- DFG-project
**"Inclusion Reconstruction with Monotonicity-based Methods for the Elasto-oscillatory Wave Equation"** - Development of monotonicity-based methods to solve an inverse problem of linear elasticity (time-independent), especially standard and linearized monotonicity tests as well as monotonicity-based regularization (minimization problem) for the detection and reconstruction of inclusions in elastic bodies.
- Simulations based on artificial and experimental data (laboratory experiment).

**Numerical Analysis:**

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 coupled with boundary elements and convolution quadrature) as well as convergence and error analysis.

**Numerical Simulation:**

Implementation and numerical experiments of FEM-BEM coupling and time discretizations for the elastodynamic wave equation.

**Multiscale Analysis:**

Multiscale decomposition based on physically motivated wavelets for the Laplace, Helmholtz and elastic wave equation with numerical experiments.

My research focus is on numerical methods applied to wave equations, with a focus on the elastic case: from wave propagation to postprocessing and the inverse problem. My goal is on the one hand to develop and analyze numerical methods and on the other hand to implement them.

S. Eberle-Blick, N. Hyvönen, **Bayesian Experimental Design for Linear Elasticity** (arXiv preprint), 2023### Publications in peer-reviewed journals and book chapter

**
Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method**,
Inverse Problems, 37 (4), 045006, 2021

### Publications in conference proceedings and extended abstracts

### Thesis

S. Eberle-Blick, V. Pohjola, **The Monotonicity Method for Inclusion Detection and the Time Harmonic Elastic Wave Equation** (arXiv preprint), accepted for publication in Inverse Problems, 2024

S. Eberle-Blick, B. Harrach, **Resolution Guarantees for the Reconstruction of Inclusions in Linear Elasticity Based on Monotonicity Methods**, Inverse Problems, 39, 075006, 2023

S. Eberle, **FEM-BEM Coupling for the Thermoelastic Wave Equation with Transparent Boundary Conditions in 3D**, ZAMP, 73, 163, 2022

S. Eberle, B. Harrach, **Monotonicity-Based Regularization for Shape Reconstruction in Linear
Elasticity**, Comput. Mech.,** ** 69, 1069-1086, 2022

S. Eberle, J. Moll, **Experimental Detection and Shape Reconstruction of Inclusions in Elastic Bodies via a Monotonicity Method**, Int. J. Solids Struct., 233, 111169, 2021

C. Blick, S. Eberle, **
A Survey on Multiscale Mollifier Decorrelation of Seismic Data**, Int. J. Geomath., 12 (16), 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

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, **Direct and Inverse Problems of Wave-type Equations and their Postprocessing,** Cumulative Habilitation Thesis, Goethe University Frankfurt, 2022

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

**The Monotonicity Method for the Time-harmonic Elastic Wave Equation****, Chemnitz Symposium on Inverse Problem - On Tour, Würzburg (2023)**

**Monotonicity-Based Methods for
Solving Inverse Problems in Linear Elasticity****, SIAM Conference on Mathematical & Computational Issues in the
Geosciences, Bergen (2023)****Shape Reconstruction of Inclusions in Elastic Bodies Based on Real Data via Monotonicity-based Methods, **Oberseminar "Optimale Steuerung und Inverse Probleme", University of Duisburg-Essen (2023)

**Reconstruction of Inclusions in Elastic Bodies Based
on Experimental Data**, Symposium on Inverse Problems: From experimental data to models and back, Potsdam (2022)

**Solving Inverse Problems of Linear Elasticity via Monotonicity Methods,**
28th Nordic Congress of
Mathematicians, Espoo (2022)

** Monotonicity-based Methods for Solving Inverse Problems of Linear Elasticity**, Rhein-Main Arbeitskreis "Mathematics of Computation", University of Mannheim (2022)

**Monotonie-Methoden zur Lösung Inverser Probleme: Die Rekonstruktion von Einschlüssen in elastischen Körpern**, "Antrittsvorlesung" as part of the habilitation process, Goethe University Frankfurt (2002)

**Reconstruction of Lamé Parameters in Linear Elasticity**, International Conference "Inverse Problems: Modeling and Simulation", Malta (2022)

** Mathematische Modellierung des Erdmagnetfeldes**, Habilitationskolloquium, Goethe University Frankfurt (2022)

**Local Multiscale Post-Processing of Seismic Data**, Conference on Mathematics of Wave Phenomena, virtual (2022)

**Experimental Detection and Shape Reconstruction of Inclusions in Elastic Bodies via Monotonicity-Based Methods**, Conference on Mathematics of Wave Phenomena, virtual (2022)

**Shape Reconstruction in Linear Elasticity via Monotonicity-based Methods**, Oberseminar "Numerik", Saarland University (2021)

**Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity**, 2nd Alps-Adriatic Inverse Problems Workshop - Chemnitz Symposium on tour, Klagenfurt (2021)

**Multiscale Mollifier Decorrelation of Seismic Data** (poster), SIAM Conference on Mathematical & Computational Issues in the Geosciences, virtual (2021)

**Experimental Detection and Shape Reconstruction of Inclusions in Elastic Bodies via Monotonicity-Based Methods**, SIAM Conference on Mathematical Aspects of Materials Science, virtual (2021)

**Shape Reconstruction of Inclusions in Elastic Bodies Based on Real Data via Monotonicity-based Methods**, GAMM Annual Meeting, virtual (2021)

**Detection and reconstruction of inclusions in elastic bodies based on monotonicity methods**, DMV Annual Meeting - Chemnitz Symposium on Inverse Problems, virtual (2020)

**Shape reconstruction in linear elasticity with monotonicity-based methods**, IFIP Workshop on Inverse Problems, Imaging, and Optimization, Essen (2020)

**Monotonicity-based methods for the reconstruction of inclusions in linear elasticity**, Chemnitz Symposium on Inverse Problems On Tour in Frankfurt, Frankfurt (2019)

**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)

**Detection and reconstruction of material inclusions in elastic bodies**, Geophysikalisches Seminar, Goethe-Universität Frankfurt (2019)

**The monotonicity method for the stationary elastic wave equation, **Workshop on Numerical Methods for Optimal Control and Inverse Problems, München (2019)

**Regularization techniques for wave equations**, Chemnitz Symposium on Inverse Problems, Chemnitz (2018)

**C****oupling Problems of Wave-type Equation****s**, 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)

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