Abstract

Abstract A longstanding issue in the numerical solution of partial differential equations concerns the reduction of an unbounded domain to a bounded domain by the imposition of nonreflecting boundary conditions at an artificial boundary. This issue arises, for example, in electromagnetic and acoustic scattering, computational fluid dynamics, crystal growth, astrophysics, elasticity, and computational chemistry. In this paper, we will briefly review recent progress in the development of fast integral equation methods for solving the most basic partial differential equations of mathematical physics: the canonical hyperbolic, parabolic and elliptic equations

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