High-Order Absorbing Boundary Conditions for Elastic Waves

The need for artificial computational boundaries in the solution of exterior wave problems, called “absorbing boundaries” among other names, arises quite often in various fields of application. In solid-earth geophysics, and in particular earthquake engineering and oil exploration, they are needed for practically every simulation. Since the mid 90’s two classes of methods have emerged as especially powerful: the Perfectly Matched Layer (PML) method, devised by Berenger [1] in 1994 and since then further developed, analyzed and used by many authors, and the method of using high-order Absorbing Boundary Conditions (ABCs), which are local and involve no high derivatives, which was originally devised by Collino [2] in 1993, followed by a few other formulations. Although usually derived by very distinct analyses, recent work has shown that, on the discrete level, the two methods are in fact quite closely related.