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Cubic spline boundary elements
Author(s) -
Ligget James A.,
Salmon James R.
Publication year - 1981
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.1620170405
Subject(s) - monotone cubic interpolation , spline interpolation , mathematics , cubic hermite spline , thin plate spline , interpolation (computer graphics) , mathematical analysis , quadrature (astronomy) , linear interpolation , spline (mechanical) , smoothing spline , hermite spline , nearest neighbor interpolation , bicubic interpolation , boundary (topology) , geometry , bilinear interpolation , physics , classical mechanics , optics , motion (physics) , statistics , polynomial , thermodynamics
The boundary integral method is formulated and applied using cubic spline interpolation along the boundary for both the geometry and the primary variables. The cubic spline interpolation has continuous first and second derivatives between elements, thus allowing the accurate calculation of derivative dependent functions (on the boundary) such as velocity in potential flow. The spline functions also smooth the geometry and can represent curved sections with fewer nodes. The results of numerical experiments indicate that the accuracy of the boundary integral equation method is improved for a given number of elements by using cubic spline interpolation. It is, however, necessary to use numerical quadrature. The quadrature slows calculation and/or degrades the accuracy. The numerical experiments indicate that most problems run faster for a given accuracy using linear interpolation. There seems to be a class of problems, however, which requires higher order interpolation and/or continuous derivatives for which the cubic spline interpolation works much better than linear interpolation.