Efficient implementation of adaptive P1-FEM in Matlab

Funken, Stefan A.; Praetorius, Dirk; Wissgott, P.

doi:10.2478/cmam-2011-0026

Cited by 94 publications

(86 citation statements)

References 16 publications

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“…They also want to thank Francisco-Javier Sayas for pointing them to the red-green-blue refinement algorithm proposed in [22]. Finally, they also want to thank Ricardo Nochetto for fruitful discussions leading to a better presentation of the paper.…”

Section: Acknowledgementsmentioning

confidence: 99%

A Posteriori Error Estimates for HDG Methods

Cockburn

Zhang

2011

J Sci Comput

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We present the first a posteriori error analysis of the so-called hybridizable discontinuous Galerkin (HDG) methods for second-order elliptic problems. We show that the error in the flux can be controlled by only two terms. The first term captures the so-called data oscillation. The second solely depends on the difference between the trace of the scalar approximation and the corresponding numerical trace. Numerical experiments verifying the reliability and efficiency of the estimate in two-space dimensions are presented.

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Section: Acknowledgementsmentioning

confidence: 99%

A Posteriori Error Estimates for HDG Methods

Cockburn

Zhang

2011

J Sci Comput

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“…Finally, by use of the same data structure as in [1,22], it is easily possible to link HILBERT to existing MATLAB finite element codes to realize, e.g., the (adaptive) coupling of FEM and BEM.…”

Section: Discretization Of the Domainmentioning

confidence: 99%

“…The assembly of the Newtonian potential N requires a volume mesh for the quadrature over the domain . To that end, we use the standard format as described in [1] and buildN uses mesh-manipulation routines as described in [22]. The assembly of the discrete boundary integral operators is significantly time consuming.…”

Section: Elements[eta]) -W = Buildw(coordinateselements[eta]) -N =mentioning

confidence: 99%

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HILBERT — a MATLAB implementation of adaptive 2D-BEM

et al. 2013

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We report on the MATLAB program package HILBERT. It provides an easily-accessible implementation of lowest-order adaptive Galerkin boundary element methods for the numerical solution of the Poisson equation in 2D. The library was designed to serve several purposes: The stable implementation of the integral operators may be used in research code. The framework of MATLAB ensures usability in lectures on boundary element methods or scientific computing. Finally, we emphasize the use of adaptivity as general concept and for boundary element methods in particular. In this work, we summarize recent analytical results on adaptivity in the context of BEM and illustrate the use of HILBERT. Various benchmarks are performed to empirically analyze the performance of the proposed adaptive algorithms and to compare adaptive and uniform mesh-refinements. In particular, we do not only focus on mathematical convergence behavior but also on the usage of critical system resources such as memory consumption and computational time. In any case, the superiority of the proposed adaptive approach is empirically supported.

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“…The vector x bn is understood as the vector of Dirichlet data (in the case here discussed equal to zero, thus b( f n) = b( f n) ) extended to length N by zero-padding for indices of free nodes. For an easily readable Matlab implementation in the 2-dimensional case we refer to [30]. The resulting system is reduced to the size N f × N f and is symmetric, positive definite and sparse.…”

Section: Fem For the Dirichlet Problemmentioning

confidence: 99%

Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

Exl

Schrefl

2014

Journal of Computational Physics

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We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet problem and evaluation of the single layer potential by a fast approximation technique based on Fourier approximation of the kernel function. The latter approximation leads to a generalization of the well-known convolution theorem used in finite difference methods. We address it by a non-uniform FFT approach. Overall, our method scales O(M + N + N log N) for N nodes and M surface triangles. We confirm our approach by several numerical tests.

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Efficient implementation of adaptive P1-FEM in Matlab

Cited by 94 publications

References 16 publications

A Posteriori Error Estimates for HDG Methods

A Posteriori Error Estimates for HDG Methods

HILBERT — a MATLAB implementation of adaptive 2D-BEM

Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

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