Microlocal approach towards construction of nonreflecting boundary conditions

Vaibhav, V.

doi:10.1016/j.jcp.2014.04.050

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Microlocal approach towards construction of nonreflecting boundary conditions

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Vaibhav, V.
Optical Quantum Information Theory, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Vaibhav, V. (2014). Microlocal approach towards construction of nonreflecting boundary conditions. JOURNAL OF COMPUTATIONAL PHYSICS, 272, 588-607. doi:10.1016/j.jcp.2014.04.050.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-65B5-3

Abstract

This paper addresses the problem of construction of non-reflecting boundary condition for certain second-order nonlinear dispersive equations. It is shown that using the concept of microlocality it is possible to relax the requirement of compact support of the initial data. The method is demonstrated for a class of initial data such that outside the computational domain it behaves like a continuous-wave. The generalization is detailed for two existing schemes in the framework of pseudo-differential calculus, namely, Szeftel's method (Szeftel (2006) [1]) and gauge transformation strategy (Antoine et al. (2006) [2]). Efficient numerical implementation is discussed and a comparative performance analysis is presented. The paper also briefly surveys the possibility of extension of the method to higher-dimensional PDEs. (C) 2014 Elsevier Inc. All rights reserved.