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Fast simplicial finite element algorithms using Bernstein polynomials. (English) Zbl 1211.65156
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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65Y20 Complexity and performance of numerical algorithms
Software:
DOLFIN
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