Publications

List of publications (1996-2024)

Preprints of the Department of Mathematics

Books
Book sections
  • R. Klein, T. Schuster and A. Wald. Sequential subspace optimization for recovering stored energy functions in hyperelastic materials from time-dependent data. In Time-dependent problems in Imaging and Parameter Identification, B. Kaltenbacher, T. Schuster, A. Wald (Eds.), Springer, 2021.
  • B. Kaltenbacher, T.T.N. Nguyen, A. Wald and T. Schuster. Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging. In Time-dependent problems in Imaging and Parameter Identification, B. Kaltenbacher, T. Schuster, A. Wald (Eds.), Springer, 2021.
  • E.Y. Derevtsov, Y.S. Volkov and T. Schuster. Integral operators at settings and investigations of tensor tomography problems. Continuum Mechanics, Applied Mathematics and Scientic Computing: Godunov's Legacy, G.V. Demidenko, E. Romenski, E. Toro, M. Dumbser (Eds.), Springer, 2020.
  • T. Schuster. The importance of the Radon transform in vector field tomography. In The first 100 years of the Radon Transform, R. Ramlau, O. Scherzer (Eds.), Springer, 2019.
  • A. Wald and T. Schuster. Tomographic terahertz imaging using sequential subspace optimization. In New Trends in Parameter Identification for Mathematical Models, B. Hofmann, A. Leitao, J. Zubelli (Eds.), Birkhäuser / Springer, 2018.
  • N. Kong, A. Sanders, M. Rösner, R. Friedrich, F. Dirksen, E. Bauma, T. Schuster, R. Lammering and J.P.~Wulfsberg. Functional integrated feed-units based on flexible mechanisms in small machine tools for small workpieces. In Small Machine Tools for Small Workpieces, J.P. Wulfsberg, A. Sanders (Eds.), Series: Lecture Notes in Production Engineering, Springer, 2017.
  • T. Schuster. 20 Years of Imaging in Vector Field Tomography: A Review. In Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), Y. Censor, M. Jiang, A. K. Louis (Eds.), Series: Publications of the Scuola Normale Superiore, CRM Series , Vol. 7, Birkhäuser, 2008.
Articles with peer review

2024

  • A. Belenkin, M. Hartz and T. Schuster. A note on Γ-convergence of Tikhonov functionals for nonlinear inverse problems. Numerical Functional Analysis and Optimization, under review, 2024.
  • M. Burger, T. Schuster and A. Wald. Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces. Inverse Problems, 40(8), 2024.

2023

  • D. Rothermel and T. Schuster. Development of a generalized photothermal measurement model for the layer thickness determination of multi-layered coating systems. Applied Sciences, 13(7), 2023.

2022

  • C. Meiser, A. Wald and T. Schuster. Learned anomaly detection with terahertz radiation in inline process monitoring. Sensing and Imaging, 23:30, 2022.
  • L. Vierus and T. Schuster. Well-dened forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations. Electronic Transactions on Numerical Analysis, 57:80-100, 2022.
  • R. Rothermel, W. Panlenko, P. Sharma, A. Wald, T. Schuster, A. Jung and S. Diebels. A method for determining the parameters in a rheological model for viscoelastic materials by minimizing Tikhonov functionals. Applied
    Mathematics in Science and Engineering, 30(1):141-165, 2022.

2021

  • D. Rothermel, T. Schuster, R. Schorr and M. Peglow. Determination of the temperature-dependent thermal material properties in the cooling process of steel plates. Mathematical Problems in Engineering,
    DOI:10.1155/2021/6653388, Article ID 6653388, 2021.
  • D. Rothermel and T. Schuster. Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method. Inverse Problems, 37(4):36pp, 2021.

2020

  • S.E. Blanke, B.N. Hahn and A. Wald. Inverse Problems with inexact forward operator: iterative regularization and application in dynamic imaging. Inverse Problems, to appear, 2020.
  • E.Y. Derevtsov, Y.S. Volkov and T. Schuster. Generalized attenuated ray transforms and their integral angular moments. Applied Mathematics and Computation, DOI:10.1016/j.amc.2020.125494, 2020.

2019

  • F. Heber, F. Schöpfer and T. Schuster. Acceleration of sequential subspace optimization in Banach spaces by orthogonal search directions. J. Comp. Appl. Math., 345:1-22, DOI:10.1016/j.cam.2018.05.049, 2019.

2018

  • A. Wald. A fast subspace optimization method for nonlinear inverse problems in Banach spaces with an application in parameter identification. Inverse Problems, 34(8):27pp, DOI:10.1088/1361-6420/aac8f3, 2018.
  • S. Diebels, T. Schuster and A. Wewior. Identifying elastic and viscoelastic material parameters by Tikhonov regularization. Mathematical Problems in Engineering,  DOI:10.1155/2018/1895208, Article ID 1895208, 11pp, 2018.

2017

  • J. Seydel and T. Schuster. Identifying the stored energy of a hyperelastic structure from surface measurements by using an attenuated Landweber method. Inverse Problems. Special Issue: Dynamic Inverse Problems, Special Issue: Dynamic Inverse Problems, 33(12):31pp, DOI:10.1088/1361-6420/aa8d91, 2017.
  • A. Katsevich, D. Rothermel, and T. Schuster. An improved exact inversion formula for solenoidal fields in cone beam vector tomography. Inverse Problems, 33(6):19pp, Special issue: 100 Years of the Radon transform, DOI:10.1088/1361-6420/aa58d5, 2017.
  • C. Schorr, L. Dörr, M. Maisl and T. Schuster. Registration of a priori information for computed laminography. NDT&E International, 86:106-112, DOI:10.1016/j.ndteint.2016.12.005, 2017.
  • A. Wald and T. Schuster. Sequential subspace optimization for nonlinear inverse problems. J. Inv. Ill-Posed Prob., 25(1), DOI:10.1515/jiip-2016-0014, 2017.
  • J. Tepe, T. Schuster, and B. Littau. A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography.
    Inverse Problems in Science and Engineering, 25:1448-1473, DOI:10.1080/17415977.2016.1267168, 2017.

2016

  • U. Schröder and T. Schuster. A numerical algorithm to determine the refractive index of an inhomogeneous medium from time-of-flight measurements.
    Inverse Problems, 32(8):35pp, DOI:10.1088/0266-5611/32/8/085009, 2016.
  • J. Seydel and T. Schuster. On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field.
    Math. Meth. Appl. Sci., DOI:10.1002/mma.3979, 2016.

2015

  • F. Binder, F. Schöpfer and T. Schuster. PDE-based defect localization in fibre-reinforced composites from surface sensor measurements.
    Inverse Problems, 31(2):22pp, DOI:10.1088/0266-5611/31/2/025006, 2015.
  • A. Wöstehoff, T. Schuster. Uniqueness and stability result for Cauchy's equation of motion for a certain class of hyperelastic materials.
    Applicable Analysis, 94(8):1561-1593, DOI:10.1080/00036811.2014.940519, 2015.

2014

  • T. Schuster, A. Wöstehoff. On the identifiable of the stored energy function of hyperelastic materials from sensor data at the boundary.
    Inverse Problems, 30(10):26pp, DOI:10.1088/0266-5611/30/10/105002, 2014.
  • I.E. Svetov, E.Y. Derevtsov, Y.S. Volkov, and T. Schuster. A numerical solver based on B-splines for 2D vector field tomography in a refracting medium.
    Mathematics and Computers in Simulation, 97:207-223, 2014. DOI:10.1016/j.matcom.2013.05.008

2013

2012

2011

2010

2009

2008

  • E. Derevtsov, V. Pickalov, and T. Schuster. Application of local operators for numerical reconstruction of the singular support of a vector field by its known ray transforms.
    Journal of Physics: Conference Series, IOP Publishing, Vol. 135, Article ID 012035, doi:10.1088/1742-6596/135/1/012035, 2008.
  • F. Schöpfer, T. Schuster, and A. K. Louis. Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods.
    Journal of Inverse and Ill-Posed Problems, 16(5):479-506, 2008. DOI:10.1515/JIIP.2008.026
  • F. Schöpfer, T. Schuster, and A. K. Louis. An iterative regularization method for the solution of the split feasibility problem in Banach spaces.
    Inverse Problems, 24(5):20pp, 2008. DOI:10.1088/0266-5611/24/5/055008

2007

  • T. Bonesky, K. Kazimierski, P. Maass, F. Schöpfer, and T. Schuster. Minimization of Tikhonov functionals in Banach spaces.
    Journal of Abstract and Applied Analysis, Article ID 192679, 19 pages, 2007. DOI:10.1155/2008/192679
  • T. Schuster and J. Weickert. On the application of projection methods for computing optical flow fields.
    Inverse Problems and Imaging, 1(4):673-690, 2007.
  • T. Schuster. The formula of Grangeat for tensor fields of arbitrary order in n dimensions.
    International Journal of Biomedical Imaging, Article ID 12839, 4 pages, 2007. DOI:10.1155/2007/12839
  • E. Derevtsov, S. Kazantsev, and T. Schuster. Polynomial bases for subspaces of potential and solenoidal vector fields in the unit ball of R3.
    Journal of Inverse and Ill-Posed Problems, 15(1):19-55, 2007. DOI:10.1515/JIIP.2007.002

2006

2005

2004

2003

2001

2000

1996

  • A. K. Louis and T. Schuster. A novel filter design technique in 2D computerized tomography. Inverse Problems, 12:685-696, 1996. DOI:10.1088/0266-5611/12/5/0112014
Articles in proceedings
  • C. Meiser, T. Schuster and A. Wald. A classication algorithm for anomaly detection in terahertz tomography. In International Conference on Large-Scale Scientic Computing, Springer, pp. 393-401, 2021.
  • A.K. Louis, S.V. Maltseva, A.P. Polyakova, T. Schuster and I.E. Svetov. On solving the slice-by-slice three-dimensional 2-tensor tomography problems using the approximate inverse method. J. Phys.: Conf. Ser., 1715, DOI:10.1088/1742-6596/1715/1/012036 , Article ID 012036, 2021.
  • E.Y. Derevtsov, Y.S. Volkov and T. Schuster. Differential equations and uniqueness theorems for the generalized attenuated ray transforms of tensor fields, Proceedings of the 3rd International Conference on Numerical Computations: Theory and Algorithms (NUMTA), Le Castella Village, Italy, 2019.
  • B. Littau, J. Tepe, S. Kremling, T. Schuster, T. Hochrein and P. Heidemeyer. Tomographische Bildgebung mit vollelektronischen Terahertz-Systemen zur Prüfung von Kunststoff-Bauteilen. DACH-Jahrestagung 2015, 2015.
  • E. Bauma, T. Schuster. A novel hybrid method for optimal control problems and its application to trajectory optimization in micro manufacturing. Proceedings of the 4th International Conference on Engineering Optimization, Instituto Superior Tecnico, Lisbon, 8-11 September 2014, 2014.
  • E. Bauma and T. Schuster. A hybrid approach to optimization of trajectories in micro manufacturing. In Proceedings in Applied Mathematics and Mechanics (PAMM), 14, 2014.
  • E. Derevtsov, I. Svetov, Y. Volkov, and T. Schuster. Numerical B-spline solution of 2D emission and vector tomography problems for media with absoption and refraction. IEEE Proceedings 2008 Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering SIBIRCON-08, Novosibirsk Scientific Center, Novosibirsk, Russia, July 21-25, pp. 212-217, 2008.
  • T. Schuster. Advances and challenges in vector field tomography. In Report Nr. 34/2006 des Workshops Mathematical Methods in Tomography, Mathematisches Forschungsinstitut Oberwolfach, 2006.
  • T. Schuster. A novel mollifier inversion scheme for the Laplace transform. In Proceedings in Applied Mathematics and Mechanics (PAMM), 1(1), 2002.
Preprints
  • R. Rothermel and T. Schuster. Development and analysis of a Bayes inversion method to identify material parameters in viscoelastic structures. Work in progress, 2024.