Perfectly matched layers for the stationary Schrodinger equation in a periodic structure

Details Perfectly matched layers for the stationary Schrodinger equation in a periodic structure Perfectly matched layers for the stationary Schrodinger equation in a periodic structure

2008-06-12

arxiv.org/abs/0806.2022v1

SIAM J. Numer. Anal. 49 (2011) pp. 309-330 (22 pages)

Physics

Mathematical Physics

ISBN-978-951-39-3062-2

Scientific paper

We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show that solution to this problem approximates a solution to the original problem with an error that exponentially tends to zero as the length of perfectly matched layer tends to infinity.

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