An operator expansions method for computing Dirichlet–Neumann operators in linear elastodynamics

The propagation of linear elastic waves arises in a wide array of applications, for instance, in mechanical engineering, materials science, and the geosciences. Many configurations of interest can be effectively modeled as layers of isotropic, homogeneous materials separated by thin interfaces across which material properties vary rapidly. In the frequency domain one must solve a system of coupled elliptic partial differential equations, however, this can be greatly simplified in the instance of layered media by considering interface unknowns. To realize this one must be able to produce normal stresses (tractions) at these interfaces and Dirichlet–Neumann Operators accomplish this. In this contribution we discuss a novel Boundary Perturbation approach to compute these operators in a rapid, high-order, and robust fashion.