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Fractional calculus and non-reflecting boundary conditions in wave propagation

Summary: Fractional calculus and non-reflecting
boundary conditions in wave propagation
Xavier ANTOINE 1
The aim of this paper is to provide a comprehensive introduction to
the modelling of wave phenomena by linear and nonlinear Schr¨odinger-
type equations. A special attention is dedicated to the construction
and discretization of truncation boundary conditions to model the ex-
terior infinite domain arising in such situations. Different numerical
simulations show that these techniques are robust in concrete situa-
1 Introduction
During the last two decades, an increasing attention has been directed to-
wards the numerical simulation of linear or nonlinear Schr¨odinger equations.
This is partially due to its central application in quantum mechanics but not
only. Indeed, Schr¨odinger-type equations are often met in practice as some
simplified models of real-world situations [11]. Among them, let us mention
for example its application in fluid mechanics, in computational ocean acous-
tics, in optical fiber design, in nonlinear electromagnetism laser devices, in
seismic migration problems... An example in acoustic wave propagation [12]


Source: Antoine, Xavier - Institut de Mathématiques Élie Cartan, Université Henri Poincaré - Nancy 1


Collections: Mathematics