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| Finite point matrix method based on cosine spline |
| Revised:January 10, 2005 |
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| DOI：10.7511/jslx20071021 |
| KeyWord:influence domain,point matrix,cosine spline function,tensor product,normalization space,numerical method |
| SUN Hai-tao WANG Yuan-han |
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| Abstract: |
| A finite point matrix method based on the cosine splines is presented by utilizing the conception of the nodal influence domain in this paper.Some important properties of the cosine spline functions are identified for deriving the formulas and exhibiting the performances of the numerical method proposed here.With applications of the cosine spline bases as solution space,a normalized space is constructed for approximation of the field functions through tensor product method.Linear combination of the cosine spline bases results in the treatment of the boundary conditions prescribed as conveniently as traditional finite element method.Coupled with the boundary type numerical methods,cosine splines can be employed for solving problems in an irregular domain by node matrix distributed on the boundary.Several numerical examples are posed to identify the method and show the advantages while the method is adopted.Results demonstrate that numerical oscillation resulted from high degree polynomial shape functions is avoided and continuity rank is limited no more.Densifying point matrix required for improving accuracy brings a lightly enhancement on the quantity of calculation only.Rapid convergence is another identification mark of the method. |
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