Dr. Matthias Kirchhart


Applied and Computational Mathematics
RWTH Aachen University
Schinkelstraße 2
52062 Aachen

Room: 325 (Rogowski building, 3rd floor)
Phone: +49 (0)241 80-98662
Email: kirchhart@acom.rwth-aachen.de
ORCID: 0000-0001-7018-6099
OpenPGP: BC55 D501 A8DC 2D9B D2C9 95F3 00D1 76A4 818C 2BCE


08/2007 – 09/2011 Bachelor of Science in Computational Engineering Science (CES),
RWTH Aachen University, Aachen, Germany.
09/2011 – 01/2014 Master of Science in Computational Engineering Science (CES),
RWTH Aachen University, Aachen, Germany.
09/2014 – 09/2017 Ph.D. in Engineering, Graduate School of Science and Technology,
Keio University, Tokyo, Japan.

Research Interests

  • Vortex Methods and Particle Methods in general
  • Boundary Element Methods (BEM)
  • Fast Multipole Methods (FMM)

Here you can see highly accurate vortex method when applied to the so-called ABC flow, as presented in ‘A Particle Method without Remesing’. Click for an animation!

Third Party Funding

My research on vortex methods is being funded by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft). DFG Project 432219818, “Vortex Methods for Incompressible Flows”, Eigene Stelle.


An easy-to-use C++ library for exactly integrating the Newton potential and evaluation in arbitrary precision is described in our preprint on the Newton potential. The source code can be downloaded here: newton.tar

solidfmm: A highly optimised C++ library of operations on the solid harmonics as they are needed in fast multipole methods. Available on Github

Publications and Preprints

Rostislav-Paul Wilhelm and Matthias Kirchhart. ‘An interpolating particle method for the Vlasov–Poisson equation’. arXiv e-Print 2202.11078 (Feb. 2022).

Matthias Kirchhart. ‘solidfmm: A highly optimised library of operations on the solid harmonics for use in fast multipole methods’. arXiv e-Print 2202.02847 (Feb. 2022).

Matthias Kirchhart and Erick Schulz. ‘Div-curl Problems and H1-regular Stream Functions in 3D Lipschitz Domains’. Mathematical Methods in the Applied Sciences 45.3 (Feb. 2022), pp. 1097–1117. issn: 1099-1476. doi: 10.1002/mma.7414.

Matthias Kirchhart. ‘On Particles and Splines in Bounded Domains’. In: ESIAM: Mathematical Modelling and Numerical Analysis 55 (Feb. 2021), pp. S301–S321. issn: 0764-583X. doi: 10.1051/m2an/20200329.

Matthias Kirchhart and Christian Rieger. ‘Discrete Projections: A Step Towards Particle Methods on Bounded Domains without Remeshing’. In: SIAM Journal on Scientific Computing 43.1 (Feb. 2021), pp. A609–A635. issn: 1064–8275. doi: 10.1137/19M1299864.

Matthias Kirchhart and Donat Weniger. ‘Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods’. Accepted by Journal of Numerical Mathematics. arXiv e-Print 2012.10304 (Dec. 2020).

Matthias Kirchhart and Shinnosuke Obi. ‘A Smooth Partition of Unity Finite Element Method for Vortex Particle Regularization’. In: SIAM Journal on Scientific Computing 39.5 (Oct. 2017), pp. A2345–A2364. issn: 1064–8275. doi: 10.1137/17M1116258.

Matthias Kirchhart and Shinnosuke Obi. ‘A Splitting-free Vorticity Redistribution Method’. In: Journal of Computational Physics 330 (Feb. 2017), pp. 282–295. issn:  0021–9991. doi: 10.1016/j.jcp.2016.11.014.

Matthias Kirchhart, Sven Groß, and Arnold Reusken. ‘Analysis of an XFEM Discretization for Stokes Interface Problems’. In: SIAM Journal on Scientific Computing 38.2 (Mar. 2016), pp. A1019–A1043. issn: 1064–8275. doi: 10.1137/15M1011779.

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Last modified:: 2022/04/11 09:38