Fast simplicial finite element algorithms using Bernstein polynomials

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 techn...

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Bibliographic Details
Published inNumerische Mathematik Vol. 117; no. 4; pp. 631 - 652
Main Author Kirby, Robert C.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.04.2011
Springer
Subjects
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical analysis. Scientific computation
Numerical and Computational Physics
Numerical linear algebra
Sciences and techniques of general use
Simulation
Theoretical
65F30
65N30
Finite element method
Stiffness matrix
Numerical analysis
Tensor product
Numerical linear algebra
Algorithm complexity
Matrix method
Fast algorithm
Bernstein polynomial
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Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-010-0327-2