- Detection and reconstruction of inclusions in elastic bodies by means of monotonicity-based methods as well as their linearization and regularization.
My research focus is on wave equations, with a focus on the elastic case: from wave propagation to postprocessing to the inverse problem. On the one hand my goal is to develop and analyze numerical methods and on the other hand to implement them.
- Stable boundary integral formulation of the acoustic wave equation as a transmission problem with mixed boundary conditions.
- Stable numerical coupling of interior and exterior problems for the elastic and thermoelastic wave equation (by use of finite elements and leapfrog as well as boundary elements and convolution quadrature) as well as convergence and error analysis.
- Implementation and numerical experiments of FEM-BEM coupling and time discretizations for the elastodynamic wave equation.
- Multiscale decomposition based on physically motivated wavelets for the Laplace, Helmholtz and elastic wave equation with numerical experiments.
S. Eberle, Direct and Inverse Problems of Wave-type Equations and their Postprocessing, cumulative habilitation thesis, Goethe University Frankfurt
S. Eberle, B. Harrach, Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity, arXiv:2105.01941
S. Eberle, FEM-BEM Coupling for the Thermoelastic Wave Equation with Transparent Boundary Conditions in 3D
Publications in peer-reviewed journals and book chapters
S. Eberle, J. Moll, Experimental Detection and Shape Reconstruction of Inclusions in Elastic Bodies via a Monotonicity Method, Int J Solids Struct, accepted for publication
C. Blick, S. Eberle, A Survey on Multiscale Mollifier Decorrelation of Seismic Data, Int J Geomath, 12 (16), 2021
S. Eberle, B. Harrach, Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method, Inverse Problems, 37 (4), 045006, 2021
S. Eberle, F. Florian, R. Hiptmair, S. Sauter, A Stable Boundary Integral Formulation of an Acoustic Wave Transmission Problem with Mixed Boundary Conditions, SIAM J. Math. Anal., 53(2), 1492–1508, 2021
S. Eberle, B. Harrach, H. Meftahi, and T. Rezgui, Lipschitz Stability Estimate and Reconstruction of Lamé Parameters in Linear Elasticity, Inverse Probl. Sci. Eng., 29 (3), 396-417, 2021
S. Eberle, An Implementation and Numerical Experiments of the FEM-BEM Coupling for the Elastodynamic Wave Equation in 3D, ZAMM, 99 (12), 2019
C. Blick, S. Eberle, Multiscale Density Decorrelation by Cauchy-Navier Wavelets, Int J Geomath, 10 (24), 2019
S. Eberle, The Elastic Wave Equation and the Stable Numerical Coupling of its Interior and Exterior Problems, ZAMM, 98 (7), 1261-1283, 2018
M. Augustin, S. Eberle, M. Grothaus, An Overview on Tools from Functional Analysis, In: Handbook of Mathematical Geodesy, 165-199, Springer, 2018
C. Blick, S. Eberle, W. Freeden, Radio Occultation: Principles and Modeling, In: Encyclopedia of Geodesy (Eds.: E. Grafarend), Springer, 2016
M. Augustin, C. Blick, S. Eberle, W. Freeden, Disturbing Potential from Gravity Anomalies: From Globally Reflected Stokes Boundary Value Problem to Locally Oriented Multiscale Modeling, In: Encyclopedia of Geodesy (Eds.: E. Grafarend), Springer, 2016
S. Eberle, W. Freeden, U. Matthes, Forest Fire Spreading, In: Handbook of Geomathematics (2nd edition) (Eds.: W. Freeden, Z. Nashed, T. Sonar), 1349-1385, Springer, Heidelberg, 2015
M. Augustin, M. Bauer, C. Blick, S. Eberle, W. Freeden, C. Gerhards, M. Ilyasov, R. Kahnt, M. Klug, S. Möhringer, T. Neu, H. Nutz, I. Ostermann, A. Punzi, Modeling Deep Geothermal Reservoirs: Recent Advances and Future Problems, In: Handbook of Geomathematics (2nd edition) (Eds.: W. Freeden, Z. Nashed, T. Sonar), 1547-1629, Springer, Heidelberg, 2015
C. Blick, S. Eberle, Radio Occultation via Satellites, In: Handbook of Geomathematics (2nd edition) (Eds.: W. Freeden, Z. Nashed, T. Sonar), 1089-1125, Springer, Heidelberg, 2015
Publications in conference proceedings and extended abstracts
S. Eberle, FEM-BEM coupling of wave-type equations: from the acoustic to the elastic wave equation, in: Mathematics of Wave Phenomena (Eds.: W. Dörfler, M. Hochbruck, D. Hundertmark, W. Reichel, A. Rieder , R. Schnaubelt, B. Schörkhuber), 109-124, Springer, 2020
S. Eberle, F. Florian, R. Hiptmair, S. Sauter, A stable integral equation for a mixed acoustic transmission problem, in: Waves 2019: 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation. Book of Abstracts. (Eds.: M. Kaltenbacher, J. M. Melenk, L. Nannen, & F. Toth), 208-209, Wien, 2019
S. Eberle, Modeling and Simulation of Forest Fire Spreading, Lecture Notes in Earth System Sciences, Mathematics of Planet Earth, 811-814, Springer, 2013
S. Eberle, Forest Fire Determination: Theory and Numerical Aspects, PhD Thesis, University of Kaiserslautern, Dr. Hut Verlag, 2015
S. Eberle, Mathematical Aspects of Climate Monitoring by Radio Occultation (RO), Diploma Thesis, University of Kaiserslautern, 2010
Multiscale Mollifier Decorrelation of Seismic Data (poster), SIAM Conference on Mathematical & Computational Issues in the Geosciences (2021)
Experimental Detection and Shape Reconstruction of Inclusions in Elastic Bodies via Monotonicity-Based Methods, SIAM Conference on Mathematical Aspects of Materials Science (2021)
Shape Reconstruction of Inclusions in Elastic Bodies Based on Real Data via Monotonicity-based Methods, GAMM Annual Meeting (2021)
Monotonicity-based detection of material inclusions for elastic bodies, Applied Inverse Problems (AIP) conference, Grenoble (2019)
Variational analysis of shape reconstruction in linear elasticity, Applied Inverse Problems (AIP) conference, Grenoble (2019)
Regularization techniques for wave equations, Chemnitz Symposium on Inverse Problems, Chemnitz (2018)
Coupling Problems of Wave-type Equations, Conference on Mathematics of Wave Phenomena, KIT Karlsruhe (2018)
Multiscale decorrelation reflected post-processing for the elastic wave equation, International Conference "Inverse Problems: Modeling and Simulation", Malta (2018)
FEM-BEM coupling for wave-type equations in 3d, Zurich Colloquium in Applied and Computational Mathematics, ETH Zürich (2017)
The 3d elastodynamic wave equation with transparent boundary conditions, SIAM Conference on Mathematical and Computational Issues in the Geosciences, Erlangen (2017)
Stable and convergent interior-exterior coupling of wave-type equations I: elastodynamics, SFB-Seminar (wave phenomena), KIT Karlsruhe (2017)
The Elastic Wave Equation and the Stable Numerical Coupling of its Interior and Exterior Problems, Kolloquium „Mathematische Methoden in den Natur- und Ingenieurswissenschaften“, TU Graz (2017)
Die Erde im Wandel - eine mathematische Herausforderung, Tag der Mathematik, Universität Tübingen (2017)
Boundary Integral Representation for the Elastic Wave Equation, Workshop Analysis and Advanced Numerical Methods for Partial Differential Equations, Strobl (2016)
Modeling of Forest Fire Spreading with Radial Basis Functions, Joint Mathematics Meetings, San Antonio (2015)