We consider the simulation of nonlocal wave propagation in an unbounded multi-scale medium. In particular, we discuss
(a) the design of artificial/absorbing boundary conditions (ABCs);
(b) the construction of an asymptotically compatible (AC) scheme for a nonlocal operator with general kernel.
The design of ABCs facilitates the reformulation of the problem on an unbounded domain into one posed on a bounded domain, which is convenient for numerical computations. The construction of an AC scheme facilitates the accurate simulation of nonlocal wave propagation in a multi-scale medium. With the proposed ABCs and AC scheme, wave propagation behaviors in local and nonlocal media are investigated through three numerical examples. Furthermore, the accuracy of our approach is also validated.
This is a joint work with Qiang Du, Houde Han and Chunxiong Zheng.