysics

Citations in the corpus

Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, unknown): “Consider a dyadic interval [a, b] = [2, 2] and let s1, · · · , sn and w1, · · · , wn be the nodes and weights for n-point Gauss-Legendre quadrature on the interval.”
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN (2007, methodology): “Although we will not explicitly perform the inverse Laplace and Fourier transforms in order to define the exact time–domain physical–space boundary conditions, we note that efficient strategies exist for numerically implementing these nonlocal operations [ 3 ].”
Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability (2003, background): “Such kind of trick has been proposed in [40] for the continuous TBC in case of the 3D wave equation, and developed in [1, 2, 41, 42, 13, 19] for various hyperbolic problems.”
High‐order doubly asymptotic open boundaries for scalar wave equation (2009, background): “Nevertheless, the open boundaries for these cases can be applied directly to solve practical problems by introducing straight or circular artificial boundaries [17, 26, 27, 29, 34].”
On approximation of functions by exponential sums (2005, methodology): “We also note that the approach in [27] is a special p optimization strategy for computing quadratures as is that in [4,5] for optimizing rational approxim in the Laplace domain resulting in a particular example of (6).”