Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

TL;DR

This paper introduces fractional buffer layers (FBLs) using variable-order fractional derivatives to effectively absorb waves at domain boundaries, outperforming traditional methods like PML in wave simulation accuracy.

Contribution

The authors develop a novel fractional buffer layer approach based on variable-order derivatives for wave absorption, extending it to multi-dimensional problems with spectral collocation methods.

Findings

FBLs effectively suppress wave reflections, including corner reflections.

FBLs outperform PML in accuracy for wave absorption.

The method is compatible with various discretization techniques.

Abstract

We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that dissipation is induced to absorb the coming waves in the buffer layers attached to the domain. In particular, we first design proper FBsL for the one-dimensional one-way and two-way wave propagation. Then, we extend our formulation to two-dimensional problems, where we introduce a consistent variable-order fractional wave equation. In each case, we obtain the fully discretized equations by employing a spectral collocation method in space and Crank-Nicolson or Adams-Bashforth method in time. We compare our results with the perfectly matched layer (PML) method and show the effectiveness of FBL in accurately suppressing any erroneously reflected waves, including corner reflections in two-dimensional rectangular domains. FBLs can be used in conjunction with any discretization method appropriate for fractional operators describing wave propagation in bounded or truncated domains.