Professur für Numerik partieller Differentialgleichungen

Prof. Dr. Bastian von Harrach

Bastian von Harrach studierte Mathematik mit Nebenfach Physik an der Universität Mainz, wurde 2006 promoviert, und war als Postdoc an der Universität Mainz und am Johann Radon-Institut der Österreichischen Akademie der Wissenschaften. Nach Professuren an der TU München, der Universität Würzburg, und einem Lehrstuhl an der Universität Stuttgart, folgte er im Oktober 2015 dem Ruf auf die W3-Professur für Numerik partieller Differentialgleichungen an die Goethe-Universität Frankfurt am Main.

Lehre

Sprechstunde und Anleitung zum wissenschaftlichen Arbeiten

  • Sprechstunde: Mittwochs 14:00 bis 15:00 Uhr
  • Sprechstunde Anleitung zum wiss. Arbeiten: Mittwochs 15:00 bis 16:00 Uhr
  • Terminvereinbarung über das Büro per E-Mail an Frau Dreibholz

Publikationen, Vorträge und Lebenslauf

Eingereichte Arbeiten / Preprints

  1. S. Eberle, B. Harrach: Resolution Guarantees for the Reconstruction of Inclusions in Linear Elasticity Based on Monotonicity Methods (arXiv:2208.06865)
     
  2. B. Harrach: The Calderón problem with finitely many unknowns is equivalent to convex semidefinite optimization (arXiv:2203.16779)
     
  3. T. Gerstner, B. Harrach, D. Roth, M. Simon: Multilevel Monte Carlo learning (arXiv:2102.08734)
     
  4. T. Gerstner, B. Harrach, D. Roth: Convergence of Milstein Brownian bridge Monte Carlo methods and stable Greeks calculation (arXiv:1906.11002)
     

Veröffentlichungen in referierten Zeitschriften und Buchkapiteln

  1. B. Harrach, Y.-H. Lin: Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
    Nonlinear Anal., accepted. (arXiv:2201.04594)
     
  2. B. Harrach, T. Jahn, R. Potthast: Regularising linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements
    IMA J. Numer. Anal., 2022. (https://doi.org/10.1093/imanum/drab098)
     
  3. S. Eberle, B. Harrach: Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity
    Comput. Mech. 69, 1069–1086, 2022. (https://doi.org/10.1007/s00466-021-02121-2)
     
  4. B. Harrach: Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming
    Optim. Lett. 16, 1599-1609, 2022. (https://doi.org/10.1007/s11590-021-01802-4)
     
  5. B. Harrach: An Introduction to Finite Element Methods for Inverse Coefficient Problems in Elliptic PDEs
    Jahresber. Dtsch. Math. Ver. 123 (3), 183-210, 2021. (https://doi.org/10.1365/s13291-021-00236-2)
     
  6. S. Eberle, B. Harrach: Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method
    Inverse Problems 37 (4), 045006, 2021. (https://doi.org/10.1088/1361-6420/abc8a9)
     
  7. S. Eberle, B. Harrach, H. Meftahi, T. Rezgui: Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity
    Inverse Probl. Sci. Eng. 29 (3), 396-417, 2021. (https://doi.org/10.1080/17415977.2020.1795151)
     
  8. B. Harrach: Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem
    Numer. Math. 147, 29-70, 2021. (https://doi.org/10.1007/s00211-020-01162-8)
     
  9. B. Harrach, T. Jahn, R. Potthast: Beyond the Bakushinkii veto: Regularising linear inverse problems without knowing the noise distribution
    Numer. Math. 145 (3), 581-603, 2020. (https://doi.org/10.1007/s00211-020-01122-2)
     
  10. T. Gerstner, B. Harrach, D. Roth: Monte Carlo pathwise sensitivities for barrier options
    J. Comput. Finance 23 (5), 75–99, 2020. (https://doi.org/10.21314/JCF.2020.385)
     
  11. B. Harrach, Y.-H. Lin: Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability
    SIAM J. Math. Anal. 52 (1), 402–436, 2020. (https://doi.org/10.1137/19M1251576)
     
  12. B. Harrach, Y.-H. Lin: Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials
    SIAM J. Math. Anal. 51 (4), 3092–3111, 2019. (https://doi.org/10.1137/18M1166298)
     
  13. B. Harrach, V. Pohjola, M. Salo: Dimension Bounds in Monotonicity Methods for the Helmholtz Equation
    SIAM J. Math. Anal. 51 (4), 2995–3019, 2019. (https://doi.org/10.1137/19M1240708)
     
  14. B. Harrach, V. Pohjola, M. Salo: Monotonicity and local uniqueness for the Helmholtz equation
    Anal. PDE 12 (7), 1741–1771, 2019. (https://doi.org/10.2140/apde.2019.12.1741)
     
  15. J. K. Seo, K. C. Kim, A. Jargal, K. Lee, B. Harrach: A Learning-Based Method for Solving Ill-Posed Nonlinear Inverse Problems: A Simulation Study of Lung EIT
    SIAM J. Imaging Sci. 12 (3), 1275–1295, 2019. (https://doi.org/10.1137/18M1222600)
     
  16. B. Harrach, H. Meftahi: Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem
    SIAM J. Appl. Math. 79 (2), 525–550, 2019. (https://doi.org/10.1137/18M1205388)
    (SIAM Journals Top Three Most Cited Papers)
     
  17. B. Harrach, J. Rieger: A Set Optimization Technique for Domain Reconstruction from Single-Measurement Electrical Impedance Tomography Data
    In: D. R. Wood, J. de Gier, C. E. Praeger, T. Tao (eds): 2017 MATRIX Annals, pp 37-49.
    MATRIX Book Ser., Vol. 2, Springer, Cham, 2019. (https://doi.org/10.1007/978-3-030-04161-8_4)
     
  18. B. Harrach: Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes
    Inverse Problems 35 (2), 024005, 2019. (https://doi.org/10.1088/1361-6420/aaf6fc)
     
  19. B. Harrach, Y.-H. Lin, H. Liu: On Localizing and Concentrating Electromagnetic Fields
    SIAM J. Appl. Math. 78 (5), 2558–2574, 2018. (https://doi.org/10.1137/18M1173605)
     
  20. R. Griesmaier, B. Harrach: Monotonicity in Inverse Medium Scattering on Unbounded Domains
    SIAM J. Appl. Math. 78 (5), 2533–2557, 2018. (https://doi.org/10.1137/18M1171679)
    R. Griesmaier, B. Harrach: Erratum: Monotonicity in Inverse Medium Scattering on Unbounded Domains
    SIAM J. Appl. Math. 81 (3), 1332–1337, 2021. (https://doi.org/10.1137/21M1399221)
     
  21. L. Zhou, B. Harrach, J. K. Seo: Monotonicity-based electrical impedance tomography for lung imaging
    Inverse Problems 34 (4), 045005, 2018. (https://doi.org/10.1088/1361-6420/aaaf84)
     
  22. D. Garmatter, B. Harrach: Magnetic Resonance Electrical Impedance Tomography (MREIT): Convergence and Reduced Basis Approach
    SIAM J. Imaging Sci. 11 (1), 863–887, 2018. (https://doi.org/10.1137/17M1155958)
     
  23. T. Brander, B. Harrach, M. Kar, M. Salo: Monotonicity and Enclosure Methods for the p-Laplace Equation
    SIAM J. Appl. Math. 78 (2), 742–758, 2018. (https://doi.org/10.1137/17M1128599)
     
  24. B. Harrach, N. M. Mach: Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography
    In: B. Hofmann, A. Leitão, J. Zubelli (eds): New Trends in Parameter Identification for Mathematical Models, pp 107–120.
    Trends Math., Birkhäuser, Cham, 2018. (https://doi.org/10.1007/978-3-319-70824-9_6)
     
  25. A. Barth, B. Harrach, N. Hyvönen, L. Mustonen: Detecting stochastic inclusions in electrical impedance tomography
    Inverse Problems 33 (11), 115012, 2017. (https://doi.org/10.1088/1361-6420/aa8f5c)
     
  26. B. Harrach, M. Ullrich: Local uniqueness for an inverse boundary value problem with partial data
    Proc. Amer. Math. Soc. 145 (3), 1087–1095, 2017. (https://doi.org/10.1090/proc/12991)
     
  27. B. Harrach, N. M. Mach: Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography
    Inverse Problems 32 (12), 125002, 2016. (http://dx.doi.org/10.1088/0266-5611/32/12/125002)
     
  28. D. Garmatter, B. Harrach, B. Haasdonk: A reduced basis Landweber method for nonlinear inverse problems
    Inverse Problems 32 (3), 035001, 2016. (http://dx.doi.org/10.1088/0266-5611/32/3/035001)
    (Inverse Problems Highlights of 2016)
     
  29. B. Harrach: Interpolation of missing electrode data in electrical impedance tomography
    Inverse Problems 31 (11), 115008, 2015. (http://dx.doi.org/10.1088/0266-5611/31/11/115008)
     
  30. B. Harrach, E. Lee, M. Ullrich: Combining frequency-difference and ultrasound modulated electrical impedance tomography
    Inverse Problems 31 (9), 095003, 2015. (http://dx.doi.org/10.1088/0266-5611/31/9/095003)
     
  31. B. Harrach, M. Ullrich: Resolution Guarantees in Electrical Impedance Tomography
    IEEE Trans. Med. Imaging 34 (7), 1513–1521, 2015. (http://dx.doi.org/10.1109/TMI.2015.2404133)
     
  32. M. K. Choi, B. Harrach, J. K. Seo: Regularizing a linearized EIT reconstruction method using a sensitivity-based factorization method
    Inverse Probl. Sci. Eng. 22 (7), 1029–1044, 2014. (http://dx.doi.org/10.1080/17415977.2013.850682)
     
  33. B. Harrach, M. Ullrich: Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
    SIAM J. Math. Anal. 45 (6), 3382–3403, 2013. (http://dx.doi.org/10.1137/120886984)
     
  34. T. Alm, B. Harrach, D. Harrach, M. Keller: A Monte Carlo pricing algorithm for autocallables that allows for stable differentiation
    J. Comput. Finance 17 (1), 43–70, 2013. (https://doi.org/10.21314/JCF.2013.265)
     
  35. L. Arnold, B. Harrach: Unique shape detection in transient eddy current problems
    Inverse Problems 29 (9), 095004 (19pp), 2013. (http://dx.doi.org/10.1088/0266-5611/29/9/095004)
     
  36. M.-E. Ts, E. Lee, J. K. Seo, B. Harrach, S. Kim: Projective Electrical Impedance Reconstruction with Two Measurements
    SIAM J. Appl. Math. 73 (4), 1659–1675, 2013. (http://dx.doi.org/10.1137/120879671)
     
  37. B. Harrach: Recent Progress on the Factorization Method for Electrical Impedance Tomography
    Comput. Math. Methods Med., vol. 2013, Article ID 425184, 8 pages, 2013. (http://dx.doi.org/10.1155/2013/425184)
     
  38. H. Kwon, H. Wi, B. Karki, E. J. Lee, A. McEwan, E. J. Woo, B. Harrach, J. K. Seo, T. I. Oh: Bioimpedance spectroscopy tensor probe for anisotropic measurements
    Electron. Lett. 48 (20), 1253–1255, 2012. (http://dx.doi.org/10.1049/el.2012.2661)
     
  39. B. Harrach: Simultaneous determination of the diffusion and absorption coefficient from boundary data
    Inverse Probl. Imaging 6 (4), 663–679, 2012. (http://dx.doi.org/10.3934/ipi.2012.6.663)
     
  40. L. Arnold, B. Harrach: A Unified Variational Formulation for the Parabolic-Elliptic Eddy Current Equations
    SIAM J. Appl. Math. 72 (2), 558–576, 2012. (http://dx.doi.org/10.1137/110831477)
     
  41. M. Hanke, B. Harrach, N. Hyvönen: Justification of point electrode models in electrical impedance tomography
    Math. Models Methods Appl. Sci. 21 (6), 1395–1413, 2011. (http://dx.doi.org/10.1142/S0218202511005362)
     
  42. B. Harrach, J. K. Seo, E. J. Woo: Factorization Method and Its Physical Justification in Frequency-Difference Electrical Impedance Tomography
    IEEE Trans. Med. Imaging 29 (11), 1918–1926, 2010. (http://dx.doi.org/10.1109/TMI.2010.2053553)
     
  43. B. Harrach, J. K. Seo: Exact Shape-Reconstruction by One-Step Linearization in Electrical Impedance Tomography
    SIAM J. Math. Anal. 42 (4), 1505–1518, 2010. (http://dx.doi.org/10.1137/090773970)
     
  44. B. Harrach: On uniqueness in diffuse optical tomography
    Inverse Problems 25 (5), 055010 (14pp), 2009. (http://dx.doi.org/10.1088/0266-5611/25/5/055010)
     
  45. B. Harrach, J. K. Seo: Detecting Inclusions in Electrical Impedance Tomography Without Reference Measurements
    SIAM J. Appl. Math. 69 (6), 1662–1681, 2009. (http://dx.doi.org/10.1137/08072142X)
     
  46. B. Gebauer, O. Scherzer: Impedance-Acoustic Tomography
    SIAM J. Appl. Math. 69 (2), 565–576, 2008. (http://dx.doi.org/10.1137/080715123)
     
  47. B. Gebauer, N. Hyvönen: Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem
    Inverse Probl. Imaging 2 (3), 355–372, 2008. (http://dx.doi.org/10.3934/ipi.2008.2.355)
     
  48. B. Gebauer: Localized potentials in electrical impedance tomography
    Inverse Probl. Imaging 2 (2), 251–269, 2008. (http://dx.doi.org/10.3934/ipi.2008.2.251)
     
  49. B. Gebauer, M. Hanke, C. Schneider: Sampling methods for low-frequency electromagnetic imaging
    Inverse Problems 24 (1), 015007 (18pp), 2008. (http://dx.doi.org/10.1088/0266-5611/24/1/015007)
     
  50. B. Gebauer, N. Hyvönen: Factorization method and irregular inclusions in electrical impedance tomography
    Inverse Problems 23 (5), 2159–2170, 2007. (http://dx.doi.org/10.1088/0266-5611/23/5/020)
     
  51. B. Gebauer: Sensitivity analysis of a parabolic-elliptic problem
    Quart. Appl. Math. 65 (3), 591–604, 2007. (http://dx.doi.org/10.1090/S0033-569X-07-01072-4)
    Preprint: RICAM Reports 2007-05, Johann Radon Institute, Linz, Austria, 2007.
     
  52. F. Frühauf, B. Gebauer, O. Scherzer: Detecting Interfaces in a Parabolic‐Elliptic Problem from Surface Measurements
    SIAM J. Numer. Anal. 45 (2), 810–836, 2007. (http://dx.doi.org/10.1137/050641545)
     
  53. B. Gebauer: The Factorization Method for Real Elliptic Problems
    Z. Anal. Anwend. 25 (1), 81–102, 2006. (http://dx.doi.org/10.4171/ZAA/1279)
     
  54. B. Gebauer, M. Hanke, A. Kirsch, W. Muniz, C. Schneider: A sampling method for detecting buried objects using electromagnetic scattering
    Inverse Problems 21 (6), 2035–2050, 2005. (http://dx.doi.org/10.1088/0266-5611/21/6/015)
     

Veröffentlichungen in Tagungsbänden und extended abstracts

  1. B. Harrach, V. Pohjola, M. Salo: The monotonicity method for inverse scattering
    Oberwolfach Rep. 14 (2), 1519–1522, 2017. (http://dx.doi.org/10.4171/OWR/2017/24)
     
  2. B. Harrach, N. M. Mach: Towards combining optimization-based techniques with shape reconstruction methods in EIT
    Oberwolfach Rep. 13 (3), 2598–2601, 2016. (http://dx.doi.org/10.4171/OWR/2016/45)
     
  3. L. Arnold, B. Harrach: Justification of regularizations for the parabolic-elliptic eddy current equation,
    In: IPDO 2013: 4th Inverse problems, design and optimization symposium, 2013 June 26–28, Albi, ed. by O. Fudym, J.-L. Battaglia, G.S. Dulikravich et al., Albi ; Ecole des Mines d'Albi-Carmaux, 2013 (ISBN 979-10-91526-01-2).
     
  4. B. Harrach, M. Ullrich: Monotony based inclusion detection in EIT for realistic electrode models,
    J. Phys.: Conf. Ser. 434, 012076, 2013. (http://dx.doi.org/10.1088/1742-6596/434/1/012076)
     
  5. L. Arnold, B. Harrach: Inverse Eddy Current Problems
    Oberwolfach Rep. 9 (1), 630–633, 2012. (http://dx.doi.org/10.4171/OWR/2012/11)
     
  6. M. K. Choi, B. Harrach, J. K. Seo: A new hybrid reconstruction method in EIT
    Proceedings of the KSIAM 6 (1), 289–291, 2011. (http://www.dbpia.co.kr/Journal/ArticleDetail/NODE01690054)
     
  7. B. Harrach, J. K. Seo: Exact shape-reconstruction by one-step linearization in electrical impedance tomography
    Oberwolfach Rep. 7 (2), 1055–1057, 2010. (http://dx.doi.org/10.4171/OWR/2010/18)
     
  8. B. Harrach, M. Ullrich: Monotony based imaging in EIT,
    AIP Conf. Proc. 1281, 1975–1978, 2010. (https://doi.org/10.1063/1.3498321)
     
  9. B. Harrach: Simultaneous imaging of absorption and scattering in dc diffuse optical tomography,
    in: O. Dössel and W. C. Schlegel (Eds.): WC2009, IFMBE Proceedings 25/II, 776–779, 2009. (http://dx.doi.org/10.1007/978-3-642-03879-2_217)
     
  10. J. K. Seo, B. Harrach, E. J. Woo: Recent progress on frequency difference electrical impedance tomography,
    ESAIM Proc. 26, 150–161, 2009. (http://dx.doi.org/10.1051/proc/2009011)
     
  11. B. Gebauer, M. Hanke, C. Schneider: Sampling methods for low-frequency electromagnetic imaging
    Oberwolfach Rep. 4 (1), 748–750, 2007. (http://dx.doi.org/10.4171/OWR/2007/13)
     

Populärwissenschaftliche Arbeiten / Hochschulkommunikation

  1. B. Harrach: Abermillionen Rechenschritte für einen Blick in den Körper: In der medizinischen Bildgebung geht nichts ohne Mathematik
    Forschung Frankfurt : Wissenschaftsmagazin der Goethe-Universität 34 (2), 79–81, 2017. (http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hebis:30:3-452487)
     
  2. B. Haasdonk, B. Harrach, C. Rohde, C. Scherer, G. Schneider, K. Siebert: Mathematik als Innovator der Simulationstechnik, Simulationstechnik als Innovator der Mathematik
    in: Simulation Technology, Themenheft Forschung 10, 60–71, Universität Stuttgart 2014, ISSN 1861-0269. (http://www.uni-stuttgart.de/hkom/publikationen/themenheft/10)

Akademische Ausbildung und beruflicher Werdegang

  • seit 10/2015: W3-Professor für Numerik partieller Differentialgleichungen, Goethe-Universität Frankfurt
  • 03/2013 - 09/2015: W3-Professor, Leitung des Lehrstuhls für Optimierung und inverse Probleme, Universität Stuttgart
  • 09/2011 - 02/2013: W2-Professor für Inverse Probleme, Universität Würzburg
  • 04/2010 - 08/2011: W2-Professor für Angewandte Mathematik II (befristet auf 5 Jahre), Technische Universität München
  • 02/2008 - 03/2010: Wissenschaftlicher Mitarbeiter, Universität Mainz
  • 10/2006 - 01/2008: Junior Scientist, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Österreichische Akademie der Wissenschaften
  • 07/2006: Promotion im Fach Mathematik, Universität Mainz
  • 03/2002: Diplomabschluss Mathematik, Universität Mainz

Mitgliedschaften/Engagement

Auszeichnungen und Stipendien

Prof. Dr. Bastian von Harrach

Prof. Dr. Bastian von Harrach
Institut für Mathematik
Goethe-Universität Frankfurt am Main
Robert-Mayer-Str. 10
60325 Frankfurt am Main
Deutschland

Raum: 101
Telefon: +49 69 798 28622
E-Mail: harrach@math.uni-frankfurt.de
http://numerical.solutions