Publications


You can find citation data on my ResearcherID page.

Recent work


  1. M. Frank, C. Lax, S. Walcher, O. Wittich: Quasi-steady state reduction for the Michaelis-Menten reaction-diffusion system, arXiv:1707.04043 [math.AP]
  2. P. Chidyagwai, M. Frank, F. Schneider, B. Seibold: A Comparative Study of Limiting Strategies in Discontinuous Galerkin Schemes for the M1 Model of Radiation Transport, arXiv:1706.10174 [math.NA]
  3. M. Frank, W. Sun, Fractional Diffusion Limits of Non-Classical Transport Equations, arXiv:1607.04028 [math.AP]
  4. J. Tervo, P. Kokkonen, M. Frank, M. Herty: On Existence of L2-solutions of Coupled Boltzmann Continuous Slowing Down Transport Equation System, arXiv:1603.05534 [math.OC]
  5. P. Richter, M. Frank, E. Abraham: Multi-objective optimization of solar tower heliostat fields

Journal publications


  1. T. Pichard, G.W. Alldredge, S. Brull, B. Dubroca, M. Frank: An approximation of the M 2 closure: application to radiotherapy dose simulation, to appear in J. Sci. Comput.
  2. K. Kuepper, M. Frank, S. Jin: An Asymptotic Preserving 2-D Staggered Grid Method for multiscale transport equations, SIAM J. Numer. Anal. 54 (2016) 440–461.
  3. P. Otte, M. Frank: Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equations, Comput. Math. Appl. Volume 72 (2016) 311–327.
  4. R.C. Barnard, M. Frank, K. Krycki: Sensitivity Analysis for Dose Deposition in Radiotherapy via a Fokker-Planck Model, Math. Med. Biol. (2016).
  5. M. Frank, C.D. Hauck, K. Kuepper: Convergence of Filtered Spherical Harmonic Equations for Radiation Transport, Commun. Math. Sci. 14 (2016) 1443–1465.
  6. T. Pichard, G. W. Alldredge, S. Brull, B. Dubroca, M. Frank: The M2 Model for Dose Simulation in Radiation Therapy, J. Comput. Theor. Transp. 45 (2016) 174-183.
  7. T. Pichard, D. Aregba-Driollet, S. Brull, B. Dubroca, M. Frank: Relaxation schemes for the M1 model with space-dependent flux: application to radiotherapy dose calculation, Commun. Comput. Phys. 19 (2015) 168-191.
  8. J. Caron, J.-L. Feugeas, B. Dubroca, G. Kantor, C. Dejean, T. Pichard, P. Nicolai, E. D'Humières, M. Frank, V. Tikhonchuk: Deterministic model for the transport of energetic particles. Application in the electron radiotherapy, Physica Medica 31 (2015) 912–921.
  9. M. Frank, K. Krycki, E.W. Larsen, R. Vasques: The Non-Classical Boltzmann Equation, and Diffusion-Based approximations to the Boltzmann Equation, SIAM J. Appl. Math. 75 (2015) 1329–1345.
  10. F. Schneider, G. Alldredge, M. Frank, A. Klar: Higher order mixed moment approximations for the Fokker-Planck equation in one space dimension, SIAM J. Appl. Math. 74 (2014) 1087–1114.
  11. B. Seibold, M. Frank: StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer, ACM Trans. Math. Softw. 41 (2014) 4.
  12. M. Frank, C.D. Hauck, E. Olbrant: Perturbed, Entropy-Based Closure for Radiative Transfer, Kinet. Relat. Models 6 (2013) 557-587.
  13. E. Olbrant, E.W. Larsen, M. Frank, B. Seibold: Asymptotic Derivation and Numerical Investigation of Time-Dependent Simplified Pn Equations, J. Comput. Phys. 238 (2013) 315-336.
  14. K. Krycki, C. Berthon, M. Frank, R. Turpault: Asymptotic preserving numerical schemes for a non-classical radiation transport model for atmospheric clouds, Math. Meth. Appl. Sci. 36 (2013) 2101–2116.
  15. R. Barnard, M. Frank, M. Herty: Optimal radiotherapy treatment planning using minimum entropy models, Appl. Math. Comput. 219 (2012) 2668–2679.
  16. E. Olbrant, C.D. Hauck, M. Frank: A Realizability-Preserving Discontinuous Galerkin Method for the M1 Model of Radiative Transfer, J. Comput. Phys. 231 (2012) 5612–5639.
  17. M. Frank, M. Herty, M. Hinze: Time-dependent Closed Loop Control of the Radiative Transfer Equations with Applications in Radiotherapy, Z. Angew. Math. Mech. 92 (2012) 8-24.
  18. M. Frank, B. Seibold: Optimal Prediction for Radiative Transfer: A New Perspective on Moment Closure, Kinet. Relat. Models 4 (2011) 717-733.
  19. M. Frank, J. Lang, M. Schäfer: Adaptive Finite Element Simulation of the Time-Dependent Simplified PN Equations, J. Sci. Comput. 49 (2011) 332-350.
  20. C. Berthon, M. Frank, C. Sarazin, R. Turpault: Numerical methods for balance laws with space dependent flux: application to radiotherapy dose calculation, Commun. Comput. Phys. 10 (2011) 1184-1210.
  21. M. Schäfer, M. Frank, C.D. Levermore: Diffusive Corrections to Pn approximations, Multiscale Model. Simul. 9 (2011) 1-28.
  22. M. Frank, A. Klar, R. Pinnau: Optimal Control of Glass Cooling Using Simplified Pn Theory, Transp. Theory Stat. Phys. 39 (2010) 282-311.
  23. B. Dubroca, J.-L. Feugeas, M. Frank: Angular moment model for the Fokker-Planck equation, Eur. Phys. J. D 60 (2010) 301–307.
  24. M. Frank, T. Goudon: On a generalized Boltzmann equation for non-classical particle transport, Kinet. Relat. Models 3 (2010) 395-407.
  25. E. Olbrant, M. Frank: Application of Generalized Fokker-Planck Theory To Electron And Photon Transport In Tissue, Comput. Math. Meth. Med. 11 (2010) 313-339.
  26. R. Duclous, B. Dubroca, M. Frank: Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy, Phys. Med. Biol. 55 (2010) 3843-3857.
  27. M. Frank, A. Fügenschuh, M. Herty, L. Schewe: The Coolest Path Problem, Netw. Heterog. Media 5 (2010) 143-162.
  28. M. Frank, M. Herty, A.N. Sandjo: Optimal Radiotherapy Treatment Planning Governed by Kinetic Equations, Math. Mod. Meth. Appl. Sci. 20 (2010) 661-678.
  29. B. Seibold, M. Frank: Optimal prediction for moment models: crescendo diffusion and reordered equations, Continuum Mech. Thermodyn. 21 (2009) 511-527.
  30. M. Frank, M. Herty, M. Schäfer: Optimal Treatment Planning in Radiotherapy Based On Boltzmann Transport Calculations, Math. Mod. Meth. Appl. Sci. 18 (2008) 573-592.
  31. M. Frank, A. Klar, E.W. Larsen, S. Yasuda: Time-dependent Simplified PN Approximation to the Equations of Radiative Transfer, J. Comput. Phys. 226 (2007) 2289-2305.
  32. M. Frank: Approximate models for radiative transfer, Bull. Inst. Math. Acad. Sinica (New Series) 2 (2007) 409-432.
  33. M. Frank, H. Hensel, A. Klar: A fast and accurate moment method for the Fokker-Planck equation and applications to electron radiotherapy, SIAM J. Appl. Math. 67 (2007) 582-603.
  34. M. Frank, R. Pinnau: Existence and Bounds for the Half Moment Entropy Approximation to Radiative Transfer, Appl. Math. Lett. 20 (2007) 189-193.
  35. M. Frank, B. Dubroca, A. Klar: Partial Moment Entropy Approximation to Radiative Heat Transfer, J. Comput. Phys. 218 (2006) 1-18.
  36. M. Schäfer, M. Frank, R. Pinnau: A Hierarchy of Approximations to the Radiative Heat Transfer Equations: Modelling, Analysis and Simulation, Math. Mod. Meth. Appl. Sci. 15 (2005) 643-665.
  37. R. Turpault, M. Frank, B. Dubroca, A. Klar: Multigroup half space moment appproximations to the radiative heat transfer equations, J. Comput. Phys. 198 (2004) 363-371.
  38. M. Seaid, M. Frank, A. Klar, R. Pinnau, G. Thömmes: Efficient numerical methods for radiation in gas turbines, J. Comput. Appl. Math. 170 (2004) 217-239.
  39. M. Frank, M. Seaid, J. Janicka, A. Klar, R. Pinnau: A comparison of approximate models for radiation in gas turbines, Progress in Computational Fluid Dynamics 4 (2004) 191-197.
  40. M. Frank, M. Buballa, M. Oertel: Flavor-mixing effects on the QCD phase diagram at non-vanishing isospin chemical potential: one or two phase transitions?, Phys. Lett. B 562 (2003) 221-226.
  41. B. Dubroca, M. Frank, A. Klar, G. Thömmes: A half space moment approximation to the radiative heat transfer equations, Z. Angew. Math. Mech. 83 (2003) 853-858.

Mathematics Education


  1. M. Frank, C. Roeckerath: Augmenting Mathematics Courses by Problem-Based Learning, International Journal of Engineering Pedagogy (iJEP) 6 (2016), doi:10.3991/ijep.v6i1.5368
  2. M. Frank, M. Hattebuhr, C. Roeckerath: Augmenting Mathematics Courses by Project-Based Learning, Proceedings of 2015 International Conference on Interactive Collaborative Learning (2015).
  3. M. Frank, C. Roeckerath: Wie kann man mit einer Handykamera Geschwindigkeiten messen?, Der Mathematikunterricht 61 (2015) 27-31.
  4. M. Frank, C. Roeckerath: Habe ich das Zeug zum MINT-Studium? Die CAMMP week als Orientierungshilfe für Schülerinnen und Schüler, in: Lehren und Lernen von Mathematik in der Studieneingangsphase, Springer-Verlag (2015) 181-195.
  5. M. Frank, C. Roeckerath: Gemeinsam mit Profis reale Probleme lösen, Mathematik Lehren 174 (2012).

Refereed Proceedings


  1. R. Barnard, M. Frank, M. Herty: Treatment Planning Optimization for Radiotherapy, Proc. Appl. Math. Mech. 13 (2013) 339–340.
  2. R. Barnard, M. Frank, M. Herty: State-Constrained Optimization of PDEs via Infinite Penalization Methods, Proc. Appl. Math. Mech. 12 (2012) 691–692.
  3. K. Krycki, M. Frank: Numerical treatment of a non-classical transport equation modelling radiative transfer in atmospheric clouds, Hyperbolic Problems: Theory, Numerics and Applications, Series in Contemporary Applied Mathematics 17&18 (2012) 502-509.
  4. B. Dubroca, M. Frank: An Iterative Method for Transport Equations in Radiotherapy, Progress in Industrial Mathematics at ECMI 2008 (2010) 407-412.
  5. M. Frank, M. Herty: Boundary control of radiative transfer equations for application in radiotherapy planning, Progress in Industrial Mathematics at ECMI 2008 (2010) 413-418.
  6. D. Wright, M. Frank, A. Klar: The minimum entropy approximation to the radiative transfer equation, Proc. Symp. Appl. Math. 67 (2009) 987-996.
  7. M. Frank, H. Hensel, A. Klar: Toward fast and accurate methods for dose calculation in radiotherapy, Proc. Appl. Math. Mech. 7 (2007) 200700407-200700408.
  8. M. Schäfer, M. Frank, M. Herty: Optimal treatment planning in radiotherapy based on Boltzmann transport calculations, Proc. Appl. Math. Mech. 7 (2007) 2060027-2060028.
  9. M. Frank, H. Hensel, A. Klar: Toward fast and accurate deterministic methods for dose calculation in electron radiotherapy, IMECS 2007, 2361-2365.
  10. M. Schäfer, M. Frank, R. Pinnau: Partial Space Moment Approximation for Radiative Transfer, Proc. Appl. Math. Mech. 6 (2006) 761-762.
  11. M. Frank: Partial Moment Entropy Approximation to Radiative Heat Transfer, Proc. Appl. Math. Mech. 5 (2005) 659-660.

Contributions to Books


  1. R. Barnard, M. Frank, M. Herty: Optimal Treatment Planning in Radiotherapy Based on Boltzmann Transport Equations, in Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, G. Leugering (et al.) (Eds.), Birkhäuser, 2014.
  2. M. Frank, K. Küpper, B. Seibold: StaRMAP - A second order staggered grid method for radiative transfer: Application in radiotherapy, in Advances In PDE Modeling and Computation, S. Sundar (ed.), Ane Books, 2014.
  3. M. Frank, A. Klar: Radiative Heat Transfer and Applications for Glass Production Processes, in Mathematical Models in the Manufacturing of Glass, Lecture Notes in Mathematics, A. Fasano (Ed.), Springer, 2011.

Theses


  • M. Frank: Partial Moment Models for Radiative Transfer, Dissertation, Fachbereich Mathematik, TU Kaiserslautern, Shaker-Verlag, Aachen, July 2005.
  • M. Frank: Das QCD-Phasendiagramm bei endlicher Isospindichte, Diplomarbeit, Fachbereich Physik, TU Darmstadt, July 2003.
  • M. Frank: Stabilitätsanalyse einer gewöhnlichen Differentialgleichung mit zeitabhängiger Retardierung, Diplomarbeit, Fachbereich Mathematik, TU Darmstadt and Robert Bosch GmbH, Schwieberdingen, September 2001.
Last modified: 2017/07/16 15:28