Fast simplicial finite element algorithms using Bernstein polynomials

Authors:
Robert C. Kirby
Affiliations:
Texas Tech University, Department of Mathematics and Statistics, PO Box 1042, 79409-1042, Lubbock, TX, USA
Venue:
Numerische Mathematik
Year:
2011

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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.