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A new method of integration over polynomal finite element boundaries
Author(s) -
Rodin E. Y.
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100511
Subject(s) - mathematics , completeness (order theory) , polynomial , finite element method , calculus (dental) , algebra over a field , mathematical analysis , pure mathematics , structural engineering , engineering , medicine , dentistry
In this note we are developing integration techniques for triangular regions in which one side is curved. Specifically, we are considering (a) general polynomial boundaries and (b) various combinations of elliptical boundaries. Integration is performed over all of these explicitly. One definite and considerable improvement achieved is the introduction of a new method of integration over polynomial type boundaries. This new method is not only exact for polynomials or other analytic functions, but also reduces the computing time considerably; for example, if for a sixth order polynomial the number of operations necessary (using previously available methods) to perform the integration was n , the method introduced here requires a number proportional to n 1/6 . Furthermore, coding time is also reduced considerably. It may be of value to mention that the availability of the results presented here could obviate the need for the use of isoparametric elements in some regions with curved boundaries. For completeness, explicit integration formulas for elliptic shaped regions are also listed.