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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)

- Thomas Hagstrom, S I Hariharan
- 1998

In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a re-cursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by nite… (More)

- Bradley Alpert, Leslie Greengard, Thomas Hagstrom
- 2002

We describe a new, efficient approach to the imposition of exact nonreflecting boundary conditions for the scalar wave equation. We compare the performance of our approach with that of existing methods by coupling the boundary conditions to finite-difference schemes. Numerical experiments demonstrate a significant gain in accuracy at no additional cost. c… (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,… (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)

- Thomas Hagstrom, Stephen Lau
- 2007

We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local… (More)

- Bradley Alpert, Leslie Greengard, Thomas Hagstrom
- 1999

We present a new time-symmetric evolution formula for the scalar wave equation. It is simply related to the classical D'Alembert or spherical means representations, but applies equally well in two space dimensions. It can be used to develop stable, robust numerical schemes on irregular meshes. c 2000 Academic Press