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| Explicit Formulas for Energy Evaluations of B-spline Surfaces |
| Lizheng Lu, Thien T. Nguyen, Hongqing Zhao |
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Abstract We derive explicit formulas for the exact integration of the product
of B-spline basis functions, which are further used to calculate the
stiffness matrix of B-spline surfaces. Based on the fact that the
B-spline product can be expressed as a linear combination of high
degree B-spline basis functions, we obtain the exact integration
that depends only on the knot vector and shares parallel computing
capability. Numerical experiments show that our method has high
levels of accuracy slightly better than Gaussian quadrature, but
with more operations required. Furthermore, the computation time can
be greatly reduced by avoiding repeated computations.
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| DOI:10.12733/jics20104491 |
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