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Manuscript Title: Tetrahedral finite element matrix primitives.
Authors: P.P. Silvester, F.U. Minhas, Z.J. Csendes
Catalogue identifier: AARB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 24(1981)173
Programming language: Fortran.
Computer: PDP-11.
Operating system: RT-11.
RAM: 25K words
Word size: 16
Keywords: General purpose, Other numerical, Finite elements, Primitives matrix, Tetrahedral elements, Three-dimensional Analysis, Boundary value problems, Universal matrices.
Classification: 4.12.

Nature of problem:
TETRAHEDRAL MATRIX PRIMITIVES is a subroutine package for constructing finite element representations of arbitrary linear second-order differential operators. Finite element matrices for any such operator may be constructed from three matrix primitives. The results are of use in three-dimensional potential and flow problems, electromagnetics of plasmas, diffusion problems, and elsewhere.

Solution method:
The primitives are constructed for any specified order N of polynomial approximation, by computing the standard tetrahedron interpolation polynomials, then differentiating and integrating them as required. Differentiations are performed analytically, while integrations use Newton-Cotes quadrature of sufficiently high order to guarantee zero discretization error. The precision level attainable on the machine used is checked by the program at run-time.

Matrices for interpolation orders beyond 7 or 8 may suffer from round- off error accumulation.

Unusual features:
The available machine precision is determined by the program itself at run-time.

Running time:
On PDP-11/03 with KEV-11, about two hours for matrices of order 4. On IBM 370/165, about 8 min.