HILBERT

HILBERT–A Matlab implementation of adaptive BEM. 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. (http://www.netlib.org/numeralgo/index.html na38)


References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas: Adaptive boundary element methods for optimal convergence of point errors (2016)
  2. Bantle, Markus; Funken, Stefan: Efficient and accurate implementation of $hp$-BEM for the Laplace operator in 2D (2015)
  3. Feischl, Michael; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, Dirk: Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation (2015)
  4. Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J.Markus; Praetorius, Dirk: Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation (2015)
  5. Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk: HILBERT -- a MATLAB implementation of adaptive 2D-BEM. $\underline \text H$ilbert $\underline \text I$s a $\underline \text L$ovely $\underline \text B$oundary $\underline \text E$lement $\underline \text R$esearch $\underline \text T$ool (2014)
  6. Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk: ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve (2014)
  7. Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk: Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity (2013)
  8. Aurada, Markus; Feischl, Michael; Praetorius, Dirk: Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems (2012)
  9. Aurada, Markus; Ferraz-Leite, Samuel; Praetorius, Dirk: Estimator reduction and convergence of adaptive BEM (2012)
  10. Aurada, M.; Feischl, M.; Karkulik, M.; Praetorius, Dirk: A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling (2012)
  11. Aurada, M.; Ferraz-Leite, S.; Goldenits, P.; Karkulik, M.; Mayr, M.; Praetorius, D.: Convergence of adaptive BEM for some mixed boundary value problem (2012)