The double absorbing boundary method for elastodynamics in homogeneous and layered media

Daniel Rabinovich,Jacobo Bielak,Thomas Hagstrom,Dan Givoli

doi:10.1186/s40323-015-0026-8

Abstract

Abstract Background Recently the Double Absorbing Boundary (DAB) method was introduced as a new approach for solving wave problems in unbounded domains. It has common features to each of two types of existing techniques: local high-order Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML). However, it is different from both and enjoys relative advantages with respect to both. Methods The DAB method is based on truncating the unbounded domain to produce a finite computational domain, and on applying a local high-order ABC on two parallel artificial boundaries, which are a small distance apart, and thus form a thin non-reflecting layer. Auxiliary variables are defined on the two boundaries and within the layer, and participate in the numerical scheme. In previous studies DAB was developed for acoustic waves which are solutions to the scalar wave equation. Here the approach is extended to time-dependent elastic waves in homogeneous and layered media. The equations are written in second-order form in space and time. Standard Finite Elements (FE) are used for space discretization and the damped Newmark scheme is used for time discretization. Results The performance of the scheme is demonstrated via numerical examples. The DAB was applied to elastodynamics problems in conjunction with the FE method to demonstrate the performance of the method. Conclusions DAB is a viable method for solving wave problems in unbounded domains.

Highlights

The Double Absorbing Boundary (DAB) method was introduced as a new approach for solving wave problems in unbounded domains
The two most prominent absorbing-boundary type schemes have been those based on the use of a high-order Absorbing Boundary Condition (ABC) and those based on the use of a Perfectly Matched Layer (PML)
In [13] we presented a new method, which shares some features of both the Perfectly Matched Layers (PML) and the high-order Absorbing Boundary Conditions (ABC), but enjoys some of the advantages that each of them lacks

Summary

Introduction

The Double Absorbing Boundary (DAB) method was introduced as a new approach for solving wave problems in unbounded domains. It turns out that in some cases it is very difficult to find an absorbing boundary scheme, as it is often called, that is at the same time stable, sufficiently accurate, computationally efficient, robust, and can be employed in conjunction with standard interior computational schemes This is especially true for some specific types of problems that. The two most prominent absorbing-boundary type schemes have been those based on the use of a high-order Absorbing Boundary Condition (ABC) and those based on the use of a Perfectly Matched Layer (PML). Research on these methods remains very active. See the review papers [1,2,3,4]

Methods

Results

Conclusion