Homepage of Michael Kraus

I am a scientiest in the numerical methods group at the Max Planck Institute for Plasma Physics, doing research at the intersection of numerical analysis, differential geometry and mathematical physics. My work concerns the development of structure-preserving discretisation methods for problems from fluid dynamics and plasma physics. The guiding principle is to take advantage of geometric properties of the equations in order to derive accurate and robust numerical schemes. The resulting geometric integrators often represent the underlying physics more realistically than standard methods in addition to exhibiting good stability properties.

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Research Interests

• Structure Preserving Discretisation Methods
• Model Reduction and Low-rank Approximation
• Numerical Methods for Fluids and Plasmas
• Geometric Mechanics and Field Theory
• Symmetries and Conservation Laws

Ongoing Work

• Geometric Discretisation of
  • Degenerate Lagrangian and Noncanonical Hamiltonian Systems
  • Vlasov-Poisson, Vlasov-Ampère and Vlasov-Maxwell Systems
  • Ideal, Reduced and Full Magnetohydrodynamics
  • Guiding Centre Dynamics, Drift Kinetics and Gyro Kinetics
• Discretisation of Action Principles, Poisson and Metriplectic Brackets using
  • Discontinuous Galerkin Methods
  • Finite Element Exterior Calculus and Mimetic Spectral Elements
  • B-Splines, NURBS, Isogeometric Analysis
  • Particle-in-Cell Methods
• Discrete Dirac Mechanics and Hamilton-Pontryagin Principles
• Discrete Euler-Poincaré and Lie-Dirac Reduction
• Discrete Noether Theorems and Conservation Laws
• Structure-preserving Model Order Reduction and Low-rank Approximation

Collaborations

• Joshua Burby (Courant Institute of Mathematical Sciences, New York University, USA)
• Leland Ellison (Lawrence Livermore National Laboratory, California, USA)
• Eero Hirvijoki (Aalto University, Helsinki, Finland)
• Philip Morrison (The University of Texas at Austin, USA)
• Emanuele Tassi (Laboratoire Lagrange, Observatoire de la Côte d’Azur, Nice, France)
• Hiroaki Yoshimura (Waseda University, Tokyo, Japan)

Mentoring

• Tobias Blickhan (11.2019-, Doctor Mathematics, Technische Universität München)
• Nicolas Legouy (10.2018-, Doctor Mathematics, Technische Universität München)
• Tobias Blickhan (10.2018-09.2019, Master Physics, Technische Universität München)
• Alexander Frank (10.2017-09.2019, Master Physics, Technische Universität München)
• Marco Orts (04.2017-09.2018, Master Mathematical Physics, Technische Universität München)
• Momose Hiroki (04.2016-03.2017, Master Engineering/Applied Mathematics, Waseda University)
• Camilla Bressan (01.2016-12.2019, Doctor Mathematics, Technische Universität München)
• Wolfgang Styn (10.2014-09.2015, Master Mathematics, Technische Universität München)
• Jakob Ameres (02.2014-10.2017, Doctor Mathematics, Technische Universität München)

Grants and Honours

• Project Team Leader at International Graduate School of Science and Engineering of TUM, 2018
• Marie Skłodowska-Curie Individual Fellowship, 2016
• Otto Hahn Medal of the Max Planck Society, 2014
• PhD awarded with highest distinction (summa cum laude), 2013

Impressum

(c) Michael Kraus, Marchenbacher Straße 12b, 85406 Gerlhausen, Germany.

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