Summary.
We construct and analyse a family of absorbing boundary conditions for diffusion equations with variable coefficients, curved artifical boundary, and arbitrary convection. It relies on the geometric identification of the Dirichlet to Neumann map and rational interpolation of \(z^{1/2}\) in the complex plane. The boundary conditions are stable, accurate, and practical for computations.
Résumé.
Nous introduisons une famille de conditions aux limites absorbantes pour des équations paraboliques à coefficients variables et une frontière quelconque. Elle repose sur l'identification géométrique de l'application Dirichlet à Neumann, et une approximation rationelle de \(z^{1/2}\) dans le plan complexe. Les conditions aux limites obtenues sont stables, précises, et faciles à mettre en œuvre.
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Received December 12, 1992 / Revised version received July 4, 1994
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Halpern, L., Rauch, J. Absorbing boundary conditions for diffusion equations . Numer. Math. 71, 185–224 (1995). https://doi.org/10.1007/s002110050141
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DOI: https://doi.org/10.1007/s002110050141