On local nonreflecting boundary conditions for time dependent wave propagation

Abstract

The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region. At the artificial boundary a boundary condition is then needed, which allows the propagating waves to exit the computational domain without spurious reflection. In 1977, Engquist and Majda proposed the first hierarchy of absorbing boundary conditions, which allows a systematic reduction of spurious reflection without moving the artificial boundary farther away from the scatterer. Their pioneering work, which initiated an entire research area, is reviewed here from a modern perspective. Recent developments such as high-order local conditions and their extension to multiple scattering are also presented. Finally, the accuracy of high-order local conditions is demonstrated through numerical experiments.

Analytical and numerical analysis of linear and nonlinear properties of an rf-SQUID based metasurface

“…Note that due to the normalization of the model and the propagation direction of the electromagnetic wave along the z-axis, it holds ω( k) = k z . From (38) and using the ansatz in (40), we find Figure 3: Graphical illustration of the ansatz for the magnetic field amplitudes in (40).…”

An absorbing boundary condition for free surface water waves

“…Furthermore numerical implementation starts to become a serious bottleneck since discretizing an arbitrary P th-order differential operator is unpractical. Indeed [25] notes that only up to 2nd-order conditions are most commonly used in practice. Nevertheless the above boundary conditions have been used in practical applications and satisfactory results have been achieved in many cases [20].…”

“…In what follows, we will demonstrate the effectiveness of the four boundary conditions, Eqs. (19), (24), (25) and (27), by displaying the amount of reflection as a function of both the angle of incidence θ and the dimensionless wave number kh.…”

“…Substituting the potential function (7) into the four boundary conditions, namely Eqs. (19), (24), (25) and (27), yields the following expressions for the reflection coefficient…”

A generating‐absorbing boundary condition for dispersive waves

“…Starting from Reference 8, much literature is available on how to accommodate the effect of wave direction in a local absorbing boundary condition (ABC), see the reviews. [9][10][11][12][13] The use of local ABCs is convenient because of their relatively easy numerical implementation and because of their applicability in changing conditions, for example, a varying water depth along the boundary. The effect of a (varying) current at the boundary can be taken into account by locally formulating the model equations in a Lagrangian frame of reference moving with the flow, applying the zero-current boundary condition, and transforming the result back to the original Eulerian frame of reference.…”