PD Dr. Sarah Eberle-Blick

Aktuelle Themen

Inverse Probleme:

Weitere Themen

  • Numerische Analysis:
    Stabile Randintegralformulierung der akustischen Wellengleichung als Transmissions-Problem mit gemischten Randbedingungen: Dirichlet, Neumannn, Impedanz (zeitabhängig).
    Stabile Kopplung von Innen- und Außenraum Problemen der elastodynamischen und thermoelastischen Wellengleichung (mittels finite Elemente und Randelemente Methoden im Ort und Leapfrog und Convolution Quadrature in der Zeit) sowie Konvergenzbeweis und Fehlerabschätzungen.
  • Numerische Simulation:
    Implementierung und numerische Experimente der FEM-BEM-Kopplung und Zeitdiskretisierungen für die elastodynamische Wellengleichung.
  • Multiskalenanalyse:
    Multiskalenzerlegung basierend auf physikalisch motivierten Wavelets für die Laplace, Helmholtz und elastische Wellengleichung mit numerischen Experimenten.

Mein Forschungsschwerpunkt sind numerische Methoden mit Anwendung auf Wellengleichungen, mit Fokus auf dem elastischen Fall: Von der Wellenausbreitung über Postprocessing bis hin zum Inversen Problem. Dabei ist mein Ziel einerseits, numerische Verfahren zu entwickeln und zu analysieren und andererseits, diese zu implementieren.


Veröffentlichungen in referierten Zeitschriften und Buchkapiteln

S. Eberle-Blick, N. Hyvönen, Bayesian Experimental Design for Linear Elasticity (arXiv preprint), zur Veröffentlichung angenommen: Inverse Problems and Imaging, 2024

S. Eberle-Blick, V. Pohjola, The Monotonicity Method for Inclusion Detection and the Time Harmonic Elastic Wave Equation, Inverse Problems, 40, 045018, 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, 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


Veröffentlichungen in Tagungsbänden und 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


Thesis

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

Ausgewählte Vorträge


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)

Experimental Detection and Shape Reconstruction of Inclusions in Elastic Bodies based on Monotonicity Methods, Oberseminar "Inverse Probleme", KIT Karlsruhe (2023)

Shape Reconstruction of Inclusions in Elastic Bodies Based on Real Data via Monotonicity-based Methods, Oberseminar "Optimale Steuerung und Inverse Probleme", Universität 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", Universität Mannheim (2022)

Monotonie-Methoden zur Lösung Inverser Probleme: Die Rekonstruktion von Einschlüssen in elastischen Körpern, "Antrittsvorlesung" im Rahmen des Habilitationsverfahrens, Goethe-Universität Frankfurt (2022)


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

Mathematische Modellierung des Erdmagnetfeldes, Habilitationskolloquium, Goethe-Universität Frankfurt (2022)

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

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

Shape Reconstruction in Linear Elasticity via Monotonicity-based Methods, Oberseminar "Numerik", Universität des Saarlandes (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, virtuell (2021)

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

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

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

Solving the inverse problem of linear elasticity with monotonicity methods, ÖMG Conference, Dornbirn (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)

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 Function, Joint Mathematics Meetings, San Antonio (2015)












PD Dr. Sarah Eberle-Blick

Institut für Mathematik
Goethe-Universität Frankfurt 
Robert-Mayer-Str. 10
60325 Frankfurt am Main
Deutschland

Raum: 103
Telefon: +49 69 798 23620
Mail: eberle[at]math.uni-frankfurt.de

http://numerical.solutions