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10.1145/800204.806308acmconferencesArticle/Chapter ViewAbstractPublication Pagessymsac86Conference Proceedingsconference-collections
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Evaluation of high-order polynomial triangular finite elements using FORMAC

Published: 23 March 1971 Publication History

Abstract

The triangular finite element method is useful for numerical solution of field problems involving elliptic partial differential equations. Two outstanding advantages of the Method are its simplicity in dealing with complicated boundary shapes and its accuracy for polynomial expressions of high-order. In this paper an analytic derivation is given for polynomials of any order, using the inhomogeneous Helmholtz equation as an example, however the method presented is equally applicable to other field equations. The process for evaluating the coefficients is clearly defined but the manipulative labour involved in finding any but the lowest order elements is formidable. FORMAC programs are presented whereby the complete element matrices associated with a triangular element can be readily obtained for any order N. Fortran programs are inadequate because of arithmetic overflows and lack of character manipulation capabilities in the FORTRAN language. The evaluation of the coefficient matrices associated with other field equations can readily be obtained by making minor alterations to the FORMAC programs presented in this paper.

References

[1]
O.C. ZIENKIEWICZ with Y.K. CHEUNG, The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill (1967).
[2]
P. SILVESTER, Int. J. Engng. Sci. Vol. 7, pp849-861
[3]
Z.J. CSENDES, Solution of Dielectric Loaded Waveguides by Finite Element Methods, (Master Thesis). Dept. of Electrical Eng., McGill University, Canada.
[4]
J.T. ODEN, Proceedings of the American Society of Civil Engineers, Vol. 96, No. EM 4, pp529-534, August 1970.
[5]
P.C. DUNNE, Jour. Roy. Aero Soc. Vol. 72, pp245, 1968.
[6]
R. COURANT and D. HILBERT, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, Inc., New York, 1953.

Cited By

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  • (1993)Symbolic computation for inverse boundary-value problems and its application to impedance tomography reconstructionIEEE Transactions on Magnetics10.1109/20.25078929:2(1943-1945)Online publication date: Mar-1993
  • (1992)Symbolic Computation for inverse Boundary-Value Problems and its Application to impedance Tomography ReconstructionDigest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation10.1109/CEFC.1992.743904(TP43-TP43)Online publication date: 1992
  • (1981)COMPUTERIZED SYMBOLIC MANIPULATION IN NONLINEAR FINITE ELEMENT ANALYSISComputational Methods in Nonlinear Structural and Solid Mechanics10.1016/B978-0-08-027299-3.50048-0(379-403)Online publication date: 1981

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cover image ACM Conferences
SYMSAC '71: Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
March 1971
464 pages
ISBN:9781450377867
DOI:10.1145/800204
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New York, NY, United States

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Published: 23 March 1971

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Cited By

View all
  • (1993)Symbolic computation for inverse boundary-value problems and its application to impedance tomography reconstructionIEEE Transactions on Magnetics10.1109/20.25078929:2(1943-1945)Online publication date: Mar-1993
  • (1992)Symbolic Computation for inverse Boundary-Value Problems and its Application to impedance Tomography ReconstructionDigest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation10.1109/CEFC.1992.743904(TP43-TP43)Online publication date: 1992
  • (1981)COMPUTERIZED SYMBOLIC MANIPULATION IN NONLINEAR FINITE ELEMENT ANALYSISComputational Methods in Nonlinear Structural and Solid Mechanics10.1016/B978-0-08-027299-3.50048-0(379-403)Online publication date: 1981

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