A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems

Authors:
S. Dong;Z. Yosibash
Affiliations:
Center for Computational and Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA;Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Venue:
Computers and Structures
Year:
2009

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Abstract

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.