The paper Automatic differentiation for performing the Cauchy-Kovalevskaya procedure in Lax-Wendroff type discretizations of Arpit Babbar, Valentin Churavy, ...
Jan Giesselmann, Fabio Leotta, Jochen Schütz, and I have published our new preprint Justification and structure- and asymptotic-preserving discretizations of...
The paper Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations of Arpit Babbar and me has been published in the Journal ...
Saurav Samantaray has been working in our group as a postdoctoral researcher funded by the Mainz Institute of Multiscale Modelling (M3ODEL). Now, he moves on...
Arpit Babbar has been working in our group as a postdoctoral researcher funded by the Mainz Institute of Multiscale Modelling (M3ODEL) and the Alexander von ...
Louis Petri from our group will be at the 20th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2026) in Stuttgart, Ger...
The paper The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable of Louis Petri, Gunnar Birke, Christian Engwer, and me has be...
Marco Artiano from our group will be at the European Geosciences Union (EGU) General Assembly 2026 in Vienna, Austria. Moreover, Hugo Dominguez (Geosciences ...
The paper Computing radially-symmetric solutions of the ultra-relativistic Euler equations with entropy-stable discontinuous Galerkin methods of Ferdinand Th...
Marco Artiano, Saurav Samantaray, and I have published our new preprint Asymptotic-Preserving and Well-Balanced Linearly Implicit IMEX Schemes for the Anelas...
Arpit Babbar, Qifan Chen, and I have published our new preprint Compact Runge-Kutta flux reconstruction methods with entropy and/or kinetic energy preserving...
Thomas Izgin, Chi-Wang Shu, and I have published our new preprint A Positivity-Preserving Relaxation Algorithm on arXiv.
Daniel Doehring, Jesse Chan, Michael Schlottke-Lakemper, Manuel Torrilhon, Gregor Gassner, and I have published our new preprint Volume Term Adaptivity for D...
Marco Artiano and Saurav Samantaray from our group will be at the International Conference on High Order Nonlinear Numerical Methods for Evolutionary PDE (HO...
Marco Artiano and I have published our new preprint On Affordable High-Order Entropy-Conservative/Stable and Well-Balanced Methods for Nonconservative Hyperb...
Marco Artiano, Arpit Babbar, Michael Schlottke-Lakemper, Gregor Gassner, and I have published our new preprint Jin-Xin relaxation as a shock-capturing method...
Marco Artiano, Arpit Babbar, Valentin Churavy, and I will be at the Trixi User and Developer Interaction (TRUDI) 2026 in Cologne, Germany.
The paper Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions of Jan Giesselmann and me has been published in the SMAI Journal...
The paper A Full Three-Dimensional GPU-Accelerated Model for Deep Borehole Heat Exchangers (DBHEs) Enabling Simulation of Well Arrays of Collin Wittenstein, ...
Collin Wittenstein, a graduate student from our group who is currently a visiting student at MIT, will present some of our research at the Stanford Geotherma...
Gunnar Birke, Christian Engwer, Sandra May, Louis Petri, and I have published our new preprint An Energy-Preserving Domain of Dependence Stabilization for th...
Louis Petri, Sigrun Ortleb, Gunnar Birke, Christian Engwer, and I have published our new preprint Domain-of-dependence-stabilized cut-cell discretizations of...
Collin Wittenstein, Vincent Marks, Mario Ricchiuto, and I have published our new preprint GPU-Accelerated Energy-Conserving Methods for the Hyperbolized Serr...
Arpit Babbar will present some of our research at the seminar of the Tata Institute for Fundamental Research - Centre for Applicable Mathematics (TIFR-CAM) o...
David I. Ketcheson and I have published our new preprint Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear...
The paper DispersiveShallowWater.jl: A Julia library of structure-preserving numerical methods for dispersive wave equations of Joshua Lampert, Collin Witten...
Arpit Babbar and I have published our new preprint Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations on arXiv.
The paper Relaxation Runge-Kutta methods with First-Same-as-Last Structure of Sebastian Bleecke and me has been published in the Journal of Scientific Comput...
Sebastian Bleecke, Abhijit Biswas, Jochen Schütz, David I. Ketcheson and I have published our new preprint Asymptotic-preserving and energy-conserving method...
The paper Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations of Joshua Lampert and me has been published in Comput...
David I. Ketcheson and I have published our new preprint High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperb...
Marco Artiano, Oswald Knoth, Peter Spichtinger, and I have published our new preprint Structure-Preserving High-Order Methods for the Compressible Euler Equa...
Arpit Babbar will present some of our research at the online seminar of the Tata Institute for Fundamental Research - Centre for Applicable Mathematics (TIFR...
The institutes of Mathematics and Computer Science at Johannes Gutenberg University Mainz have joined forces to present their research and activities to the ...
Ángel Durán has organized the workshop Topics on Geometric Integration for Partial Differential Equations in Valladolid, Spain. Together with Cipriano Escala...
Valentin Churavy has presented some of his work at the ML Coupling Workshop in Cambridge, UK in Cambridge, UK.
Marco Artiano will present some of our research at the ECCOMAS 8th Young Investigators Conference 2025 in Pescara, Italy.
Ferdinand Thein and I have published our new preprint Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Di...
Louis Petri will present some of our research at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2025 in Heidelberg.
The paper Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs of Cordu...
Louis Petri, Gunnar Birke, Christian Engwer, and I have published our new preprint The domain-of-dependence stabilization for cut-cell meshes is fully discre...
Jan Giesselmann and I have published our new preprint Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions on arXiv.
Niklas Dieckow, Katharina Ostaszewski, Philip Heinisch, Henriette Struckmann, and I have published our new preprint Real-time rail vehicle localisation using...
The whitepaper Open-Source Software for Structure-Preserving Computational Fluid Dynamics of Francesco Capuano, Artur Palha, Francesc Xavier Trias Miquel, an...
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner, Jan Nordström, Sigrun Ortleb, and I have published our new preprint Stability of the Active Flux Metho...
Daniel Doehring, Manuel Torrilhon, and I have published our new preprint Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Sta...
Marco Artiano, Arpit Babbar, and Louis Petri from our group will be at the International Conference on Spectral and High Order Methods (ICOSAHOM 2025) in Mon...
I have been invited to give a talk Hyperbolic approximations of partial differential equations at the RMU Seminar Solution Concepts in PDEs in June 2025.
The paper Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form of Mario Ricchiuto and me has been publishe...
Arpit Babbar, Valentin Churavy, Michael Schlottke-Lakemper, and I have published our new preprint Automatic differentiation for Lax-Wendroff-type discretizat...
Marco Artiano, Arpit Babbar, Louis Petri, and I will be at the conference Numerical Methods for Hyperbolic Problems (numhyp25) in Darmstadt.
The paper PositiveIntegrators.jl: A Julia library of positivity-preserving time integration methods of Stefan Kopecz, Joshua Lampert, and me has been publish...
I have been invited to give a talk Structure-preserving time integration methods for dispersive wave equations at the workshop Efficient high-order time disc...
The paper Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation of Abhijit Bis...
The paper Pseudo-Energy-Preserving Explicit Runge-Kutta Methods of Gabriel A. Barrios de León, David I. Ketcheson, and me has been published in ESAIM: Mathem...
Sebastian Bleecke will present some of our work at the SIAM CSE 2025 conference in Forth Worth, Texas, USA.
The paper Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods of Jan Glaubitz, Andrew R. Winters, M...
Valentin Churavy will present some of his work at the 5th conference for Research Software Engineering in Germany (deRSE25) in Karlsruhe.
The paper t8code - modular adaptive mesh refinement in the exascale era of Johannes Holke, Johannes Markert, David Knapp, Lukas Dreyer, Sandro Elsweijer, Nik...
Saurav Samantaray has joined our group as a postdoc in February 2025. He will work on a joint project with Friederike Schmid (Institute of Physics, Johannes ...
I will give a talk Structure-preserving numerical methods for dispersive wave equations at the Rhein-Main-Arbeitskreis Mathematics of Computation on Friday, ...
I will give a talk Robust and efficient time integration methods for compressible fluid dynamics at the collaborative research center TRR 146: Multiscale Sim...
Abhijit Biswas, David I. Ketcheson, Jochen Schütz, and I have published our new preprint Traveling-wave solutions and structure-preserving numerical methods ...
The paper An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements of David A. Kopriva, Andrew R. Winters, Michael Schlottke-Lakem...
Arpit Babbar has been awarded a prestigious Humboldt Research Fellowship for postdocs by the Alexander von Humboldt Foundation. He will work on “Discontinuou...
The paper Structure-preserving numerical methods for Fokker-Planck equations of Hanna Bartel, Joshua Lampert, and me has been published in the Proceedings in...
The paper GeophysicalModelGenerator.jl: A Julia package to visualise geoscientific data and create numerical model setups of Boris J. P. Kaus, Marcel Thielma...
The paper On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws of Andrew R. Winters, Michael Schlottke-Lakemper,...
Arpit Babbar will present some of his PhD work at the Indo-German Workshop on Hardware-aware Scientific Computing (IGHASC) in Heidelberg.
Marco Artiano, Arpit Babbar, and I will be at the Mathematics of the Weather 2024 conference in Bad Orb.
Marco Artiano has published his first paper On the Performances of Standard and Kinetic Energy Preserving Time-Integration Methods for Incompressible-Flow Si...
The paper Stability of step size control based on a posteriori error estimates of Jan Giesselmann and me has been published in Computational Science and Engi...
I will teach a course on “Climate Modelling and Simulation” for pupils/students (age 15 to 18 years old) at the Mainzer Mathe-Akademie 2024 (in German).
Stefan Kopecz from the University of Kassel will present our new Julia package PositiveIntegrators.jl at NUMDIFF-17 in Halle, Germany. His abstract is
Mario Ricchiuto and I have published our new preprint Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form...
Gabriel A. Barrios de León, David I. Ketcheson, and I have published our new preprint Pseudo-Energy-Preserving Explicit Runge-Kutta Methods on arXiv.
Sebastian Bleecke will present some of our work at the International Conference on Scientific Computation and Differential Equations (SciCADE) in Singapore i...
Jan Glaubitz, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Gregor J. Gassner, and I have published our new preprint Generalized upwind summ...
The paper Multiderivative time integration methods preserving nonlinear functionals via relaxation of Jochen Schütz and me has been published in Communicatio...
I am organizing the minisymposium “Julia for High-Performance Computing” at JuliaCon 2024. The minisymposium will take place on Friday, July 12, from 14:00 t...
Hanna Bartel, Joshua Lampert, and I have published our new preprint Structure-Preserving Numerical Methods for Fokker-Planck Equations on arXiv.
Joshua Lampert and I have published our new preprint Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations on arXiv.
I was invited to give a talk Structure-preserving numerical methods for nonlinear dispersive wave equations at the Séminaire de Calcul Scientifique et Modéli...
We have initiated a new Julia User Group in Mainz (Germany). It provides a platform for everybody interested in Julia - both people new to Julia and people h...
Thomas Izgin and I have published our new preprint Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar-Run...
Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Jan Glaubitz, Gregor J. Gassner, and I have published our new preprint On the robustness of hi...
Sebastian Bleecke and I have published our new preprint Step size control for explicit relaxation Runge-Kutta methods preserving invariants on arXiv.
Jochen Schütz and I have published our new preprint Multiderivative time integration methods preserving nonlinear functionals via relaxation on arXiv.
I was invited to give lectures at the summer school Research Software Engineering with Julia: Basics, Visualization, and Statistics in Stuttgart in the week ...
The paper Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws of Michael Sch...
I was invited to give a talk Adaptive and structure-preserving numerical methods at the Computational Mathematics Seminar at Hasselt University (Belgium) on ...
The paper Resolving Entropy Growth from Iterative Methods of Viktor Linders, Philipp Birken, and me has been published in BIT Numerical Mathematics.
The paper Functional-preserving predictor-corrector multiderivative schemes of Jochen Schütz, Eleni Theodosiou, and me has been published in Proceedings in A...
Jan Giesselmann and I have published our new preprint Stability of step size control based on a posteriori error estimates on arXiv.
My paper A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators has been publis...
I was invited to give a talk Efficient and robust numerical methods based on adaptivity and structure preservation at the Seminar of Computational and Numeri...
Jochen Schütz, Eleni Theodosiou, and I have published our new preprint Functional-preserving predictor-corrector multiderivative schemes.
The paper On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics of Andrew R. Winters, Hugo Guillermo Castro, Li...
I will give a tutorial on the Julia programming language and Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic PDEs in Ka...
I gave the keynote talk Structure-preserving numerical methods for dispersive wave equations in the section S18: Numerical methods for differential equations...
Cordula Reisch and I have published our new preprint Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biol...
Viktor Linders, Philipp Birken, and I have published our new preprint Resolving Entropy Growth from Iterative Methods on arXiv.
I have published my new preprint A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts o...
I submitted the talk A Discretization of Elliptic Terms with Improved Convergence Properties Using Summation by Parts Operators to the SIAM CSE Conference 20...
Michael Schlottke-Lakemper and I have organized the minisymposium Research Software Engineering with Julia at the SIAM CSE Conference 2023 in Amsterdam (The ...
I gave the talk Structure-preserving time integration methods based on relaxation at the Numerical Analysis Seminar at Lund University (Sweden) on Tuesday, 2...
The paper Computing with B-series of David I. Ketcheson and me has been published in ACM Transactions on Mathematical Software.
Valentin Churavy, William F Godoy, Carsten Bauer, Michael Schlottke-Lakemper, Ludovic Räss, Johannes Blaschke, Mosè Giordano, Erik Schnetter, Samuel Omlin, J...
I gave the talk Robust and efficient high-performance computational fluid dynamics enabled by modern numerical methods and technologies at the MUSEN center f...
Michael Schlottke-Lakemper and I gave the talk Reproducibility as a service: collaborative scientific computing with Julia at the MaRDI Workshop for Scientif...
Andrew R. Winters, Hugo Guillermo Castro, Lisandro Dalcin, Michael Schlottke-Lakemper, Gregor J. Gassner, Matteo Parsani, and I have published our new prepri...
I gave a talk Efficient and Robust Time Integration with Automatic Step Size Control for Compressible Computational Fluid Dynamics at the 92nd annual meeting...
The paper Issues with positivity-preserving Patankar-type schemes of Davide Torlo, Philipp Öffner, and me has been published in Applied Numerical Mathematics.
The paper On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows of Jesse Chan, An...
I gave a talk Efficient and robust step size control for computational fluid dynamics at the workshop Efficient high-order time discretization methods for PD...
My paper A Note on Numerical Fluxes Conserving a Member of Harten’s One-Parameter Family of Entropies for the Compressible Euler Equations has been published...
Jesse Chan, Andrés M. Rueda-Ramírez, Gregor J. Gassner, Tim Warburton, and I have published our new preprint On the entropy projection and the robustness of ...
The paper Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing of Michael Schlottke-Lakemper, Andrew R. Winters, Erik...
I have published my new preprint A Note on Numerical Fluxes Conserving Harten’s Entropies for the Compressible Euler Equations on arXiv.
The paper Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure P...
Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R Winters, Florian Hindenlang, Gregor J. Gassner, and I have published our new prepri...
David I. Ketcheson and I have published our new preprint Computing with B-series on arXiv.
The paper Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics of Lisandro Dalcin, Matteo Parsani, Da...
The paper Positivity-Preserving Adaptive Runge-Kutta Methods of Stephan Nüßlein, David I. Ketcheson, and me has been published in Communications in Applied M...
The paper On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations of Manuel Quezada de Luna, David I. Ketcheson, a...
My paper SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties has been published in the Jou...
Davide Torlo, Philipp Öffner, and I have published our new preprint A New Stability Approach for Positivity-Preserving Patankar-type Schemes on arXiv.
Michael Schlottke-Lakemper, Andrew R. Winters, Erik Faulhaber, Jesse Chan, Gregor J. Gassner, and I have published our new preprint Adaptive numerical simula...
The paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes of Gregor J. Gassner and...
I gave a talk Combining Analysis and Data: Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics in th...
On this page
On this page
The paper A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics of Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. G...
The paper A conservative fully-discrete numerical method for the regularized shallow water wave equations of Dimitrios Mitsotakis, David I Ketcheson, Endre S...
I gave a talk Introduction to Julia and Trixi, a numerical simulation framework for hyperbolic PDEs in the Applied Mathematics Seminar, University of Münster...
Lisandro Dalcin, Matteo Parsani, David I. Ketcheson, and I have published our new preprint Optimized Runge-Kutta Methods with Automatic Step Size Control for...
The paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts of Philippe G. LeFloch and me has been published in J...
The paper A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions of Jan Nordström and me has been published in Jo...
The paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations of Dimitrios Mitsotakis, David I. Ketcheson, and me has been publishe...
Manuel Quezada de Luna, David I. Ketcheson, and I have published our new paper On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispe...
Katharina Ostaszewski, Karl-Heinz Glassmeier, Charlotte Goetz, Philip Heinisch, Pierre Henri, Ingo Richter, Martin Rubin, Bruce Tsurutani, and I have publish...
The paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems of David I. Ketcheson and me has been published in SIAM J...
The paper NodePy: A package for the analysis of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Umair bin Waheed, Yiannis Hadjimichael, and me h...
The paper On the robustness and performance of entropy stable discontinuous collocation methods of Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C...
The paper RK-Opt: A package for the design of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Zachary J Grant, Aron Ahmadia, and me has been pub...
The paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes of Lajos Lóczi, David I. Ketcheson, and me has been pub...
Gregor J. Gassner and I have published our new paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form ...
Dimitrios Mitsotakis, David I Ketcheson, Endre Süli, and I have published our new paper A conservative fully-discrete numerical method for the regularised sh...
Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. Gassner, and I have published our new paper A purely hyperbolic discontinuous Galerkin approach for ...
My conference paper Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators has been pu...
Philippe G. LeFloch and I have published our new paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts on arXiv.
The paper Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Lisandro Dalcin, Matteo Parsani, a...
The paper Relaxation Runge-Kutta Methods for Hamiltonian Problems of David I. Ketcheson and me has been published in Journal of Scientific Computing. As usua...
Dimitrios Mitsotakis, David I. Ketcheson, and I have published our new paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations on...
Philip Heinisch, Katharina Ostaszewski, and I have published our contribution Towards Green Computing: A Survey of Performance and Energy Efficiency of Diffe...
Stephan Nüßlein, David I. Ketcheson, and I have published our new paper Positivity-Preserving Adaptive Runge-Kutta Methods on arXiv.
My paper On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators has been published in IMA Journal of Numerical Analysis. As ...
Lisandro Dalcin, Matteo Parsani, and I have published our new paper Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Nav...
The paper Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Mohammed S...
Jan Nordström and I have published our new paper A Class of A Stable Summation by Parts Time Integration Schemes on arXiv.
Philip Heinisch, Katharina Ostaszewski, and I have published our new paper Towards Green Computing: A Survey of Performance and Energy Efficiency of Differen...
Lajos Lóczi, David I. Ketcheson, and I have published our new paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schem...
The conference paper Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes of ...
The paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators of Katharina Ostaszewski, P...
David I. Ketcheson and I have published our new paper Relaxation Runge-Kutta Methods for Hamiltonian Problems on arXiv.
Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C Del Rey Fernández, David E Keyes, Matteo Parsani, and I have published our new paper On the robust...
David I. Ketcheson and I have published our new paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems on arXiv.
Katharina Ostaszewski, Philip Heinisch, and I have published our new paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Di...
Rémi Abgrall, Philipp Öffner, and I have published our new paper Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Dis...
Mohammed Sayyari, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson, and I have published our new paper Relaxation Runge-Kutta Methods: Fully-Discrete Expl...
The paper Automatic differentiation for performing the Cauchy-Kovalevskaya procedure in Lax-Wendroff type discretizations of Arpit Babbar, Valentin Churavy, ...
Jan Giesselmann, Fabio Leotta, Jochen Schütz, and I have published our new preprint Justification and structure- and asymptotic-preserving discretizations of...
The paper Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations of Arpit Babbar and me has been published in the Journal ...
The paper The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable of Louis Petri, Gunnar Birke, Christian Engwer, and me has be...
The paper Computing radially-symmetric solutions of the ultra-relativistic Euler equations with entropy-stable discontinuous Galerkin methods of Ferdinand Th...
Marco Artiano, Saurav Samantaray, and I have published our new preprint Asymptotic-Preserving and Well-Balanced Linearly Implicit IMEX Schemes for the Anelas...
Arpit Babbar, Qifan Chen, and I have published our new preprint Compact Runge-Kutta flux reconstruction methods with entropy and/or kinetic energy preserving...
Thomas Izgin, Chi-Wang Shu, and I have published our new preprint A Positivity-Preserving Relaxation Algorithm on arXiv.
Daniel Doehring, Jesse Chan, Michael Schlottke-Lakemper, Manuel Torrilhon, Gregor Gassner, and I have published our new preprint Volume Term Adaptivity for D...
Marco Artiano and I have published our new preprint On Affordable High-Order Entropy-Conservative/Stable and Well-Balanced Methods for Nonconservative Hyperb...
Marco Artiano, Arpit Babbar, Michael Schlottke-Lakemper, Gregor Gassner, and I have published our new preprint Jin-Xin relaxation as a shock-capturing method...
The paper Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions of Jan Giesselmann and me has been published in the SMAI Journal...
The paper A Full Three-Dimensional GPU-Accelerated Model for Deep Borehole Heat Exchangers (DBHEs) Enabling Simulation of Well Arrays of Collin Wittenstein, ...
Gunnar Birke, Christian Engwer, Sandra May, Louis Petri, and I have published our new preprint An Energy-Preserving Domain of Dependence Stabilization for th...
Louis Petri, Sigrun Ortleb, Gunnar Birke, Christian Engwer, and I have published our new preprint Domain-of-dependence-stabilized cut-cell discretizations of...
Collin Wittenstein, Vincent Marks, Mario Ricchiuto, and I have published our new preprint GPU-Accelerated Energy-Conserving Methods for the Hyperbolized Serr...
David I. Ketcheson and I have published our new preprint Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear...
The paper DispersiveShallowWater.jl: A Julia library of structure-preserving numerical methods for dispersive wave equations of Joshua Lampert, Collin Witten...
Arpit Babbar and I have published our new preprint Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations on arXiv.
The paper Relaxation Runge-Kutta methods with First-Same-as-Last Structure of Sebastian Bleecke and me has been published in the Journal of Scientific Comput...
Sebastian Bleecke, Abhijit Biswas, Jochen Schütz, David I. Ketcheson and I have published our new preprint Asymptotic-preserving and energy-conserving method...
The paper Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations of Joshua Lampert and me has been published in Comput...
David I. Ketcheson and I have published our new preprint High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperb...
Marco Artiano, Oswald Knoth, Peter Spichtinger, and I have published our new preprint Structure-Preserving High-Order Methods for the Compressible Euler Equa...
Ferdinand Thein and I have published our new preprint Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Di...
The paper Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs of Cordu...
Louis Petri, Gunnar Birke, Christian Engwer, and I have published our new preprint The domain-of-dependence stabilization for cut-cell meshes is fully discre...
Jan Giesselmann and I have published our new preprint Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions on arXiv.
Niklas Dieckow, Katharina Ostaszewski, Philip Heinisch, Henriette Struckmann, and I have published our new preprint Real-time rail vehicle localisation using...
The whitepaper Open-Source Software for Structure-Preserving Computational Fluid Dynamics of Francesco Capuano, Artur Palha, Francesc Xavier Trias Miquel, an...
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner, Jan Nordström, Sigrun Ortleb, and I have published our new preprint Stability of the Active Flux Metho...
Daniel Doehring, Manuel Torrilhon, and I have published our new preprint Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Sta...
The paper Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form of Mario Ricchiuto and me has been publishe...
Arpit Babbar, Valentin Churavy, Michael Schlottke-Lakemper, and I have published our new preprint Automatic differentiation for Lax-Wendroff-type discretizat...
The paper PositiveIntegrators.jl: A Julia library of positivity-preserving time integration methods of Stefan Kopecz, Joshua Lampert, and me has been publish...
The paper Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation of Abhijit Bis...
The paper Pseudo-Energy-Preserving Explicit Runge-Kutta Methods of Gabriel A. Barrios de León, David I. Ketcheson, and me has been published in ESAIM: Mathem...
The paper Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods of Jan Glaubitz, Andrew R. Winters, M...
The paper t8code - modular adaptive mesh refinement in the exascale era of Johannes Holke, Johannes Markert, David Knapp, Lukas Dreyer, Sandro Elsweijer, Nik...
Abhijit Biswas, David I. Ketcheson, Jochen Schütz, and I have published our new preprint Traveling-wave solutions and structure-preserving numerical methods ...
The paper An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements of David A. Kopriva, Andrew R. Winters, Michael Schlottke-Lakem...
The paper Structure-preserving numerical methods for Fokker-Planck equations of Hanna Bartel, Joshua Lampert, and me has been published in the Proceedings in...
The paper GeophysicalModelGenerator.jl: A Julia package to visualise geoscientific data and create numerical model setups of Boris J. P. Kaus, Marcel Thielma...
The paper On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws of Andrew R. Winters, Michael Schlottke-Lakemper,...
Marco Artiano has published his first paper On the Performances of Standard and Kinetic Energy Preserving Time-Integration Methods for Incompressible-Flow Si...
The paper Stability of step size control based on a posteriori error estimates of Jan Giesselmann and me has been published in Computational Science and Engi...
Mario Ricchiuto and I have published our new preprint Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form...
Gabriel A. Barrios de León, David I. Ketcheson, and I have published our new preprint Pseudo-Energy-Preserving Explicit Runge-Kutta Methods on arXiv.
Jan Glaubitz, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Gregor J. Gassner, and I have published our new preprint Generalized upwind summ...
The paper Multiderivative time integration methods preserving nonlinear functionals via relaxation of Jochen Schütz and me has been published in Communicatio...
Hanna Bartel, Joshua Lampert, and I have published our new preprint Structure-Preserving Numerical Methods for Fokker-Planck Equations on arXiv.
Joshua Lampert and I have published our new preprint Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations on arXiv.
Thomas Izgin and I have published our new preprint Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar-Run...
Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Jan Glaubitz, Gregor J. Gassner, and I have published our new preprint On the robustness of hi...
Sebastian Bleecke and I have published our new preprint Step size control for explicit relaxation Runge-Kutta methods preserving invariants on arXiv.
Jochen Schütz and I have published our new preprint Multiderivative time integration methods preserving nonlinear functionals via relaxation on arXiv.
The paper Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws of Michael Sch...
The paper Resolving Entropy Growth from Iterative Methods of Viktor Linders, Philipp Birken, and me has been published in BIT Numerical Mathematics.
The paper Functional-preserving predictor-corrector multiderivative schemes of Jochen Schütz, Eleni Theodosiou, and me has been published in Proceedings in A...
Jan Giesselmann and I have published our new preprint Stability of step size control based on a posteriori error estimates on arXiv.
My paper A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators has been publis...
Jochen Schütz, Eleni Theodosiou, and I have published our new preprint Functional-preserving predictor-corrector multiderivative schemes.
The paper On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics of Andrew R. Winters, Hugo Guillermo Castro, Li...
Cordula Reisch and I have published our new preprint Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biol...
Viktor Linders, Philipp Birken, and I have published our new preprint Resolving Entropy Growth from Iterative Methods on arXiv.
I have published my new preprint A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts o...
The paper Computing with B-series of David I. Ketcheson and me has been published in ACM Transactions on Mathematical Software.
Valentin Churavy, William F Godoy, Carsten Bauer, Michael Schlottke-Lakemper, Ludovic Räss, Johannes Blaschke, Mosè Giordano, Erik Schnetter, Samuel Omlin, J...
Andrew R. Winters, Hugo Guillermo Castro, Lisandro Dalcin, Michael Schlottke-Lakemper, Gregor J. Gassner, Matteo Parsani, and I have published our new prepri...
The paper Issues with positivity-preserving Patankar-type schemes of Davide Torlo, Philipp Öffner, and me has been published in Applied Numerical Mathematics.
The paper On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows of Jesse Chan, An...
My paper A Note on Numerical Fluxes Conserving a Member of Harten’s One-Parameter Family of Entropies for the Compressible Euler Equations has been published...
Jesse Chan, Andrés M. Rueda-Ramírez, Gregor J. Gassner, Tim Warburton, and I have published our new preprint On the entropy projection and the robustness of ...
The paper Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing of Michael Schlottke-Lakemper, Andrew R. Winters, Erik...
I have published my new preprint A Note on Numerical Fluxes Conserving Harten’s Entropies for the Compressible Euler Equations on arXiv.
The paper Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure P...
Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R Winters, Florian Hindenlang, Gregor J. Gassner, and I have published our new prepri...
David I. Ketcheson and I have published our new preprint Computing with B-series on arXiv.
The paper Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics of Lisandro Dalcin, Matteo Parsani, Da...
The paper Positivity-Preserving Adaptive Runge-Kutta Methods of Stephan Nüßlein, David I. Ketcheson, and me has been published in Communications in Applied M...
The paper On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations of Manuel Quezada de Luna, David I. Ketcheson, a...
My paper SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties has been published in the Jou...
Davide Torlo, Philipp Öffner, and I have published our new preprint A New Stability Approach for Positivity-Preserving Patankar-type Schemes on arXiv.
Michael Schlottke-Lakemper, Andrew R. Winters, Erik Faulhaber, Jesse Chan, Gregor J. Gassner, and I have published our new preprint Adaptive numerical simula...
The paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes of Gregor J. Gassner and...
The paper A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics of Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. G...
The paper A conservative fully-discrete numerical method for the regularized shallow water wave equations of Dimitrios Mitsotakis, David I Ketcheson, Endre S...
Lisandro Dalcin, Matteo Parsani, David I. Ketcheson, and I have published our new preprint Optimized Runge-Kutta Methods with Automatic Step Size Control for...
The paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts of Philippe G. LeFloch and me has been published in J...
The paper A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions of Jan Nordström and me has been published in Jo...
The paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations of Dimitrios Mitsotakis, David I. Ketcheson, and me has been publishe...
Manuel Quezada de Luna, David I. Ketcheson, and I have published our new paper On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispe...
Katharina Ostaszewski, Karl-Heinz Glassmeier, Charlotte Goetz, Philip Heinisch, Pierre Henri, Ingo Richter, Martin Rubin, Bruce Tsurutani, and I have publish...
The paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems of David I. Ketcheson and me has been published in SIAM J...
The paper NodePy: A package for the analysis of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Umair bin Waheed, Yiannis Hadjimichael, and me h...
The paper On the robustness and performance of entropy stable discontinuous collocation methods of Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C...
The paper RK-Opt: A package for the design of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Zachary J Grant, Aron Ahmadia, and me has been pub...
The paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes of Lajos Lóczi, David I. Ketcheson, and me has been pub...
Gregor J. Gassner and I have published our new paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form ...
Dimitrios Mitsotakis, David I Ketcheson, Endre Süli, and I have published our new paper A conservative fully-discrete numerical method for the regularised sh...
Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. Gassner, and I have published our new paper A purely hyperbolic discontinuous Galerkin approach for ...
My conference paper Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators has been pu...
Philippe G. LeFloch and I have published our new paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts on arXiv.
The paper Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Lisandro Dalcin, Matteo Parsani, a...
The paper Relaxation Runge-Kutta Methods for Hamiltonian Problems of David I. Ketcheson and me has been published in Journal of Scientific Computing. As usua...
Dimitrios Mitsotakis, David I. Ketcheson, and I have published our new paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations on...
Philip Heinisch, Katharina Ostaszewski, and I have published our contribution Towards Green Computing: A Survey of Performance and Energy Efficiency of Diffe...
Stephan Nüßlein, David I. Ketcheson, and I have published our new paper Positivity-Preserving Adaptive Runge-Kutta Methods on arXiv.
My paper On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators has been published in IMA Journal of Numerical Analysis. As ...
Lisandro Dalcin, Matteo Parsani, and I have published our new paper Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Nav...
The paper Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Mohammed S...
Jan Nordström and I have published our new paper A Class of A Stable Summation by Parts Time Integration Schemes on arXiv.
Philip Heinisch, Katharina Ostaszewski, and I have published our new paper Towards Green Computing: A Survey of Performance and Energy Efficiency of Differen...
Lajos Lóczi, David I. Ketcheson, and I have published our new paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schem...
The conference paper Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes of ...
The paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators of Katharina Ostaszewski, P...
David I. Ketcheson and I have published our new paper Relaxation Runge-Kutta Methods for Hamiltonian Problems on arXiv.
Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C Del Rey Fernández, David E Keyes, Matteo Parsani, and I have published our new paper On the robust...
David I. Ketcheson and I have published our new paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems on arXiv.
Katharina Ostaszewski, Philip Heinisch, and I have published our new paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Di...
Rémi Abgrall, Philipp Öffner, and I have published our new paper Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Dis...
Mohammed Sayyari, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson, and I have published our new paper Relaxation Runge-Kutta Methods: Fully-Discrete Expl...
Jan Giesselmann, Fabio Leotta, Jochen Schütz, and I have published our new preprint Justification and structure- and asymptotic-preserving discretizations of...
Marco Artiano, Saurav Samantaray, and I have published our new preprint Asymptotic-Preserving and Well-Balanced Linearly Implicit IMEX Schemes for the Anelas...
Arpit Babbar, Qifan Chen, and I have published our new preprint Compact Runge-Kutta flux reconstruction methods with entropy and/or kinetic energy preserving...
Thomas Izgin, Chi-Wang Shu, and I have published our new preprint A Positivity-Preserving Relaxation Algorithm on arXiv.
Daniel Doehring, Jesse Chan, Michael Schlottke-Lakemper, Manuel Torrilhon, Gregor Gassner, and I have published our new preprint Volume Term Adaptivity for D...
Marco Artiano and I have published our new preprint On Affordable High-Order Entropy-Conservative/Stable and Well-Balanced Methods for Nonconservative Hyperb...
Marco Artiano, Arpit Babbar, Michael Schlottke-Lakemper, Gregor Gassner, and I have published our new preprint Jin-Xin relaxation as a shock-capturing method...
Gunnar Birke, Christian Engwer, Sandra May, Louis Petri, and I have published our new preprint An Energy-Preserving Domain of Dependence Stabilization for th...
Louis Petri, Sigrun Ortleb, Gunnar Birke, Christian Engwer, and I have published our new preprint Domain-of-dependence-stabilized cut-cell discretizations of...
Collin Wittenstein, Vincent Marks, Mario Ricchiuto, and I have published our new preprint GPU-Accelerated Energy-Conserving Methods for the Hyperbolized Serr...
David I. Ketcheson and I have published our new preprint Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear...
Arpit Babbar and I have published our new preprint Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations on arXiv.
Sebastian Bleecke, Abhijit Biswas, Jochen Schütz, David I. Ketcheson and I have published our new preprint Asymptotic-preserving and energy-conserving method...
David I. Ketcheson and I have published our new preprint High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperb...
Marco Artiano, Oswald Knoth, Peter Spichtinger, and I have published our new preprint Structure-Preserving High-Order Methods for the Compressible Euler Equa...
Ferdinand Thein and I have published our new preprint Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Di...
Louis Petri, Gunnar Birke, Christian Engwer, and I have published our new preprint The domain-of-dependence stabilization for cut-cell meshes is fully discre...
Jan Giesselmann and I have published our new preprint Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions on arXiv.
Niklas Dieckow, Katharina Ostaszewski, Philip Heinisch, Henriette Struckmann, and I have published our new preprint Real-time rail vehicle localisation using...
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner, Jan Nordström, Sigrun Ortleb, and I have published our new preprint Stability of the Active Flux Metho...
Daniel Doehring, Manuel Torrilhon, and I have published our new preprint Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Sta...
Arpit Babbar, Valentin Churavy, Michael Schlottke-Lakemper, and I have published our new preprint Automatic differentiation for Lax-Wendroff-type discretizat...
Abhijit Biswas, David I. Ketcheson, Jochen Schütz, and I have published our new preprint Traveling-wave solutions and structure-preserving numerical methods ...
Mario Ricchiuto and I have published our new preprint Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form...
Gabriel A. Barrios de León, David I. Ketcheson, and I have published our new preprint Pseudo-Energy-Preserving Explicit Runge-Kutta Methods on arXiv.
Jan Glaubitz, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Gregor J. Gassner, and I have published our new preprint Generalized upwind summ...
Hanna Bartel, Joshua Lampert, and I have published our new preprint Structure-Preserving Numerical Methods for Fokker-Planck Equations on arXiv.
Joshua Lampert and I have published our new preprint Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations on arXiv.
Thomas Izgin and I have published our new preprint Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar-Run...
Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Jan Glaubitz, Gregor J. Gassner, and I have published our new preprint On the robustness of hi...
Sebastian Bleecke and I have published our new preprint Step size control for explicit relaxation Runge-Kutta methods preserving invariants on arXiv.
Jochen Schütz and I have published our new preprint Multiderivative time integration methods preserving nonlinear functionals via relaxation on arXiv.
Jan Giesselmann and I have published our new preprint Stability of step size control based on a posteriori error estimates on arXiv.
Cordula Reisch and I have published our new preprint Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biol...
Viktor Linders, Philipp Birken, and I have published our new preprint Resolving Entropy Growth from Iterative Methods on arXiv.
I have published my new preprint A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts o...
Valentin Churavy, William F Godoy, Carsten Bauer, Michael Schlottke-Lakemper, Ludovic Räss, Johannes Blaschke, Mosè Giordano, Erik Schnetter, Samuel Omlin, J...
Andrew R. Winters, Hugo Guillermo Castro, Lisandro Dalcin, Michael Schlottke-Lakemper, Gregor J. Gassner, Matteo Parsani, and I have published our new prepri...
Jesse Chan, Andrés M. Rueda-Ramírez, Gregor J. Gassner, Tim Warburton, and I have published our new preprint On the entropy projection and the robustness of ...
I have published my new preprint A Note on Numerical Fluxes Conserving Harten’s Entropies for the Compressible Euler Equations on arXiv.
Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R Winters, Florian Hindenlang, Gregor J. Gassner, and I have published our new prepri...
David I. Ketcheson and I have published our new preprint Computing with B-series on arXiv.
Davide Torlo, Philipp Öffner, and I have published our new preprint A New Stability Approach for Positivity-Preserving Patankar-type Schemes on arXiv.
Michael Schlottke-Lakemper, Andrew R. Winters, Erik Faulhaber, Jesse Chan, Gregor J. Gassner, and I have published our new preprint Adaptive numerical simula...
The paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes of Gregor J. Gassner and...
The paper A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics of Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. G...
The paper A conservative fully-discrete numerical method for the regularized shallow water wave equations of Dimitrios Mitsotakis, David I Ketcheson, Endre S...
Lisandro Dalcin, Matteo Parsani, David I. Ketcheson, and I have published our new preprint Optimized Runge-Kutta Methods with Automatic Step Size Control for...
The paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts of Philippe G. LeFloch and me has been published in J...
The paper A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions of Jan Nordström and me has been published in Jo...
The paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations of Dimitrios Mitsotakis, David I. Ketcheson, and me has been publishe...
Manuel Quezada de Luna, David I. Ketcheson, and I have published our new paper On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispe...
The paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems of David I. Ketcheson and me has been published in SIAM J...
The paper On the robustness and performance of entropy stable discontinuous collocation methods of Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C...
The paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes of Lajos Lóczi, David I. Ketcheson, and me has been pub...
Gregor J. Gassner and I have published our new paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form ...
Dimitrios Mitsotakis, David I Ketcheson, Endre Süli, and I have published our new paper A conservative fully-discrete numerical method for the regularised sh...
Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. Gassner, and I have published our new paper A purely hyperbolic discontinuous Galerkin approach for ...
Philippe G. LeFloch and I have published our new paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts on arXiv.
The paper Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Lisandro Dalcin, Matteo Parsani, a...
The paper Relaxation Runge-Kutta Methods for Hamiltonian Problems of David I. Ketcheson and me has been published in Journal of Scientific Computing. As usua...
Dimitrios Mitsotakis, David I. Ketcheson, and I have published our new paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations on...
Philip Heinisch, Katharina Ostaszewski, and I have published our contribution Towards Green Computing: A Survey of Performance and Energy Efficiency of Diffe...
Stephan Nüßlein, David I. Ketcheson, and I have published our new paper Positivity-Preserving Adaptive Runge-Kutta Methods on arXiv.
My paper On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators has been published in IMA Journal of Numerical Analysis. As ...
Lisandro Dalcin, Matteo Parsani, and I have published our new paper Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Nav...
The paper Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Mohammed S...
Jan Nordström and I have published our new paper A Class of A Stable Summation by Parts Time Integration Schemes on arXiv.
Philip Heinisch, Katharina Ostaszewski, and I have published our new paper Towards Green Computing: A Survey of Performance and Energy Efficiency of Differen...
Lajos Lóczi, David I. Ketcheson, and I have published our new paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schem...
The paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators of Katharina Ostaszewski, P...
David I. Ketcheson and I have published our new paper Relaxation Runge-Kutta Methods for Hamiltonian Problems on arXiv.
Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C Del Rey Fernández, David E Keyes, Matteo Parsani, and I have published our new paper On the robust...
David I. Ketcheson and I have published our new paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems on arXiv.
Katharina Ostaszewski, Philip Heinisch, and I have published our new paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Di...
Rémi Abgrall, Philipp Öffner, and I have published our new paper Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Dis...
Mohammed Sayyari, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson, and I have published our new paper Relaxation Runge-Kutta Methods: Fully-Discrete Expl...
The paper Automatic differentiation for performing the Cauchy-Kovalevskaya procedure in Lax-Wendroff type discretizations of Arpit Babbar, Valentin Churavy, ...
The paper Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations of Arpit Babbar and me has been published in the Journal ...
The paper The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable of Louis Petri, Gunnar Birke, Christian Engwer, and me has be...
The paper Computing radially-symmetric solutions of the ultra-relativistic Euler equations with entropy-stable discontinuous Galerkin methods of Ferdinand Th...
The paper Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions of Jan Giesselmann and me has been published in the SMAI Journal...
The paper A Full Three-Dimensional GPU-Accelerated Model for Deep Borehole Heat Exchangers (DBHEs) Enabling Simulation of Well Arrays of Collin Wittenstein, ...
The paper DispersiveShallowWater.jl: A Julia library of structure-preserving numerical methods for dispersive wave equations of Joshua Lampert, Collin Witten...
The paper Relaxation Runge-Kutta methods with First-Same-as-Last Structure of Sebastian Bleecke and me has been published in the Journal of Scientific Comput...
The paper Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations of Joshua Lampert and me has been published in Comput...
The paper Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs of Cordu...
The whitepaper Open-Source Software for Structure-Preserving Computational Fluid Dynamics of Francesco Capuano, Artur Palha, Francesc Xavier Trias Miquel, an...
The paper Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form of Mario Ricchiuto and me has been publishe...
The paper PositiveIntegrators.jl: A Julia library of positivity-preserving time integration methods of Stefan Kopecz, Joshua Lampert, and me has been publish...
The paper Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation of Abhijit Bis...
The paper Pseudo-Energy-Preserving Explicit Runge-Kutta Methods of Gabriel A. Barrios de León, David I. Ketcheson, and me has been published in ESAIM: Mathem...
The paper Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods of Jan Glaubitz, Andrew R. Winters, M...
The paper t8code - modular adaptive mesh refinement in the exascale era of Johannes Holke, Johannes Markert, David Knapp, Lukas Dreyer, Sandro Elsweijer, Nik...
The paper An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements of David A. Kopriva, Andrew R. Winters, Michael Schlottke-Lakem...
The paper Structure-preserving numerical methods for Fokker-Planck equations of Hanna Bartel, Joshua Lampert, and me has been published in the Proceedings in...
The paper GeophysicalModelGenerator.jl: A Julia package to visualise geoscientific data and create numerical model setups of Boris J. P. Kaus, Marcel Thielma...
The paper On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws of Andrew R. Winters, Michael Schlottke-Lakemper,...
Marco Artiano has published his first paper On the Performances of Standard and Kinetic Energy Preserving Time-Integration Methods for Incompressible-Flow Si...
The paper Stability of step size control based on a posteriori error estimates of Jan Giesselmann and me has been published in Computational Science and Engi...
The paper Multiderivative time integration methods preserving nonlinear functionals via relaxation of Jochen Schütz and me has been published in Communicatio...
The paper Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws of Michael Sch...
The paper Resolving Entropy Growth from Iterative Methods of Viktor Linders, Philipp Birken, and me has been published in BIT Numerical Mathematics.
The paper Functional-preserving predictor-corrector multiderivative schemes of Jochen Schütz, Eleni Theodosiou, and me has been published in Proceedings in A...
My paper A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators has been publis...
The paper On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics of Andrew R. Winters, Hugo Guillermo Castro, Li...
The paper Computing with B-series of David I. Ketcheson and me has been published in ACM Transactions on Mathematical Software.
The paper Issues with positivity-preserving Patankar-type schemes of Davide Torlo, Philipp Öffner, and me has been published in Applied Numerical Mathematics.
The paper On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows of Jesse Chan, An...
My paper A Note on Numerical Fluxes Conserving a Member of Harten’s One-Parameter Family of Entropies for the Compressible Euler Equations has been published...
The paper Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing of Michael Schlottke-Lakemper, Andrew R. Winters, Erik...
The paper Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure P...
The paper Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics of Lisandro Dalcin, Matteo Parsani, Da...
The paper Positivity-Preserving Adaptive Runge-Kutta Methods of Stephan Nüßlein, David I. Ketcheson, and me has been published in Communications in Applied M...
The paper On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations of Manuel Quezada de Luna, David I. Ketcheson, a...
My paper SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties has been published in the Jou...
The paper Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes of Gregor J. Gassner and...
The paper A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics of Michael Schlottke-Lakemper, Andrew R. Winters, Gregor J. G...
The paper A conservative fully-discrete numerical method for the regularized shallow water wave equations of Dimitrios Mitsotakis, David I Ketcheson, Endre S...
The paper Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts of Philippe G. LeFloch and me has been published in J...
The paper A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions of Jan Nordström and me has been published in Jo...
The paper A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations of Dimitrios Mitsotakis, David I. Ketcheson, and me has been publishe...
The paper Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems of David I. Ketcheson and me has been published in SIAM J...
The paper NodePy: A package for the analysis of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Umair bin Waheed, Yiannis Hadjimichael, and me h...
The paper On the robustness and performance of entropy stable discontinuous collocation methods of Diego Rojas, Radouan Boukharfane, Lisandro Dalcin, David C...
The paper RK-Opt: A package for the design of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Zachary J Grant, Aron Ahmadia, and me has been pub...
The paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes of Lajos Lóczi, David I. Ketcheson, and me has been pub...
The paper Relaxation Runge-Kutta Methods for Hamiltonian Problems of David I. Ketcheson and me has been published in Journal of Scientific Computing. As usua...
My paper On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators has been published in IMA Journal of Numerical Analysis. As ...
The paper Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations of Mohammed S...
The paper Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators of Katharina Ostaszewski, P...
Louis Petri from our group will be at the 20th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2026) in Stuttgart, Ger...
Marco Artiano from our group will be at the European Geosciences Union (EGU) General Assembly 2026 in Vienna, Austria. Moreover, Hugo Dominguez (Geosciences ...
Marco Artiano and Saurav Samantaray from our group will be at the International Conference on High Order Nonlinear Numerical Methods for Evolutionary PDE (HO...
Marco Artiano, Arpit Babbar, Valentin Churavy, and I will be at the Trixi User and Developer Interaction (TRUDI) 2026 in Cologne, Germany.
Collin Wittenstein, a graduate student from our group who is currently a visiting student at MIT, will present some of our research at the Stanford Geotherma...
Arpit Babbar will present some of our research at the seminar of the Tata Institute for Fundamental Research - Centre for Applicable Mathematics (TIFR-CAM) o...
Arpit Babbar will present some of our research at the online seminar of the Tata Institute for Fundamental Research - Centre for Applicable Mathematics (TIFR...
Ángel Durán has organized the workshop Topics on Geometric Integration for Partial Differential Equations in Valladolid, Spain. Together with Cipriano Escala...
Valentin Churavy has presented some of his work at the ML Coupling Workshop in Cambridge, UK in Cambridge, UK.
Marco Artiano will present some of our research at the ECCOMAS 8th Young Investigators Conference 2025 in Pescara, Italy.
Louis Petri will present some of our research at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2025 in Heidelberg.
Marco Artiano, Arpit Babbar, and Louis Petri from our group will be at the International Conference on Spectral and High Order Methods (ICOSAHOM 2025) in Mon...
I have been invited to give a talk Hyperbolic approximations of partial differential equations at the RMU Seminar Solution Concepts in PDEs in June 2025.
Marco Artiano, Arpit Babbar, Louis Petri, and I will be at the conference Numerical Methods for Hyperbolic Problems (numhyp25) in Darmstadt.
I have been invited to give a talk Structure-preserving time integration methods for dispersive wave equations at the workshop Efficient high-order time disc...
Sebastian Bleecke will present some of our work at the SIAM CSE 2025 conference in Forth Worth, Texas, USA.
Valentin Churavy will present some of his work at the 5th conference for Research Software Engineering in Germany (deRSE25) in Karlsruhe.
I will give a talk Structure-preserving numerical methods for dispersive wave equations at the Rhein-Main-Arbeitskreis Mathematics of Computation on Friday, ...
I will give a talk Robust and efficient time integration methods for compressible fluid dynamics at the collaborative research center TRR 146: Multiscale Sim...
Arpit Babbar will present some of his PhD work at the Indo-German Workshop on Hardware-aware Scientific Computing (IGHASC) in Heidelberg.
Marco Artiano, Arpit Babbar, and I will be at the Mathematics of the Weather 2024 conference in Bad Orb.
Stefan Kopecz from the University of Kassel will present our new Julia package PositiveIntegrators.jl at NUMDIFF-17 in Halle, Germany. His abstract is
Sebastian Bleecke will present some of our work at the International Conference on Scientific Computation and Differential Equations (SciCADE) in Singapore i...
I am organizing the minisymposium “Julia for High-Performance Computing” at JuliaCon 2024. The minisymposium will take place on Friday, July 12, from 14:00 t...
I was invited to give a talk Structure-preserving numerical methods for nonlinear dispersive wave equations at the Séminaire de Calcul Scientifique et Modéli...
I was invited to give lectures at the summer school Research Software Engineering with Julia: Basics, Visualization, and Statistics in Stuttgart in the week ...
I was invited to give a talk Adaptive and structure-preserving numerical methods at the Computational Mathematics Seminar at Hasselt University (Belgium) on ...
I was invited to give a talk Efficient and robust numerical methods based on adaptivity and structure preservation at the Seminar of Computational and Numeri...
I will give a tutorial on the Julia programming language and Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic PDEs in Ka...
I gave the keynote talk Structure-preserving numerical methods for dispersive wave equations in the section S18: Numerical methods for differential equations...
I submitted the talk A Discretization of Elliptic Terms with Improved Convergence Properties Using Summation by Parts Operators to the SIAM CSE Conference 20...
Michael Schlottke-Lakemper and I have organized the minisymposium Research Software Engineering with Julia at the SIAM CSE Conference 2023 in Amsterdam (The ...
I gave the talk Structure-preserving time integration methods based on relaxation at the Numerical Analysis Seminar at Lund University (Sweden) on Tuesday, 2...
I gave the talk Robust and efficient high-performance computational fluid dynamics enabled by modern numerical methods and technologies at the MUSEN center f...
Michael Schlottke-Lakemper and I gave the talk Reproducibility as a service: collaborative scientific computing with Julia at the MaRDI Workshop for Scientif...
I gave a talk Efficient and Robust Time Integration with Automatic Step Size Control for Compressible Computational Fluid Dynamics at the 92nd annual meeting...
I gave a talk Efficient and robust step size control for computational fluid dynamics at the workshop Efficient high-order time discretization methods for PD...
I gave a talk Combining Analysis and Data: Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics in th...
I gave a talk Introduction to Julia and Trixi, a numerical simulation framework for hyperbolic PDEs in the Applied Mathematics Seminar, University of Münster...
We have initiated a new Julia User Group in Mainz (Germany). It provides a platform for everybody interested in Julia - both people new to Julia and people h...
I was invited to give lectures at the summer school Research Software Engineering with Julia: Basics, Visualization, and Statistics in Stuttgart in the week ...
On this page
On this page
I gave a talk Introduction to Julia and Trixi, a numerical simulation framework for hyperbolic PDEs in the Applied Mathematics Seminar, University of Münster...
In this blog post, I want to share my current default choice of plotting options for articles and presentations. After some motivation, you will find the cod...
Saurav Samantaray has been working in our group as a postdoctoral researcher funded by the Mainz Institute of Multiscale Modelling (M3ODEL). Now, he moves on...
Arpit Babbar has been working in our group as a postdoctoral researcher funded by the Mainz Institute of Multiscale Modelling (M3ODEL) and the Alexander von ...
Saurav Samantaray has joined our group as a postdoc in February 2025. He will work on a joint project with Friederike Schmid (Institute of Physics, Johannes ...
Arpit Babbar has been awarded a prestigious Humboldt Research Fellowship for postdocs by the Alexander von Humboldt Foundation. He will work on “Discontinuou...
My conference paper Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators has been pu...
Philip Heinisch, Katharina Ostaszewski, and I have published our contribution Towards Green Computing: A Survey of Performance and Energy Efficiency of Diffe...
The conference paper Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes of ...
On this page
On this page
I gave a talk Introduction to Julia and Trixi, a numerical simulation framework for hyperbolic PDEs in the Applied Mathematics Seminar, University of Münster...
The paper NodePy: A package for the analysis of numerical ODE solvers of David I. Ketcheson, Matteo Parsani, Umair bin Waheed, Yiannis Hadjimichael, and me h...
In this blog post, I want to share my current default choice of plotting options for articles and presentations. After some motivation, you will find the cod...
The institutes of Mathematics and Computer Science at Johannes Gutenberg University Mainz have joined forces to present their research and activities to the ...
I will teach a course on “Climate Modelling and Simulation” for pupils/students (age 15 to 18 years old) at the Mainzer Mathe-Akademie 2024 (in German).
In this blog post, I want to share my current default choice of plotting options for articles and presentations. After some motivation, you will find the cod...
In this blog post, I want to share my current default choice of plotting options for articles and presentations. After some motivation, you will find the cod...
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