Publikationen

Eingereichte Arbeiten / Preprints

  1. B. Harrach: An introduction to finite element methods for inverse coefficient problems in elliptic PDEs (arXiv:2103.00888)
     
  2. T. Gerstner, B. Harrach, D. Roth, M. Simon: Multilevel Monte Carlo learning (arXiv:2102.08734)
     
  3. B. Harrach, T. Jahn, R. Potthast: Regularising linear inverse problems under unknown non-Gaussian white noise (arXiv:2010.04519)
     
  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. 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)
     
  2. 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)
     
  3. 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)
     
  4. 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)
     
  5. 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)
     
  6. 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)
     
  7. 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)
     
  8. 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)
     
  9. 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)
     
  10. 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)
     
  11. 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)
     
  12. 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)
     
  13. 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)
     
  14. 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)
     
  15. 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., to appear.
     
  16. 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)
     
  17. 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)
     
  18. 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)
     
  19. 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)
     
  20. 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)
     
  21. 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)
     
  22. 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)
     
  23. 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)
     
  24. 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)
     
  25. 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)
     
  26. 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)
     
  27. 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)
     
  28. 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)
     
  29. 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)
     
  30. 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)
     
  31. 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)
     
  32. 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)
     
  33. 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)
     
  34. 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)
     
  35. 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)
     
  36. 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)
     
  37. 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)
     
  38. 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)
     
  39. 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)
     
  40. 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)
     
  41. B. Gebauer, O. Scherzer: Impedance-Acoustic Tomography
    SIAM J. Appl. Math. 69 (2), 565–576, 2008. (http://dx.doi.org/10.1137/080715123)
     
  42. 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)
     
  43. 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)
     
  44. 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)
     
  45. 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)
     
  46. 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.
     
  47. 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)
     
  48. 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)
     
  49. 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)