Programs in Physics & Physical Chemistry
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|Manuscript Title: Tetrahedral finite element matrix primitives.|
|Authors: P.P. Silvester, F.U. Minhas, Z.J. Csendes|
|Program title: TETRAHEDRAL MATRIX PRIMITIVES|
|Catalogue identifier: AARB_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 24(1981)173|
|Programming language: Fortran.|
|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.|
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.
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.
The available machine precision is determined by the program itself at run-time.
On PDP-11/03 with KEV-11, about two hours for matrices of order 4. On IBM 370/165, about 8 min.
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