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 23 articles , 1 standard article )

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  1. Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel: Functional a posteriori error estimates for boundary element methods (2021)
  2. Erath, Christoph; Schorr, Robert: Stable non-symmetric coupling of the finite volume method and the boundary element method for convection-dominated parabolic-elliptic interface problems (2020)
  3. Führer, Thomas; Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan: Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods (2019)
  4. Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan: Adaptive BEM with inexact PCG solver yields almost optimal computational costs (2019)
  5. Egger, Herbert; Erath, Christoph; Schorr, Robert: On the nonsymmetric coupling method for parabolic-elliptic interface problems (2018)
  6. Faustmann, Markus; Melenk, Jens Markus: Local convergence of the boundary element method on polyhedral domains (2018)
  7. Zieniuk, Eugeniusz; Szerszeń, Krzysztof: Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials (2018)
  8. Erath, Christoph; Schorr, Robert: An adaptive nonsymmetric finite volume and boundary element coupling method for a fluid mechanics interface problem (2017)
  9. Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P.: Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations (2017)
  10. Führer, Thomas; Heuer, Norbert: Robust coupling of DPG and BEM for a singularly perturbed transmission problem (2017)
  11. Führer, Thomas; Heuer, Norbert; Karkulik, Michael: On the coupling of DPG and BEM (2017)
  12. Melenk, J. M.; Praetorius, D.; Wohlmuth, B.: Simultaneous quasi-optimal convergence rates in FEM-BEM coupling (2017)
  13. Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas: Adaptive boundary element methods for optimal convergence of point errors (2016)
  14. Bantle, Markus; Funken, Stefan: Efficient and accurate implementation of (hp)-BEM for the Laplace operator in 2D (2015)
  15. Feischl, Michael; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, Dirk: Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation (2015)
  16. 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)
  17. 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\textH)ilbert (\underline\textI)s a (\underline\textL)ovely (\underline\textB)oundary (\underline\textE)lement (\underline\textR)esearch (\underline\textT)ool (2014)
  18. Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk: ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve (2014)
  19. Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk: Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity (2013)
  20. Aurada, Markus; Feischl, Michael; Praetorius, Dirk: Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems (2012)

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