Kolja Brix

Publications

• Kolja Brix, Yasemin Hafizogullari, and Andreas Platen
  Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge–Ampère Equations.
  Journal of the Optical Society of America A, Volume 32, Issue 11, pp. 2227-2236, 2015.
  DOI - Preprint (arXiv.org, IGPM Report #427, local copy)
• Kolja Brix (joint with Martin Campos Pinto, Claudio Canuto, and Wolfgang Dahmen)
  Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods.
  In: Oberwolfach Reports, Report 2/2015, to appear (probably in Vol. 12, 2015).
  DOI - Preprint
• Kolja Brix, Yasemin Hafizogullari, and Andreas Platen
  Solving the Monge–Ampère Equations for the Inverse Reflector Problem.
  Mathematical Models and Methods in Applied Sciences, Volume 25, Issue 5, pp. 803-837, 2015.
  DOI - Preprint (arXiv.org, IGPM Report #396, local copy)
• Kolja Brix, Claudio Canuto, and Wolfgang Dahmen
  Nested dyadic grids associated with Legendre–Gauss–Lobatto grids.
  Numerische Mathematik, Volume 131, Issue 2, pp. 205-239, 2015.
  DOI - Preprint (arXiv.org, IGPM Report #378, local copy; Title: Legendre–Gauss–Lobatto grids and associated nested dyadic grids.)
• Kolja Brix, Martin Campos Pinto, Claudio Canuto, and Wolfgang Dahmen
  Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods,
  Part I: Geometrically Conforming Meshes.
  IMA Journal of Numerical Analysis, 2014 (published online).
  DOI - Preprint (arXiv.org, IGPM Report #355, local copy)
• Kolja Brix, Claudio Canuto, and Wolfgang Dahmen
  Robust Preconditioners for DG-Discretizations with Arbitrary Polynomial Degrees.
  In: J. Erhel, M.J. Gander, L. Halpern, G. Pichot, T. Sassi, and O. B. Widlund (eds.), Domain Decomposition Methods in Science and Engineering XXI (Proceedings of 21st International Conference on Domain Decomposition Methods, INRIA Rennes-Bretagne-Atlantique, Rennes, France, June 25-29, 2012), Lecture Notes in Computational Science and Engineering, Vol. 98, Springer, Heidelberg, pp. 537-545, 2014.
  DOI - Preprint (arXiv.org, IGPM Report #353) - Proceedings preview
• Kolja Brix, Silvia Sorana Melian, Siegfried Müller, and Mathieu Bachmann
  Adaptive Multiresolution Methods: Practical issues on Data Structures, Implementation and Parallelization.
  In: V. Louvet and M. Massot (eds.), Proceedings of Ecole Thématique du GDR Calcul: "Méthodes multirésolution et méthodes de raffinement adaptatif de maillage", Fréjus, France, June 14-18, 2010.
  ESAIM: Proceedings, Volume 34, pp. 151-183, 2011.
  DOI
• Silvia Sorana Melian, Kolja Brix, Siegfried Müller, and Gero Schieffer
  Space-Filling Curve Techniques for Parallel, Multiscale-Based Grid Adaptation: Concepts and Applications.
  In: A. Kuzmin (ed.), Proceedings of the Sixth International Conference on Computational Fluid Dynamics (ICCFD6), St. Petersburg, Russia, July 12-16th, 2010, Springer, Heidelberg, pp. 591-600, 2011.
  DOI
• Kolja Brix, Ralf Massjung, and Alexander Voss
  Refinement and Connectivity Algorithms for Adaptive Discontinuous Galerkin Methods.
  SIAM Journal on Scientific Computing, Volume 33, Issue 1, pp. 66-101, 2011.
  DOI - Journal webpage - Preprint (IGPM Report #302, Title: A hash data structure for adaptive PDE-solvers based on Discontinuous Galerkin discretizations.)
  
  Presentation notes: Adaptive Multiresolution Methods: Practical issues on Data Structures, Implementation and Parallelization. Part I: Data Structures and Implementation.
  Ecole d'Eté AMR-MR, June 14-18, 2010, Fréjus, France.
• Josef Ballmann, Marek Behr, Kolja Brix, Wolfgang Dahmen, Christoph Hohn, Ralf Massjung, Sorana Melian, Siegfried Müller, and Gero Schieffer
  Parallel and Adaptive Methods for Fluid–Structure–Interactions.
  In: W. Schröder (ed.), Summary of Flow Modulation and Fluid-Structure Interaction Findings - Results of the Collaborative Research Center SFB 401 at the RWTH Aachen University, Aachen, Germany, 1997-2008
  Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 109, pp. 265-294, Springer, Berlin, 2010.
  DOI - Preprint (IGPM Report #296)
• Kolja Brix, Silvia Sorana Melian, Siegfried Müller, and Gero Schieffer
  Parallelisation of Multiscale-Based Grid Adaptation using Space-Filling Curves.
  ESAIM Proceedings, Volume 29, pp. 108-129, 2009.
  DOI - Preprint (IGPM Report #299)
• Kolja Brix, Martin Campos Pinto, Wolfgang Dahmen, and Ralf Massjung
  Multilevel Preconditioners for the Interior Penalty Discontinuous Galerkin Method II - Quantitative Studies.
  Communications in Computational Physics, Volume 5, pp. 296-325, 2009.
  Preprint (IGPM Report #282)
• Kolja Brix, Martin Campos Pinto, and Wolfgang Dahmen
  A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method.
  SIAM Journal on Numerical Analysis, Volume 46, Issue 5, pp. 2742-2768, 2008.
  DOI - Journal webpage - Preprint (IGPM Report #277)