Thomas Hagstrom

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We present a systematic approach to the computation of exact nonreflecting boundary conditions for the wave equation. In both two and three dimensions, the critical step in our analysis involves convolution with the inverse Laplace transform of the logarithmic derivative of a Hankel function. The main technical result in this paper is that the logarithmic(More)
Since its introduction the Perfectly Matched Layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limted to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains(More)
The numerical solution of partial differential equations in unbounded domains requires a finite computational domain. Often one obtains a finite domain by introducing an artificial boundary and imposing boundary conditions there. This paper derives exact boundary conditions at an artificial boundary for partial differential equations in cylinders. An(More)
Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation Bradley Alpert,∗,1 Leslie Greengard,†,2 and Thomas Hagstrom‡,3 ∗National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305; †Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1110; and ‡Department of(More)
We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple 3-term recurrence relation for differentiation, which(More)
We construct and analyze new local radiation boundary condition sequences for first-order, isotropic, hyperbolic systems. The new conditions are based on representations of solutions of the scalar wave equation in terms of modes which both propagate and decay. Employing radiation boundary conditions which are exact on discretizations of the complete wave(More)
We develop complete plane wave expansions for time-dependent waves in a halfspace and use them to construct arbitrary-order local radiation boundary conditions for the scalar wave equation and equivalent first order systems. We demonstrate that, unlike other local methods, boundary conditions based on complete plane wave expansions provide nearly uniform(More)