Transversely isotropic homogeneous medium with absorbing boundary conditions: elastic wave propagation using spectral element method. (English) Zbl 07827999
Sharma, Rajesh Kumar (ed.) et al., Frontiers in industrial and applied mathematics. Selected papers based on the presentations at the 4th international conference, FIAM-2021, Punjab, India, December 21–22, 2021. Singapore: Springer. Springer Proc. Math. Stat. 410, 443-462 (2023).
Summary: Particle displacements and stresses are calculated for studying elastic wave propagation in a transversely isotropic homogeneous medium. A mesh consisting of rectangular elements is considered for discretization of two-dimensional domain. The spectral element method is applied through the non-uniformly distributed Gauss-Lobatto-Legendre nodes. The tensor product of high order Lagrangian interpolation polynomials is used as shape functions. Lagrangian interpolation polynomials along with Gauss-Lobatto-Legendre quadrature rule for numerical integration results in diagonal mass matrix which leads to an efficient fully explicit solver for time integration. Second order accurate, central difference method is applied for time discretization. The displacements and stress components are exhibited through time series at a point and snapshots in the domain. The influence of absorbing boundary conditions is demonstrated on the displacement components at different times. The validation of numerical solution is ensured through its comparison with known analytical solution for the two dimensional homogeneous transversely isotropic model.
For the entire collection see [Zbl 1524.76004].
For the entire collection see [Zbl 1524.76004].
MSC:
| 76-XX | Fluid mechanics |
Keywords:
transversely isotropic; wave propagation; absorbing boundary conditions; spectral element method; Lagrange type shape function; Gauss-Lobatto-Legendre nodesReferences:
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