134 citations · 1.1k across the 79 of their papers we have counts for
9 papers · 1 filter
Using Machine Learning to Design Time Step Size Controllers for Stable Time Integrators
Thomas Izgin, Hendrik Ranocha
We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have…
Step size control for explicit relaxation Runge-Kutta methods preserving invariants
Sebastian Bleecke, Hendrik Ranocha
Many time-dependent differential equations are equipped with invariants. Preserving such invariants under discretization can be important, e.g., to improve the qualitative and quan…
On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper +3
We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this con…
Multiderivative time integration methods preserving nonlinear functionals via relaxation
Hendrik Ranocha, Jochen Schütz
We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial different…
Functional-preserving predictor-corrector multiderivative schemes
Hendrik Ranocha, Jochen Schütz, Eleni Theodosiou
In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recen…
Stability of step size control based on a posteriori error estimates
Hendrik Ranocha, Jan Giesselmann
A posteriori error estimates based on residuals can be used for reliable error control of numerical methods. Here, we consider them in the context of ordinary differential equation…
Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biology and numerical methods for ODEs
Cordula Reisch, Hendrik Ranocha
We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with…
Resolving Entropy Growth from Iterative Methods
Viktor Linders, Hendrik Ranocha, Philipp Birken
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative method…
A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators
Hendrik Ranocha
Nishikawa (2007) proposed to reformulate the classical Poisson equation as a steady state problem for a linear hyperbolic system. This results in optimal error estimates for both t…