A Parallel Spectral Element Method For Dynamic Three-Dimensional Nonlinear Elasticity Problems


We present a high-order method employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics, for solving dynamic three-dimensional geometrically nonlinear elasticity problems. We demonstrate that the method has an exponential convergence rate spatially and a second-order accuracy temporally for the four classes of problems of linear/geometrically nonlinear elastostatics/elastodynamics. The method is parallelized through domain decomposition and message passing interface (MPI), and is scaled to over 2000 processors with high parallel performance.


Spectral element method; hp finite element method; Exponential convergence; Jacobi polynomial; Nonlinear elasticity; Message passing interface

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