Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains

Details Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains

2011-10-21

arxiv.org/abs/1110.4912v1

SIAM J. Math. Anal. 44 (2012), pp. 355-382

Mathematics

Analysis of PDEs

to appear in SIAM Journal on Mathematical Analysis

Scientific paper

10.1137/110834287

We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum or acoustically-soft waveguides associated with quasi-cylindrical domains. We construct a uniquely solvable problem with perfectly matched layers of finite length. We prove that solutions of the latter problem approximate outgoing or incoming solutions with an error that exponentially tends to zero as the length of layers tends to infinity. Outgoing and incoming solutions are characterized by means of the limiting absorption principle.

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