Continued-Fraction Absorbing Boundary Conditions for the Wave Equation

Abstract

Absorbing boundary conditions are generally required for numerical modeling of wave phenomena in unbounded domains. Local absorbing boundary conditions are generally preferred for transient analysis because of their computational efficiency. However, their accuracy is severely limited because the more accurate high-order boundary conditions cannot be implemented easily. In this paper, a new arbitrarily high-order absorbing boundary condition based on continued fraction approximation is presented. Unlike the existing boundary conditions, this one does not contain high-order derivatives, thus making it amenable to implementation in conventional C 0 finite element and finite difference methods. The superior numerical properties and implementation aspects of this boundary condition are discussed. Numerical examples are presented to illustrate the performance of these new high-order boundary condition.

High-order Absorbing Boundary Conditions for anisotropic and convective wave equations

“…In contrast, the high-order ABCs devised by Collino [4], Grote and Keller [12,13], Hagstrom and Hariharan [14] Guddati and Tassoulas [15], Givoli and Neta [16,17] and Hagstrom and Warburton [6] involve no high derivatives owing to the use of special auxiliary variables / j ðj ¼ 1; . .…”

The Effect of P-Wave Propagation on the Seismic Behavior of Steel Pipelines

“…Despite the fact that they are more applicable than the previous approaches, they have not been able to achieve a good name and reputation yet as far as practical issues are concerned, due to the inherent complexities as well as the restrictions in terms of applying them in some seismic issues. In addition to these boundaries, Guddati and Tassoulas in 2000 [43] presented absorbed boundaries based on complex mathematic model. Lee and Tassoulas in 2011 [44] implemented the mentioned boundaries into soil-structure interaction issues and observed a satisfactory performance.…”

Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling

“…Since k = Àix R , we have j/ t+Dt j = j/ t j. This implies asymptotic stability of the time discretized form (49). Note that (46) models only the exterior and hence the numerical stability assured by (51) does not consider the effect of the interior on the stability of the coupled (interior + exterior) model.…”