Dr. Holger Heumann

INRIA Starting Researcher at Team Castor
Contact
Adresse : INRIA, EPI CASTOR 2004 Route des Lucioles BP 93 06902 Sophia Antipolis, France 
Telephone :
+33 (0) 7 82 03 48 19 Fax : Mail : Holger.Heumann [at] inria [dot] fr 
News
 January 2016: Here you can find my new homepage.
 June 2015: Python tutorial for LJAD.
 June 2015: I would like to draw your attention to FEEQS.M , my MATLAB implementation of the methods for toroidal free boundary plasma equilibria that we describe in [Heumann2015]. The code is fully vectorized and therefore the running time is comparable to C/C++ implementations. It contains also a fixed boundary mode and the possibility to do calculations with (localised) mesh refinement for increased accuracy. I am using FEEQS.M basically as test bed for fast prototyping and testing of new ideas, but I feel there might be a broader interest in a lightweight free boundary equilibrium code. Drop me an email (holger.heumann@inria.fr) if you face problems. Feedback is warmly appreciated and I am planning to post updated versions. Many things are tested and validated, but for the moment I can not give a warranty that all and everything works correctly.
 April 2015: We are looking for interns working with us on computational methods for plasma equilibrium problems in tokamaks. Projects may include
 algorithms for inverse problems/optimal control problems, Matlab or C++;
 implementations/testing of FEM with nonmatching meshes, Matlab or C++;
 implementations/testing of FEM/BEM coupling methods, Matlab; Please contact me for the details.
 January 2015: Quasistatic FreeBoundary Equilibrium of Toroidal Plasma with CEDRES++: Computational Methods and Applications accepted in Journal of Plasma Physics.
 Optimal Control for QuasiStatic Evolution of Plasma Equilibrium in Tokamaks.
Research
 Computational methods for simulation of plasmas in tokamaks
 Algorithms for optimal control and PDEconstrained optimization in
nuclear fusion [introduction 1 & 2, Zürich 2012] [movie]
 Finite element methods for Maxwells equation and magnetohydrodynamics
 Numerical analysis and fast algorithms for practical
semiLagrangian methods [slides, Rom 2011]
 Discrete Lie derivatives, advection of differential forms, finite element exterior calculus [poster, ICERM 2012] [slides, Fribourg 2008]
Publications
Journals H. Heumann, J. Blum, C. Boulbe, B. Faugeras, G. Selig, J.M. Ane, S. Bremond, V. Grandgirard, P. Hertout and E. Nardon, Quasistatic freeboundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications, Journal of Plasmaphysics, 81, 2015.
 H. Heumann and M. Vogelius, Analysis of an enhanced approximate cloaking scheme for the conductivity problem, Asymptotic Analysis, 87, 223246, 2014.
 H. Heumann and S. Kurz, Modelling and Finite Element Simulation of the WilsonWilson Experiment, IEEE Transactions on Magnetics, 50, p. 6568, 2014.
 H. Heumann and R. Hiptmair, Stabilized Galerkin methods for magnetic advection, ESAIM: Mathematical Modelling and Numerical Analysis, 47, p. 17131732, 2013.
 H. Heumann and R. Hiptmair, Convergence of
Lowest Order SemiLagrangian Schemes, Foundations of Computational Mathematics, 13(2), p. 187220, 2013.
 H. Heumann, R. Hiptmair, K. Li and J. Xu, Fully discrete SemiLagrangian Methods for
Advection of Differential Forms, BIT Numerical Mathematics, 52(4), p. 9811007, 2012.
 H. Heumann and R. Hiptmair, Eulerian and SemiLagrangian Methods for AdvectionDiffusion for Differential Forms, Discrete and Continuous Dynamical Systems, 29(4), p. 1471  1495, 2011.
 F. Henrotte, H. Heumann, E. Lange and K. Haymeyer, Upwind 3D Vector Potential Formulation
for Electromagnetic Braking Simulations, IEEE Transactions on Magnetics, 46, p. 28352838, 2010.
 H. Heumann and G. Wittum, The TreeEdit Distance: A Measure for
Quantifying Neuronal Morphology, Neuroinformatics, 7, p. 179190,
2009.
 C. Gründl, H. Heumann, D. Peretti and C. Wagner, Numerical Methods for Risk Aggregation based on Copulas, in Copulas: From Theory to Application in Finance, J. Rank, 2006.
 H. Heumann, Differential Involutions, Discrete Differential Forms and Constraint Preserving Discretizations on Unstructured Meshes, Oberwolfach Reports 47/2013, p. 27152717, 2013.
 H. Heumann and R. Hiptmair, Stabilized Galerkin Methods for Magnetic Advection, Oberwolfach Reports 03/2013, p.457459, 2010.
 H. Heumann and R. Hiptmair, Stabilized Galerkin methods for advection of vector fields, accepted in Numerical Methods and Advanced Applications, ENUMATH 2013, 2014.
 H. Heumann and R. Hiptmair, Discrete Lie Derivatives: The Eulerian Approach, Oberwolfach Reports 10/2010, p. 457459, 2010.
 J. Blum and H. Heumann, Optimal Control for QuasiStatic Evolution of Plasma Equilibrium in Tokamaks, 2014,
 S. Kurz and H. Heumann, Transmission Conditions in premetric Electrodynamics, SAMReport, 201028.
 H. Heumann and R. Hiptmair, Extrusion Contraction Upwind Schemes for
ConvectionDiffusion Problems, SAMReport, 200830.
 Ph.D. thesis: Eulerian and SemiLagrangian Methods for AdvectionDiffusion of Differential Forms, SAM, ETH Zürich, 2011.
 Diploma thesis: Eine Metrik zur Klassifizierung von Neuronen,
IWR, Universität Heidelberg, 2006.
Software
 CEDRES++, a plasma equilibrium code. [introduction 1 & 2, Zürich 2012]
 LehrFEM, a 2D Finite Element Toolbox. [poster, Basel 2009] [manual]
 TreeEdit, neuronal cells can be represented as node labeled tree, the tree edit distance is a metric for node labeled trees. [slides, Frankfurt 2009]
Selected Talks
 SemiLagrangian Methods for AdvectionDiffusion for Differential Forms, Recent advances on theory and applications of SemiLagrangian methods, Workshop, December 56, 2011, SAPIENZA Universita di Roma.
 Galerkin Methods for General Advection Problems, NonStandard Numerical Methods for PDEs, June 29July 2, 2010, Pavia
 Discrete Lie Derivatives: Eulerian approach, MFOworkshop: Computational Electromagnetics and Acoustics, February 1420, 2010, Oberwolfach
 SemiLagrangian Galerkin methods for Discrete Differential Forms; Compatible and Innovative Discretizations for Partial Differential Equations, June 1719, 2009, Oslo
Teaching TU Munich 20132014
Teaching AssistantTeaching Nice 20112012
Term Projects  Josefine Ladda: Fast Methods for Computing Mesh Intersections
 Jonas Hollander: Optimal Control of 2D Parabolic Problems in FEniCS
Teaching ETH Zürch 20062011
Term and Intern Projects Implementation of numerical methods in Python for teaching purposes, Fall 2010  Spring 2011.
 Andreas Hiltebrand: Fast solvers for Eulerian advection schemes, Spring 2010.
 Jonas Sukys: Discontinuous Galerkin discretization of magnetic convection, Spring 2010.
 Christoph Wiesmeyr: Implementation of semiLagrangian methods in LehrFEM, Fall 2009.
 Annegret Burtscher: Manual and documentation for LehrFEM, Fall 2008.
 Nana Arisumi: Scattering and PMLs in LehrFEM, Fall 2007.
 Eivind Fonn: Stabilized finite volume methods for advectiondiffusion problems Fall 2007.
 Numerische Mathematik DPHYS, Spring 2011.
 Numerische Mathematik DMATH, Spring 2010.
 Numerical Solution of Differential Equations DMATH/DPHYS, Fall 2009.
 Numerische Mathematik DMATH, Spring 2009.
 Linear Algebra für Informatiker, Fall 2008.
 Numerik der hyperbolischen Differentialgleichungen, Spring 2008.
 Numerische Methoden für CSE/RW, Fall 2007.
 Inverse Problems: Theory and Numerical Treatment, Spring 2007.
 Numerik der hyperbolischen Differentialgleichungen, Spring 2007.
 Numerical analysis of elliptic PDEs, Fall 2006.