Publikationen

K. Diethelm, K. Kitzing, R. Picard, S. Siegmund, S. Trostorff & M. Waurick:
A Hilbert Space Approach to Fractional Differential Equations,
J. Dyn. Differ. Equations, 34, 481-504, 2022.
Link zum Volltext / DOI

K. Diethelm, V. Kiryakova, Y. Luchko, J. A. T. Machado & V. E. Tarasov:
Trends, directions for further research, and some open problems of fractional calculus,
Nonlinear Dynam., 107, 3245-3270, 2022.
Link zum Volltext / DOI

K. Diethelm & H. T. Tuan:
Upper and lower estimates for the separation of solutions to fractional differential equations,
Fract. Calc. Appl. Anal., 25, 166-180, 2022.
Link zum Volltext / DOI

K. Diethelm:
A new diffusive representation for fractional derivatives, Part I: Construction, implementation and numerical examples,
Herausgeber: In R. Garrappa (Ed.), Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers, 2022. / Link zum Preprint

K. Diethelm:
A new diffusive representation for fractional derivatives, Part II: Convergence analysis of the numerical scheme,
Mathematics, 10, Article No. 1245, 2022.
Link zum Volltext / DOI

K. Diethelm:
Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials,
Proc. 9th International Conference on Systems and Control (ICSC 2021), 2022. / Link zum Preprint

K. Diethelm, H. D. Thai & H. T. Tuan:
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems,
2022. / Link zum Preprint

M. Bier, M. Mußotter, S. Dietrich:
Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales,
Phys. Rev. E, 106, 054801, 2022. / Link zum Preprint / DOI

H. Bartsch, M. Bier & S. Dietrich:
The role of counterions in ionic liquid crystals,
J. Chem. Phys., 154, 14901, 2021.
Link zum Volltext / Link zum Preprint / DOI

L. Kiefer, S. Petra, M. Storath & A. Weinmann:
Multi-channel Potts-based reconstruction for multi-spectral computed tomography,
Inverse Problems, 37(4), 045004, 2021.

M. Storath & A. Weinmann:
Variational regularization of inverse problems for manifold-valued data. Information and Inference,
A Journal of the IMA, 10 (1), 195-230, 2021.

G. Saueressig, Ch. Bauer, R. Löbmann, C. Wunderlich, W. Wilke, V. Bräutigam & J. Arnholdt:
Zweite Förderphase BEST-FIT: Maßnahmen zur Verbesserung von Bestehensquoten und Praxisfitness der Absolvierenden,
DiNa, 12, Didaktikzentrum, Ingolstadt, 18-25, 2020.
DiZ - DiNa und Tagungsbände (diz-bayern.de)

P. G. Kjeldsberg, R. Schöne, M. Gerndt, L. Riha, V. Kannan, K. Diethelm, M.-C. Sawley, J. Zapletal, A. Gocht, N. Reissmann, O. Vysocki, M. Kumaraswamy & W. E. Nagel:
Run-time Exploitation of Application Dynamism for Energy-efficient Exascale Computing,
Herausgeber: In F. Catthoor, T. Basten, N. Zompakis, M. Geilen & P. G. Kjeldsberg (Eds.), System-Scenario-based Design Principles and Applications, Springer International, Cham, 113-126, 2020.
Abstract und Link zum Volltext

K. Diethelm, R. Garrappa & M. Stynes:
Good (and Not So Good) Practices in Computational Methods for Fractional Calculus,
Mathematics, 8, Article No. 324, 2020.
Abstract Volltext (PDF) / DOI

K. Diethelm, R. Garrappa, A. Giusti & M. Stynes:
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used,
Fract. Calc. Appl. Anal., 23, 610-634, 2020.
Abstract und Link zum Volltext / Volltext bei arXiv.org

L. Kiefer, M. Storath & A. Weinmann:
Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements -- the multivariate case,
Foundations of Computational Mathematics, 1-46, 2020.

L. Kiefer, M. Storath & A. Weinmann:
PALMS Image Partitioning - A New Parallel Algorithm for the Piecewise Affine-Linear Mumford-Shah Model,
Image Processing Online, 10, 124-149, 2020.
DOI

M. Storath & A. Weinmann:
Wavelet sparse regularization for manifold-valued data. Multiscale Modeling and Simulation,
A SIAM Interdisciplinary Journal, 18(2), 674-706, 2020.

A. Majee, M. Bier, R. Blossey & R. Podgornik:
Charge symmetry broken complex coacervation,
Phys. Rev. Research, 2, 43417, 2020.
Link zum Volltext / Link zum Preprint / DOI

M. Mußotter, M. Bier & S. Dietrich:
Heterogeneous surface charge confining an electrolyte solution,
J. Chem. Phys., 152, 234703, 2020.
Link zum Volltext / Link zum Preprint / DOI

G. Wimmer & S. Lange:
Transient magnetic field formulation for solid source conductors,
International Journal of Applied Electromagnetics and Mechanics, 64, 1539-1545, 2020.
Abstract und Link zum Volltext

H. Ables, J. Daube & C. Kraus:
Pressure reconstruction for weak solutions of the two-phase incompressible Navier- Stokes equations with surface tension,
Asymptotic Analysis, 113, 51-86, 2019.
Abstract und Link zum Volltext / Link zum Preprint / DOI

K. Diethelm:
General Theory of Caputo-Type Fractional Differential Equations,
Herausgeber: In A. Kochubei, Y. Luchko (Eds.), Handbook of Fractional Calculus with Applications, Vol. 2, Artikel: Fractional Differential EquationsDe Gruyter, Berlin, 1-20, 2019.
Abstract und Link zum Volltext / DOI

K. Diethelm:
Fundamental Approaches for the Numerical Handling of Fractional Operators and Time-Fractional Differential Equations,
Herausgeber: In G. E. Karniadakis (Ed.), Handbook of Fractional Calculus with Applications, Vol. 3, Artikel: Numerical MethodsDe Gruyter, Berlin, 1-22, 2019.
Abstract und Link zum Volltext / DOI

L. Kiefer, M. Storath & A. Weinmann:
An efficient algorithm for the piecewise affine-linear Mumford-Shah model based on a Taylor jet splitting,
IEEE Transactions on Image Processing, 29, 921-933, 2019.

M. Storath, L. Kiefer & A. Weinmann:
Smoothing for signals with discontinuities using higher order Mumford-Shah models,
Numerische Mathematik, 143(2), 423-460, 2019.

M. Esposito, C. Hennersperger, R. Göbl, L. Demaret, M. Storath, N. Navab, M. Baust & A. Weinmann:
Total variation regularization of pose signals with an application to 3D freehand ultrasound,
IEEE Transactions on Medical Imaging, 38(10), 2245-2258, 2019.

A. Bendinger, C. Debus, C. Glowa, C. Karger, J. Peter & M. Storath:
Bolus arrival time estimation in dynamic contrast-enhanced MRI of small animals based on spline models,
Physics in Medicine and Biology, 64(4), 45003, 2019.

A. Majee, M. Bier, R. Blossey & R. Podgornik:
Charge regulation radically modifies electrostatics in membrane stacks,
Phys. Rev. E, 100, 50601, 2019.
Link zum Volltext / Link zum Preprint / DOI

M. Janssen & M. Bier:
Transient response of an electrolyte to a thermal quench,
Phys. Rev. E, 99, 42136, 2019.
Link zum Volltext / Link zum Preprint / DOI

H. Bartsch, M. Bier & S. Dietrich:
Interface structures in ionic liquid crystals,
Soft Matter, 15, 4109, 2019.
Link zum Volltext / Link zum Preprint / DOI

H. Li, M. Bier, J. Mars, H. Weiss, A.-C. Dippel, O. Gutowski, V. Honkimäki & M. Mezger:
Interfacial premelting of ice in nano composite materials,
Phys. Chem. Chem. Phys., 21, 3734, 2019.
Link zum Volltext / DOI

G. Wimmer & S. Lange:
Transient Magnetic Field Formulation for Solid Source Conductors,
Proceedings of ISEM 2019, Nanjing, China, 2019.

G. Wimmer & S. Lange:
Discrete Differential Forms for the Numerical Solution of Helmholtz Equations,
Proceedings of ICTCA 2019, Beijing, China, 2019.

H. Ables, J. Daube, C. Kraus & D. Kröner:
The Sharp-Interface Limit for the Navier-Stokes-Korteweg Equations,
Hyperbolic Problems: Theory, Numerics, Applications, 1-13, 2018.
Abstract und Link zum Volltext / Link zum Preprint

K. Diethelm & N. J. Ford:
A Note on the Well-posedness of Terminal Value Problems for Fractional Differential Equations,
J. Integral Equations Appl., 30, 371-376, 2018.
Abstract und Link zum Volltext

K. Diethelm:
Numerical Methods for the Fractional Differential Equations of Viscoelasticity,
Herausgeber: In H. Altenbach, A. Öchsner (Eds.), Encyclopedia of Continuum Mechanics, Springer, Berlin, 2018.
Abstract und Link zum Volltext

D. Fortun, M. Storath, D. Rickert, A. Weinmann & M. Unser:
Fast piecewise-affine motion estimation without segmentation,
IEEE Transactions on Image Processing, 27(11), 5612-5624, 2018.

L. Kiefer, S. Petra, M. Storath & A. Weinmann:
Direct MRI segmentation from k-space data by iterative Potts minimization,
International Conference on Scale Space and Variational Methods (SSVM), 2018.

M. Weiler, F. Hamprecht & M. Storath:
Learning steerable filters for rotation equivariant CNNs,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 849-858, 2018.

K. Bredies, M. Holler, M. Storath & A. Weinmann:
Total generalized variation for manifold-valued data,
SIAM Journal on Imaging Sciences, 11(3), 1785-1848, 2018.

W. Erb, A. Weinmann, M. Ahlborg, C. Brandt, G. Bringout, T. Buzug, J. Frikel, C. Kaethner, T. Knopp, T. März, M. Möddel, M. Storath & A. Weber:
Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging,
Inverse Problems, 34(5), 55012, 2018.

M. Kiechle, M. Storath, A. Weinmann & M. Kleinsteuber:
Model-based learning of local image features for unsupervised texture segmentation,
IEEE Transactions on Image Processing, 27(4), 1994-2007, 2018.

M. Storath & A. Weinmann:
Fast median filtering for phase or orientation data,
IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(3), 639-652, 2018.

G. Zarubin, M. Bier & S. Dietrich:
A ferronematic slab in external magnetic fields,
Soft Matter, 14, 9806, 2018.
Link zum Volltext / Link zum Preprint / DOI

A. Majee, M. Bier & S. Dietrich:
Electrostatic interaction of particles trapped at fluid interfaces: Effects of geometry and wetting properties,
Soft Matter, 14, 9436, 2018.
Link zum Volltext / Link zum Preprint / DOI