A new way for decreasing of amplitude of wave reflected from artificial boundary condition for 1D nonlinear Schrödinger equation

Vyacheslav A.  Trofimov; Evgeny M.  Trykin

doi:10.3934/proc.2015.1070

Article Contents

2015, Volume 2015: 1070-1078. Doi: 10.3934/proc.2015.1070 open access

This issue Previous Article Simulation of complex dynamics using POD 'on the fly' and residual estimates Next Article Solvability of generalized nonlinear heat equations with constraints coupled with Navier--Stokes equations in 2D domains

A new way for decreasing of amplitude of wave reflected from artificial boundary condition for 1D nonlinear Schrödinger equation

Vyacheslav A. Trofimov^1, and
Evgeny M. Trykin^1,

1.
Lomonosov Moscow State University, Leninskie Gory, Moscow 119992

Received: September 2014

Revised: January 2015

Published: October 2015

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Abstract

In this report, we focus on computation performance enhancing at computer simulation of a laser pulse interaction with optical periodic structure (photonic crystal). Decreasing the domain before the photonic crystal one can essentially increases a computation performance. With this aim, firstly, we provide a computation in linear medium and storage the complex amplitude at chosen section of coordinate along which a laser light propagates. Then we use this time-dependent value of complex amplitude as left boundary condition for the 1D nonlinear Schrödinger equation in decreased domain containing a nonlinear photonic crystal. Because a part of a laser pulse reflects from faces of photonic crystal layers, we use artificial boundary condition. To decrease amplitude of the wave reflected from artificial boundary we introduce in consideration some additional number of waves related with the equation under consideration.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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