Jacobian-free Multigrid Preconditioner for Discontinuous Galerkin Methods applied to Numerical Weather Prediction.

Andreas Dedner https://orcid.org/0000-0003-4387-9791

Philipp Birken Andreas Dedner Robert Klöfkorn Jacobian-free Multigrid Preconditioner for Discontinuous Galerkin Methods applied to Numerical Weather Prediction. 2025 May abs/2505.24504 CoRR https://doi.org/10.48550/arXiv.2505.24504 db/journals/corr/corr2505.html#abs-2505-24504 streams/journals/corr

Markus Blatt Samuel Burbulla Ansgar Burchardt Andreas Dedner Christian Engwer Carsten Gräser Christoph Grüninger Robert Klöfkorn Timo Koch Santiago Ospina De Los Ríos Simon Praetorius Oliver Sander The Distributed and Unified Numerics Environment (DUNE), Version 2.10. 2025 June abs/2506.23558 CoRR https://doi.org/10.48550/arXiv.2506.23558 db/journals/corr/corr2506.html#abs-2506-23558 streams/journals/corr

Luke Benfield Andreas Dedner DDFEM: A Python Package for Diffuse Domain Methods. 2025 July abs/2507.16964 CoRR https://doi.org/10.48550/arXiv.2507.16964 db/journals/corr/corr2507.html#abs-2507-16964 streams/journals/corr

Benjamin Terschanski Robert Klöfkorn Andreas Dedner Julia Kowalski Bryne: sustainable prototyping of finite element models. 2025 September abs/2509.02378 CoRR https://doi.org/10.48550/arXiv.2509.02378 db/journals/corr/corr2509.html#abs-2509-02378 streams/journals/corr

Luke Benfield Andreas Dedner Diffuse Domain Methods with Dirichlet Boundary Conditions. 2025 September abs/2509.25115 CoRR https://doi.org/10.48550/arXiv.2509.25115 db/journals/corr/corr2509.html#abs-2509-25115 streams/journals/corr

Andreas Dedner Jan Giesselmann Kiwoong Kwon Tristan Pryer A posteriori analysis for nonlinear convection-diffusion systems. 2025 October abs/2510.09449 CoRR https://doi.org/10.48550/arXiv.2510.09449 db/journals/corr/corr2510.html#abs-2510-09449 streams/journals/corr

Andreas Dedner Alice Hodson A Higher Order Nonconforming Virtual Element Method for the Cahn-Hilliard Equation. 81 2024 December 101 J. Sci. Comput. 3 https://doi.org/10.1007/s10915-024-02721-z db/journals/jscic/jscic101.html#DednerH24 streams/journals/jscic

Andreas Dedner Alice Hodson A Framework for Implementing General Virtual Element Spaces. 229- 2024 46 SIAM J. Sci. Comput. 3 https://doi.org/10.1137/23m1573653 db/journals/siamsc/siamsc46.html#DednerH24

Linda Alzaben Daniele Boffi Andreas Dedner Lucia Gastaldi On the stabilization of a virtual element method for an acoustic vibration problem. 2024 abs/2401.04485 CoRR https://doi.org/10.48550/arXiv.2401.04485 db/journals/corr/corr2401.html#abs-2401-04485

Andrea Cangiani Andreas Dedner Matthew E. Hubbard Harry Wells Isoparametric Virtual Element Methods. 2024 abs/2404.11603 CoRR https://doi.org/10.48550/arXiv.2404.11603 db/journals/corr/corr2404.html#abs-2404-11603

Valentina Schüller Philipp Birken Andreas Dedner Convergence Properties of Iteratively Coupled Surface-Subsurface Models. 2024 abs/2408.12582 CoRR https://doi.org/10.48550/arXiv.2408.12582 db/journals/corr/corr2408.html#abs-2408-12582 streams/journals/corr

Samuel Burbulla Andreas Dedner Maximilian Hörl Christian Rohde Dune-MMesh: The Dune Grid Module for Moving Interfaces. 3959 2022 7 J. Open Source Softw. 74 https://doi.org/10.21105/joss.03959 db/journals/jossw/jossw7.html#BurbullaDHR22

Andreas Dedner Alice Hodson A framework for implementing general virtual element spaces. 2022 abs/2208.08978 CoRR https://doi.org/10.48550/arXiv.2208.08978 db/journals/corr/corr2208.html#abs-2208-08978

Peter Bastian Markus Blatt Andreas Dedner Nils-Arne Dreier Christian Engwer René Fritze Carsten Gräser Christoph Grüninger Dominic Kempf Robert Klöfkorn Mario Ohlberger Oliver Sander The Dune framework: Basic concepts and recent developments. 75-112 2021 81 Comput. Math. Appl. https://doi.org/10.1016/j.camwa.2020.06.007 db/journals/cma/cma81.html#BastianBDDEFGGK21

Andreas Dedner Jan Giesselmann Tristan Pryer Jennifer K. Ryan Residual Estimates for Post-processors in Elliptic Problems. 34 2021 88 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-021-01502-2 db/journals/jscic/jscic88.html#DednerGPR21

Andreas Dedner Alice Hodson A higher order nonconforming virtual element method for the Cahn-Hilliard equation. 2021 abs/2111.11408 CoRR https://arxiv.org/abs/2111.11408 db/journals/corr/corr2111.html#abs-2111-11408

Björn Stinner Andreas Dedner Adam Nixon A Finite Element Method for a Fourth Order Surface Equation With Application to the Onset of Cell Blebbing. 21 2020 6 Frontiers Appl. Math. Stat. https://doi.org/10.3389/fams.2020.00021 db/journals/fams/fams6.html#StinnerDN20

Björn Stinner Andreas Dedner Adam Nixon A surface finite element method for computational modelling of cell blebbing. 2020 abs/2003.00961 CoRR https://arxiv.org/abs/2003.00961 db/journals/corr/corr2003.html#abs-2003-00961

Andreas Dedner Alice Hodson A general approach for constructing robust virtual element methods for fourth order problems. 2020 abs/2008.01617 CoRR https://arxiv.org/abs/2008.01617 db/journals/corr/corr2008.html#abs-2008-01617

Andreas Dedner Robert Klöfkorn Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method. 2020 abs/2009.13416 CoRR https://arxiv.org/abs/2009.13416 db/journals/corr/corr2009.html#abs-2009-13416

Andreas Dedner Jan Giesselmann Tristan Pryer Jennifer K. Ryan Residual estimates for post-processors in elliptic problems. 2019 abs/1906.04658 CoRR http://arxiv.org/abs/1906.04658 db/journals/corr/corr1906.html#abs-1906-04658

Peter Bastian Markus Blatt Andreas Dedner Nils-Arne Dreier Christian Engwer René Fritze Carsten Gräser Dominic Kempf Robert Klöfkorn Mario Ohlberger Oliver Sander The DUNE Framework: Basic Concepts and Recent Developments. 2019 abs/1909.13672 CoRR http://arxiv.org/abs/1909.13672 db/journals/corr/corr1909.html#abs-1909-13672

Andreas Dedner Birane Kane Robert Klöfkorn Martin Nolte Python Framework for HP Adaptive Discontinuous Galerkin Method for Two Phase Flow in Porous Media. 2018 abs/1805.00290 CoRR http://arxiv.org/abs/1805.00290 db/journals/corr/corr1805.html#abs-1805-00290

Andreas Dedner Martin Nolte The Dune Python Module. 2018 abs/1807.05252 CoRR http://arxiv.org/abs/1807.05252 db/journals/corr/corr1807.html#abs-1807-05252

Andreas Dedner Pravin Madhavan Adaptive discontinuous Galerkin methods on surfaces. 369-398 2016 132 Numerische Mathematik 2 https://doi.org/10.1007/s00211-015-0719-4 db/journals/nm/nm132.html#DednerM16

Andreas Dedner Jan Giesselmann A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws. 3523-3549 2016 54 SIAM J. Numer. Anal. 6 https://doi.org/10.1137/15M1046265 db/journals/siamnum/siamnum54.html#DednerG16

Paola F. Antonietti Andreas Dedner Pravin Madhavan Simone Stangalino Björn Stinner Marco Verani High Order Discontinuous Galerkin Methods for Elliptic Problems on Surfaces. 1145-1171 2015 53 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/140957172 db/journals/siamnum/siamnum53.html#AntoniettiDMSSV15

Markus Jehl Andreas Dedner Timo Betcke Kirill Y. Aristovich Robert Klöfkorn David S. Holder A Fast Parallel Solver for the Forward Problem in Electrical Impedance Tomography. 126-137 2015 62 IEEE Trans. Biomed. Eng. 1 https://doi.org/10.1109/TBME.2014.2342280 https://www.wikidata.org/entity/Q35214321 db/journals/tbe/tbe62.html#JehlDBAKH15

Andreas Dedner Robert Klöfkorn On Efficient Time Stepping using the Discontinuous Galerkin Method for Numerical Weather Prediction. 627-636 2015 PARCO https://doi.org/10.3233/978-1-61499-621-7-627 conf/parco/2015 db/conf/parco/parco2015.html#DednerK15

Andreas Dedner Robert Klöfkorn Martin Nolte The DUNE-ALUGrid Module. 2014 abs/1407.6954 CoRR http://arxiv.org/abs/1407.6954 db/journals/corr/corr1407.html#DednerKN14

Andreas Dedner Eike Hermann Müller Robert Scheichl Efficient Multigrid Preconditioners for Anisotropic Problems in Geophysical Modelling. 2014 abs/1408.2981 CoRR http://arxiv.org/abs/1408.2981 db/journals/corr/corr1408.html#DednerMS14

Thomas Albrecht Andreas Dedner Marcel Lüthi Thomas Vetter Finite Element Surface Registration Incorporating Curvature, Volume Preservation, and Statistical Model Information. 2013 2013 Comput. Math. Methods Medicine https://doi.org/10.1155/2013/674273 https://www.wikidata.org/entity/Q37245029 db/journals/cmmm/cmmm2013.html#AlbrechtDLV13 674273:1-674273:14

Slavko Brdar Andreas Dedner Robert Klöfkorn Compact and Stable Discontinuous Galerkin Methods for Convection-Diffusion Problems. 2012 34 SIAM J. Sci. Comput. 1 https://doi.org/10.1137/100817528 db/journals/siamsc/siamsc34.html#BrdarDK12

Andreas Dedner Robert Klöfkorn A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems. 365-388 2011 47 J. Sci. Comput. 3 https://doi.org/10.1007/s10915-010-9448-0 db/journals/jscic/jscic47.html#DednerK11

Andreas Dedner Robert Klöfkorn Martin Nolte Mario Ohlberger A generic interface for parallel and adaptive discretization schemes: abstraction principles and the Dune-Fem module. 165-196 2010 90 Computing 3-4 https://doi.org/10.1007/s00607-010-0110-3 db/journals/computing/computing90.html#DednerKNO10

Peter Bastian Markus Blatt Andreas Dedner Christian Engwer Robert Klöfkorn Mario Ohlberger Oliver Sander A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework. 103-119 2008 82 Computing 2-3 https://doi.org/10.1007/s00607-008-0003-x db/journals/computing/computing82.html#BastianBDEKOS08

Peter Bastian Markus Blatt Andreas Dedner Christian Engwer Robert Klöfkorn Ralf Kornhuber Mario Ohlberger Oliver Sander A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE. 121-138 2008 82 Computing 2-3 https://doi.org/10.1007/s00607-008-0004-9 db/journals/computing/computing82.html#BastianBDEKKOS08

Andreas Dedner Charalambos G. Makridakis Mario Ohlberger Error Control for a Class of Runge-Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws. 514-538 2007 45 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/050624248 db/journals/siamnum/siamnum45.html#DednerMO07

Andreas Dedner Marcel Lüthi Thomas Albrecht Thomas Vetter Curvature Guided Level Set Registration Using Adaptive Finite Elements. 527-536 2007 conf/dagm/2007 DAGM-Symposium https://doi.org/10.1007/978-3-540-74936-3_53 db/conf/dagm/dagm2007.html#DednerLAV07

Rolf Backofen Hans-Gunther Borrmann Werner Deck Andreas Dedner Luc De Raedt Klaus Desch Markus Diesmann Martin Geier Andreas Greiner Wolfgang R. Hess Josef Honerkamp Stefan Jankowski Ingo Krossing Andreas W. Liehr Andreas Karwath Robert Klöfkorn Raphaël Pesché Tobias C. Potjans Michael C. Röttger Lars Schmidt-Thieme Gerhard Schneider 0001 Björn Voß Bernd Wiebelt Peter Wienemann Volker-Henning Winterer A Bottom-up approach to Grid-Computing at a University: the Black-Forest-Grid Initiative. 81-87 2006 29 Prax. Inf.verarb. Kommun. 2 https://doi.org/10.1515/PIKO.2006.81 https://www.wikidata.org/entity/Q62661290 db/journals/pik/pik29.html#BackofenBDDRDDGGHHJKLKKPPRSSVWWW06

Andreas Dedner Christian Rohde Numerical approximation of entropy solutions for hyperbolic integro-differential equations. 441-471 2004 97 Numerische Mathematik 3 https://doi.org/10.1007/s00211-003-0502-9 db/journals/nm/nm97.html#DednerR04

Thomas Albrecht Linda Alzaben Paola F. Antonietti Kirill Y. Aristovich Rolf Backofen Peter Bastian Luke Benfield Timo Betcke Philipp Birken Markus Blatt Daniele Boffi Hans-Gunther Borrmann Slavko Brdar Samuel Burbulla Ansgar Burchardt Andrea Cangiani Werner Deck Klaus Desch Markus Diesmann Nils-Arne Dreier Christian Engwer René Fritze Lucia Gastaldi Martin Geier Jan Giesselmann Carsten Gräser Andreas Greiner Christoph Grüninger Wolfgang R. Hess Alice Hodson David S. Holder Josef Honerkamp Maximilian Hörl Matthew E. Hubbard Stefan Jankowski Markus Jehl Birane Kane Andreas Karwath Andreas W. Kempa-LiehrAndreas W. Liehr Dominic Kempf Robert Klöfkorn Timo Koch Ralf Kornhuber Julia Kowalski Ingo Krossing Kiwoong Kwon Marcel Lüthi Pravin Madhavan Charalambos G. Makridakis Eike Hermann Müller Adam Nixon Martin Nolte Mario Ohlberger Raphaël Pesché Tobias C. Potjans Simon Praetorius Tristan Pryer Luc De Raedt Santiago Ospina De Los Ríos Christian Rohde Michael C. Röttger Jennifer K. Ryan Oliver Sander Robert Scheichl Lars Schmidt-Thieme Gerhard Schneider 0001 Valentina Schüller Simone Stangalino Björn Stinner Benjamin Terschanski Marco Verani Thomas Vetter Björn Voß Harry Wells Bernd Wiebelt Peter Wienemann Volker-Henning Winterer