ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRODINGER EQUATION WITH AN EXTERIOR POTENTIAL. PART I: CONSTRUCTION AND A PRIORI ESTIMATES

被引：25
作者：
Antoine, Xavier [1 ]
Besse, Christophe [2 ]
Klein, Pauline [3 ]
机构：
[1] Nancy Univ, Inst Elie Cartan Nancy, CNRS UMR 7502, INRIA CORIDA Team, F-54506 Vandoeuvre Les Nancy, France
[2] Univ Lille 1 Sci & Technol, Lab Paul Painleve, Univ Lille Nord France, INRIA SIMPAF Team,CNRS UMR 8524, F-59655 Villeneuve Dascq, France
[3] Univ Franche Comte, Lab Math Besancon, CNRS UMR 6623, F-25030 Besancon, France
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2012年 / 22卷 / 10期
关键词：
Schrodinger equation; absorbing boundary conditions; variable potential; PERFECTLY MATCHED LAYER; TRANSPARENT; SIMULATION; SCHEMES;
D O I：
10.1142/S0218202512500261
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrodinger 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 Dirichletto-Neumann operator. Furthermore, 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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页数：38
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