Fast simplicial finite element algorithms using Bernstein polynomials |
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Authors: | Robert C Kirby |
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Institution: | (1) Department of Earth Sciences, Utrecht University, Budapestlaan 4, 3584 Utrecht, CE, The Netherlands |
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Abstract: | Fast algorithms for applying finite element mass and stiffness operators to the B-form of polynomials over d-dimensional simplices are derived. These rely on special properties of the Bernstein basis and lead to stiffness matrix algorithms
with the same asymptotic complexity as tensor-product techniques in rectangular domains. First, special structure leading
to fast application of mass matrices is developed. Then, by factoring stiffness matrices into products of sparse derivative
matrices with mass matrices, fast algorithms are also obtained for stiffness matrices. |
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Keywords: | |
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