Method, code and computational aspects

AxiSEM3D solves the weak form of the elastodynamic momentum equations by means of an explicit time-domain, mixed spectral-element and pseudo-spectral method. Relying on a cylindrical coordinate system, it merely requires a 2D mesh to honor major discontinuities, generated by the external package SalvusMeshLite. A spectral-element discretisation is applied within this 2D domain. The third dimension along the azimuth is adapted to the complexity of the azimuthal wavefield, determined either by means of trial simulations (larger speedup) or more crudely by mere input parameters (smaller speedup). Sources are located along the cylindrical axis, such that the entire configuration is internally rotated to this configuration. Analytical axial boundary conditions ensure exact treatment of all source terms and wavefields. Undulating discontinuities are handled by a particle transformation [Leng et al., 2019], which leaves the 2D mesh unaltered by transforming undulations to a strongly anisotropic stiffness tensor. SEM discretisation is usually done at 4th-order accuracy, but can be freely adapted. Explicit time marching is done with 2nd (Newmark) or 4th-order (symplectic) schemes and global time stepping. For truncated domains, a mix of absorbing boundary conditions and sponge boundaries is used [Haindl et al., 2021]. The method is fully convergent and benchmarked [Fernando et al., 2020, Haindl et al., 2021, Leng et al., 2020, Leng et al., 2016, Leng et al., 2019, Tesoniero et al., 2020] against numerous independent reference solutions.

• The Code
  • Languages
  • Understanding inputs and outputs
  • AxiSEM3D architecture
  • Computing architectures
• Physical and mathematical background
• Meshes
• Physical Constraints
  • Boundary conditions
  • Discontinuities
• More on undulation
• Cost and resolution