Hendrik Ranocha

Hendrik Ranocha is a Professor in Numerical Mathematics at Johannes Gutenberg University Mainz, Germany. His research focuses on the analysis and development of numerical methods for partial and ordinary differential equations, with particular emphasis on stability and structure-preserving techniques that transfer results from continuous to discrete levels.

His educational background includes:

• PhD in Mathematics from TU Braunschweig (2016-2018), advised by Thomas Sonar
• MSc in Mathematics from TU Braunschweig (2014-2016)
• BSc in Mathematics from TU Braunschweig (2011-2014)
• Exchange student at Yonsei University, Seoul (2013)
• BSc in Physics from TU Braunschweig (2010-2013)

Hendrik Ranocha's research spans Numerical Analysis and Scientific Computing. His work focuses on developing numerical schemes for hyperbolic balance laws and dispersive-dissipative equations, including Discontinuous Galerkin methods, spectral element methods, finite difference schemes, and flux reconstruction. He specializes in structure-preserving methods that conserve entropy/energy, utilizing summation by parts operators and mimetic properties. His research also encompasses Runge-Kutta methods, stability of time integration schemes, adaptivity in time and space, data-driven approaches, and uncertainty quantification.

His recent publications demonstrate a strong focus on entropy-stable numerical methods, structure-preserving discretizations, and high-performance computing implementations in Julia. The research trends show increasing emphasis on practical software implementations (Trixi.jl, SummationByPartsOperators.jl), applications to physical systems like compressible Euler equations and shallow water equations, and addressing fundamental numerical challenges in stability and convergence.

Hendrik Ranocha leads a research group at Johannes Gutenberg University Mainz with several PhD students and postdocs, including Louis Petri, Marco Artiano, Sebastian Bleecke, Saurav Samantaray, Arpit Babbar, and Valentin Churavy. He collaborates extensively with researchers such as Gregor Gassner, Andrew R. Winters, Michael Schlottke-Lakemper, and Jesse Chan on numerical methods and software development.

He is actively involved in open-source scientific computing, contributing to projects like Trixi.jl (a Julia package for adaptive high-order numerical simulations of conservation laws), SummationByPartsOperators.jl, OrdinaryDiffEq.jl, NodePy, and RK-Opt. He is part of the SciML organization, which develops high-performance Julia libraries for scientific machine learning and computational science.