Abstract

Elastic waves are waves that propagate by causing deformations in an elastic medium such as metal, rock, or rubber. The main characteristic of elastic wave motion is the coexistence of multiple types of waves at once in the medium, including compressional and shear wave components. This type of motion can be used to study the impacts of physical phenomena such as earthquakes. In this paper, we discuss our research on the time-harmonic scattering of elastic waves in a medium by multiple circular cylindrical obstacles that the wave cannot penetrate. Using the Helmholtz decomposition, we break down the vector-valued physical system of displacements into a set of coupled scalar potentials. To numerically approximate solutions in this scenario, we propose a novel set of high-order local absorbing boundary conditions that can be imposed around each obstacle based off Karp's Farfield Expansions, extending previous research done in acoustic wave scattering problems. We also present an iterative method that decouples the BVPs at each scatterer. We discuss results achieved by discretization of the resulting system using a second-order finite difference scheme and present a set of promising future research directions.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

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