An FC-based spectral solver for elastodynamic problems in general three-dimensional domains. (English) Zbl 1351.74162
Summary: 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.
MSC:
| 74S25 | Spectral and related methods applied to problems in solid mechanics |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 74J05 | Linear waves in solid mechanics |
Keywords:
elastic wave equation; spectral solver; general domain; FC solver; seismic simulations; non-destructive testingSoftware:
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