Prof. dr. Jochen SCHUETZ

Research interests

• Efficient time integration schemes:
  • IMEX
  • Multiderivative schemes
  • Predictor/corrector schemes
  • Parallel-in-time
• Singular perturbed problems
• High-Order Methods for flow problems
• Specifically:
  • Hybridized DG / Hybrid Mixed methods
  • Asymptotic Preserving Schemes with IMEX-DG methods
  • Biological flows
• Adjoint Error Control

Short biography

Publications

Please send me an e-mail if you are interested in preprints that are not listed here.

1. A. Thenery Manikantan and J. Schütz, Multi-Step Hermite–Birkhoff Predictor-Corrector Schemes, UP2402, 2024 [PDF] (pdf, 1,5 MB)
2. E. Theodosiou, C. Bringedal and J. Schütz, A two-derivative time integrator for the Cahn-Hilliard equation, UP2401, 2024 [PDF] (pdf, 677 KB)
3. H. Ranocha and J. Schütz, Multiderivative time integration methods preserving nonlinear functionals via relaxation, accepted for publication in Communications in Applied Mathematics and Computational Science [Arxiv], 2023
4. H. Ranocha, J. Schütz and E. Theodosiou, Functional-preserving predictor-corrector multiderivative schemes, Proceedings in Applied Mathematics and Mechanics, 00, e202300025, 2023 [PDF] (pdf, 485 KB) [Link]
5. A. Moradi, J. Chouchoulis, R. D’Ambrosio, J. Schütz, Jacobian-Free Explicit Multiderivative General Linear Methods for Hyperbolic Conservation Laws, Numerical Algorithms, 2024 [PDF] (pdf, 659 KB) The final publication is available at [link.springer.com]
6. A. Thenery Manikantan, J. Zeifang and J. Schütz, Strong Stability Preserving and A(α)-Stable Two-Derivative Time Discretization for Discontinuous Galerkin Method, UP2302, 2023 [PDF] (pdf, 546 KB)
7. J. Chouchoulis and J. Schütz, Jacobian-free implicit MDRK methods for stiff systems of ODEs, Applied Numerical Mathematics, 2024, 196, 45-61. [Arxiv] [Link]
8. E. Theodosiou, J. Schütz and D. Seal, An explicitness-preserving IMEX-split multiderivative method, Computers & Mathematics with Applications, 158, Pages 139-149, 2024 [PDF] (pdf, 787 KB) [Link]
9. L. Fonteyne, T. De Laet, A. Marconato, I. Melis, J. Schütz and B. Tambuyzer, Ijkingstoetsen in Vlaanderen, TH&MA (Den Haag), 2022.
10. J. Zeifang, A. Thenery Manikantan and J. Schütz, Time Parallelism and Newton-Adaptivity of the Two-Derivative Deferred Correction Discontinuous Galerkin Method, Applied Mathematics and Computation, 2023, 457, Nr. 128198 [PDF] (pdf, 589 KB) [Link]
11. J. Zeifang, J. Schütz and D. Seal, Stability of Implicit Multiderivative Deferred Correction Methods, BIT Numerical Mathematics, 2022. The final publication is available at [link.springer.com]
12. J. Zeifang and J. Schütz, Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method, Journal of Computational Physics, 2022, 464, Nr. 111353. [Link]
13. J. Chouchoulis, J. Schütz and J. Zeifang, Jacobian-free explicit multiderivative Runge-Kutta methods for hyperbolic conservation laws, Journal of Scientific Computing, 2022, 90, Nr. 96. The final publication is available at [link.springer.com]
14. J. Schütz, D. Seal and J. Zeifang, Parallel-in-time high-order multiderivative IMEX methods, Journal of Scientific Computing, 2022, 90 [PDF] The final publication is available at [link.springer.com]
15. V. Kucera, M. Lukacova-Medvidova, S. Noelle and J. Schütz, Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations, Numerische Mathematik, 2021, 150, 79-103 [PDF] The final publication is available at [link.springer.com]
16. J. Schütz and D. Seal, An asymptotic preserving semi-implicit multiderivative solver, Applied Numerical Mathematics, 2021, 160, 84-101 [PDF] [Link]
17. J. Zeifang, J. Schütz, K. Kaiser, A. Beck, M. Lukacova-Medvidova and S. Noelle, A novel full-Euler low Mach number IMEX splitting, Communications in Computational Physics, 2020, 27, 292-320 [Link]
18. Rineau et al., Towards more predictive and interdisciplinary climate change ecosystem experiments, Nature Climate Change, 2019, 9, 809-816. [Link]
19. V. Aizinger, A. Rupp, J. Schütz and P. Knabner, Analysis of a mixed discontinuous Galerkin method for instationary Darcy flow, Computational Geosciences, 2018, 22, 179-194, [Link]
20. K. Kaiser and J. Schütz, Asymptotic Error Analysis of an IMEX Runge-Kutta method.  Journal of Computational and Applied Mathematics, 2018, 13, 243-270, [PDF] [Link]
21. A. Jaust, B. Reuter, V. Aizinger, J. Schütz and P. Knabner, FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation. Computers & Mathematics with Applications, 2018, 75, 4505-4533, [Link]
22. J. Zeifang, K. Kaiser, A. Beck, J. Schütz and C.-D. Munz, Efficient high-order discontinuous Galerkin computations of low Mach number flows. Communications in Applied Mathematics and Computational Science, 2018, 13, 243-270, [PDF] [Link]
23. A. Jaust and J. Schütz, General linear methods for time-dependent PDEs. In: Klingenberg, Christian; Westdickenberg, Michael (Ed.). Theory Numerics and Applications of Hyperbolic Problems II, Springer, 2018, 59-70. [PDF] The final publication is available at [link.springer.com]
24. J. Schütz, D. Seal and A. Jaust, Implicit multiderivative collocation solvers for linear partial differential equations with discontinuous Galerkin spatial discretizations. Journal of Scientific Computing, 2017, 73, 1145-1163 [PDF]. The final publication is available at [link.springer.com]
25. K. Kaiser and J. Schütz, The influence of the asymptotic regime on the RS-IMEX. In: Quintela et al., ECMI 2016: Progress in Industrial Mathematics at ECMI 2016, Springer, 2016, 55-66. The final publication is available at [link.springer.com]
26. K. Kaiser and J. Schütz, A high-order method for weakly compressible flows. Communications in Computational Physics, 2017, 22, 1150-1174 [PDF] [Link]
27. A. Jaust, J. Schütz and V. Aizinger, An efficient linear solver for the hybridized discontinuous Galerkin method. PAMM, 2016, 16, 845-846 [Link]
28. K. Kaiser, J. Schütz, R. Schöbel and S. Noelle, A new stable splitting for the isentropic Euler equations. Journal of Scientific Computing, 2017, 70, 1390-1409 [PDF]. The final publication is available at [link.springer.com]
29. J. Schütz and V. Aizinger, A hierarchical scale separation approach for the hybridized discontinuous Galerkin method. Journal of Computational and Applied Mathematics, 2017, 317, 500-509 [PDF] [Link]
30. A. Jaust, J. Schütz and D. Seal, Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws, Journal of Scientific Computing, 2016, 69, 866-891 [PDF]. The final publication is available at [link.springer.com]
31. K. Kaiser and J. Schütz, Asymptotic Preserving Discontinuous Galerkin Method. in Conference Proceedings of the YIC GACM 2015, 2015 [PDF]
32. A. Jaust, J. Schütz and D. Seal, Multiderivative time-integrators for the hybridized discontinuous Galerkin method. in Conference Proceedings of the YIC GACM 2015, 2015 [PDF]
33. J. Schütz, K. Kaiser and S. Noelle, The RS-IMEX splitting for the isentropic Euler equations. in Conference Proceedings of the YIC GACM 2015, 2015 [PDF]
34. J. Schütz and K. Kaiser, A new stable splitting for singularly perturbed ODEs. Applied Numerical Mathematics, 2016, 107, 18-33 [PDF] [Link]
35. A. Jaust, J. Schütz and M. Woopen, An HDG Method for unsteady compressible flows. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, R. Kirby, M. Berzins and J. Hesthaven (eds.), Springer, 2015, 267-274. The final publication is available at [link.springer.com].
36. A. Jaust, J. Schütz and M. Woopen, A Hybridized Discontinuous Galerkin Method for Unsteady Flows with Shock-Capturing. AIAA Paper 2014-2781, 2014 [PDF]
37. J. Schütz and S. Noelle, Flux Splitting for stiff equations: A notion on stability. Journal of Scientific Computing, 2015, 64, 522-540 [PDF]. The final publication is available at [link.springer.com].
38. M. Woopen, G. May and J. Schütz, Adjoint-Based Error Estimation and Mesh Adaptation for Hybridized Discontinuous Galerkin Methods. International Journal for Numerical Methods in Fluids, 2014, 76, 811-834 [PDF][Link]
39. M. Woopen, A. Balan, G. May and J. Schütz, A Comparison of Hybridized and Standard DG Methods for Target-Based hp-Adaptive Simulation of Compressible Flow. Computers and Fluids, 2014, 98, 3-16 [PDF][Link]
40. A. Jaust and J. Schütz, A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows.Computers and Fluids, 2014, 98, 177-185 [PDF][Link]
41. J. Schütz, An asymptotic preserving method for linear systems of balance laws based on Galerkin's method. Journal of Scientific Computing, 2014, 60, 438-456 [PDF]. The final publication is available at [link.springer.com].
42. J. Schütz, M. Woopen and G. May, A Combined Hybridized Discontinuous Galerkin / Hybrid Mixed Method for Viscous Conservation Laws. In F. Ancona, A. Bressan, P. Marcati, and A. Marson, editors, Hyperbolic Problems: Theory, Numerics, Applications, pages 915–922. American Institute of Mathematical Sciences, 2012.[PDF]
43. J. Schütz, S. Noelle, C. Steiner and G. May, A Note on adjoint error estimation for one-dimensional stationary balance laws with shocks. SIAM Journal on Numerical Analysis, 2013, 1, 126-136 [PDF][Link]
44. J. Schütz and G. May, An Adjoint Consistency Analysis for a Class of Hybrid Mixed Methods. IMA Journal of Numerical Analysis, 2014, 34, 1222-1239 [PDF][Link]
45. J. Schütz, M. Woopen and G. May, A Hybridized DG/Mixed Scheme for Nonlinear Advection-Diffusion Systems, Including the Compressible Navier-Stokes Equations. AIAA Paper 2012-0729, 2012 [PDF]
46. J. Schütz and G. May, A Hybrid Mixed Method for the Compressible Navier-Stokes Equations. Journal of Computational Physics, 2013, 240, 58-75 [PDF][Link]
47. J. Schütz and G. May, A Numerical Study of Adjoint-Based Mesh Adaptation for Compressible Flow Simulation. AIAA Paper 2011-213, 2011
48. J. Schütz, A Hybrid Mixed Finite Element Scheme for the Compressible Navier-Stokes Equations and Adjoint-Based Error Control for Target Functionals. Dissertation accepted at RWTH Aachen University, 2011 [PDF]
49. J. Schütz; G. May and S. Noelle, Analytical and numerical investigation of the influence of artificial viscosity in Discontinuous Galerkin methods on an adjoint-based error estimator. Computational Fluid Dynamics 2010 Proceedings to ICCFD2010, A. Kuzmin (ed.), Springer, 2010, 203-209. The final publication is available at [link.springer.com].

Codes developed in my group

Most of my work is dedicated to the numerical simulation of (ordinary/partial) differential equations. Sporadically, I will upload codes to this webpage whenever I think they can be useful to somebody else. If you are interested in some specific code, please do not hesitate to contact me via mail. Disclaimer: Please note that the codes provided below are "as is", without any warranty, in particular not whether they are suited for some specific purpose!

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