Finite Element Methods with B-Splines

Höllig, Klaus

doi:10.1137/1.9780898717532

Cited by 291 publications

(274 citation statements)

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“…The electrostatic potential is discretized in toroidal Fourier space with Bsplines finite elements [29] on a (r, χ) grid with (N r , N χ ) grid points, where r is a radial coordinate and χ is a poloidal angle-like coordinate.…”

Section: The Fourier Solvermentioning

confidence: 99%

Parallel filtering in global gyrokinetic simulations

Jolliet

McMillan

Villard

et al. 2012

Journal of Computational Physics

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Section: The Fourier Solvermentioning

confidence: 99%

Parallel filtering in global gyrokinetic simulations

Jolliet

McMillan

Villard

et al. 2012

Journal of Computational Physics

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“…However it is nor clear that this result will generalize to other, less well-behaved, applications. (Verfürth, 1996), the Weighted extended B-splines Finite Element approach (Höllig, 2003) and ElementFree Galerkin Methods (Belytschko et al, 1996) that improve on the basic Finite Elements approach exploiting local information and error estimator values for the elements.…”

Section: Discussionmentioning

confidence: 99%

“…In particular we use lines of code as a proxy for the implementation complexity. 23 The Undetermined Coefficients method (in level and in logs) takes only a miniscule fraction of a second in a 1.7 Mhz Xeon PC running Windows XP (the reference computer for all times below), and it is very simple to implement (the code for both methods takes less than 24 The reader is invited to explore by himself all these issues (and reproduce our results) looking at our code available on-line. 23 Unfortunately, as we explained before, the difficulties of Matlab and Fortran 95 to handle at the moment higher order perturbations stops us from using only one programing language.…”

Section: Implementation and Computing Timementioning

confidence: 96%

Comparing Solution Methods for Dynamic Equilibrium Economies

2003

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This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using Undetermined Coefficients in levels and in logs, Finite Elements, Chebyshev Polynomials, Second and Fifth Order Perturbations and Value Function Iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity and accuracy and we present some conclusions about our preferred approaches based on the reported evidence.

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“…For example, one can localize the construction of w with the aid of a B-spline blending technique (cf. [10] for details).…”

Section: Web-basismentioning

confidence: 99%

“…Details of the arguments can be found in [10]. With the aid of the dual functions we define a canonical projector…”

Section: Theorem 1 (Stability) For An -Regular Weight Function Of Ordermentioning

confidence: 99%

Introduction to the Web-method and its applications

2005

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The Web-method is a meshless finite element technique which uses weighted extended B-splines (Web-splines) on a tensor product grid as basis functions. It combines the computational advantages of B-splines and standard mesh-based elements. In particular, degree and smoothness can be chosen arbitrarily without substantially increasing the dimension. Hence, accurate approximations are obtained with relatively few parameters. Moreover, the regular grid is well suited for hierarchical refinement and multigrid techniques. This article should serve as an introduction to finite element approximation with B-splines. We first review the construction of Web-bases and discuss their basic properties. Then we illustrate the performance of Ritz-Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects.

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Finite Element Methods with B-Splines

Cited by 291 publications

References 0 publications

Parallel filtering in global gyrokinetic simulations

Parallel filtering in global gyrokinetic simulations

Comparing Solution Methods for Dynamic Equilibrium Economies

Introduction to the Web-method and its applications

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