This paper presents a spectral numerical algorithm for the solution of elastodynamics problems in general three-dimensional domains. Based on a recently introduced "Fourier continuation" (FC) methodology for accurate Fourier expansion of non-periodic functions, the proposed approach possesses a number of appealing properties: it yields results that are essentially free of dispersion errors, it entails mild CFL constraints, it runs at a cost that scales linearly with the discretization sizes, and it lends itself easily to efficient parallelization in distributed-memory computing clusters. The proposed algorithm is demonstrated in this paper by means of a number of applications to problems of isotropic elastodynamics that arise in the fields of materials science and seismology. These examples suggest that the new approach can yield solutions within a prescribed error tolerance by means of significantly smaller discretizations and shorter computing times than those required by other methods.

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A realistic outflow boundary condition model for pulsatile flow in a compliant vessel is studied by taking into account physiological effects: compliance, resistance, and wave reflection of the downstream vasculature. The new model extends the computational domain with an elastic tube terminated in a rigid contraction. The contraction ratio, the length, and elasticity of the terminal tube can be adjusted to represent effects of the truncated vasculature. Using the wave intensity analysis method, we apply the model to the test cases of a straight vessel and the aorta and find good agreement with the physiological characteristics of blood flow and pressure. The model is suitable for cardiac transient (non-periodic) events and easily employed using so-called black box software.

Tsunami generation from earthquake-induced seafloor deformations has long been recognized as a major hazard to coastal areas. Strike-slip faulting has generally been considered insufficient for triggering large tsunamis, except through the generation of submarine landslides. Herein, we demonstrate that ground motions due to strike-slip earthquakes can contribute to the generation of large tsunamis (>1 m), under rather generic conditions. To this end, we developed a computational framework that integrates models for earthquake rupture dynamics with models of tsunami generation and propagation. The three-dimensional time-dependent vertical and horizontal ground motions from spontaneous dynamic rupture models are used to drive boundary motions in the tsunami model. Our results suggest that supershear ruptures propagating along strike-slip faults, traversing narrow and shallow bays, are prime candidates for tsunami generation. We show that dynamic focusing and the large horizontal displacements, characteristic of strike-slip earthquakes on long faults, are critical drivers for the tsunami hazard. These findings point to intrinsic mechanisms for sizable tsunami generation by strike-slip faulting, which do not require complex seismic sources, landslides, or complicated bathymetry. Furthermore, our model identifies three distinct phases in the tsunamic motion, an instantaneous dynamic phase, a lagging coseismic phase, and a postseismic phase, each of which may affect coastal areas differently. We conclude that near-source tsunami hazards and risk from strike-slip faulting need to be re-evaluated.

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