In the standard low-order finite element method, also known as h-version, convergence is achieved with the refinement of the mesh and the order of the polynomial shape functions remains unchanged. The high-order or spectral finite element method [1], also known as p- and hp-versions, increases the polynomial order of the shape functions.

The high-order finite element method has considerably evolved in the recent years. In solid mechanics, it has advantages over the low-order approximations, such as considerably higher convergence rates, flexibility of using a large aspect ratio of elements without significant deterioration in accuracy, locking-free behavior with respect to thickness (for plate and shell structures) and to the Poisson's ratio for nearly incompressible materials [2,3].

The code has been used for testing news procedures for the solution of finite elements problems using domain decomposition techniques and distributed computing. In recent years, an increased interest in the these techniques has been observed, mainly for their potential application in computer systems with multiple processors [4,5].

The two- and three-dimensional shape functions of the code are constructed by the tensorial product of the one dimensional shape functions, i.e. the interpolation functions for squares, triangles, hexahedral and tetrahedral are generated from one-dimensional functions. The solver supports nodal and modal shape functions with Lagrange and Jacobi polynomials. Additionally, it is possible choose between hierarchical and non-hierarchical bases.

Using GiD as a pre and postprocessor software, it is possible to generate a geometric model or to import one from some computer-aided design system. The finite element model is created and saved in two ASCII files. The code has been tested in many different problems including: Poisson's operator, plane stress, plane strain, linear and nonlinear elasticity, optimization, contact and Reynold's Equation.

Based on preliminary results for linear elasticity, it was observed that the solution using domain decomposition was generally faster than that on a single processor, but it still presents problems that require investigation. The solver showed good results for the calculations of stiffness matrices and the load vector but shows an increase in CPU time for solving the linear system equations for the boundary nodes.

1

G.E. Karniadakis, S.J. Sherwin, "Spectral/hp element methods for computational fluid dynamics", 2nd ed., Oxford University Press, New York, USA, 2005.

2

A. Düster, E. Rank, "The p-version of the finite element method compared to an adaptive h-version for the deformation theory of plasticity", Computer Methods in Applied Mechanics and Engineering, 190, 1925-1935, 2001. doi:10.1016/S0045-7825(00)00215-2

3

S. Dong, Z. Yosibash, "A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems", Computers and Structures, 87, 59-72, 2009. doi:10.1016/j.compstruc.2008.08.008

4

Y. Saad, "Iterative Methods for Sparse Linear System", 2nd ed., SIAM, 382, 2003.

5

A. Toselli, O.B. Widlund, "Domain Decomposition Methods-Algorithms and Theory", Springer Series in Computational Mathematics, 34, Springer, Berlin, Heidelberg, 2005. doi:10.1007/b137868

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