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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2012

Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates

Résumé

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, \textit{a priori} estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.
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hal-00755639 , version 1 (21-11-2012)

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Xavier Antoine, Christophe Besse, Pauline Klein. Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates. Mathematical Models and Methods in Applied Sciences, 2012, 22 (10), pp.1250025. ⟨10.1142/S021820251250025X⟩. ⟨hal-00755639⟩
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