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Project: Regularization and discretization of in...

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Title:	Regularization and discretization of inverse problems for PDEs in Banach spaces
Description:	The aim of this project is a combined analysis of regularization and discretization of ill-posed problems in Banach spaces specifically in the context of partial differential equations. Such problems play a crucial role in numerous applications ranging from medical imaging via nondestructive testing to geophysical prospecting, with the Banach space setting mandated by the inherent regularity of the sought coefficients as well as structural features such as sparsity. Our goal is to fill the gap between the existing abstract regularization theory in general Banach spaces and the adaptive discretization of well-posed optimization problems in Hilbert spaces with pointwise constraints to derive explicit source conditions and practical parameter choice rules and to develop adaptive discretization methods based on functional and goal-oriented error estimates that take into account the interdependence of regularization parameter, data noise level and discretization error. This will lead to an integrated approach for the stable and efficient numerical solution method of parameter identification problems in Banach spaces.
Keywords:	parameter identification, inverse problems, partial differential equations, regularization, discretization

Short title:	Inverse problems in Banach spaces
Period:	01.03.2016 - 31.08.2019
Contact e-mail:	barbara.kaltenbacher@aau.at
Homepage:	-

Employees

Role

Time period

(internal)

Project leader

01.03.2016 - 28.02.2019

(internal)

Research staff

01.03.2016 - 14.11.2018

(internal)

Research staff

01.12.2018 - 15.03.2019

(internal)

Research staff

01.12.2018 - 15.03.2019

Assignment

Organisational unit

Fakultät für Technische Wissenschaften

Categorisation

Project type	Research funding (on request / by call for proposals)
Funding type	§26
Research type	Applied research Fundamental research
Subject areas	101014 - Numerical mathematics 101002 - Analysis
Research Cluster	No research Research Cluster selected
Gender aspects	0%
Project focus	Science to Science (Quality indicator: I) Classification raster of the assigned organisational units: Institut für Mathematik
working groups	No working group selected

Funding

Funding program

Cooperations

Organisation

Address

400 Bizzell St
US - TX 77843 College Station

Universitätsplatz 3
AT - 8010 Graz

Universitätsstraße 2
DE - 45141 Essen

Straße der Nationen 62
DE - 09111 Chemnitz

DE Hamburg

Ingolstädter Landstraße 1
DE - 85764 Neuherberg

Sanderring 2
DE - 97070 Würzburg

Research activities

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Projects	Solving inverse problems without using forward operators (FWF) Solving inverse problems without using forward operators (FWF) Univ.-Prof. Dipl.-Ing. Dr. Barbara Kaltenbacher 01.10.2017 - 31.03.2022 To project
Publications	Continuous analogue to iterative optimization for PDE-constrained inverse problems Continuous analogue to iterative optimization for PDE-constrained inverse problems (2018) R. Boiger, A. Fiedler, H. Jan, B. Kaltenbacher Inverse Problems in Science and Engineering No Publisher selected to publication On the identification of a nonlinear term in a reaction-diffusion equation On the identification of a nonlinear term in a reaction-diffusion equation (2019) B. Kaltenbacher, W. Rundell Inverse Problems No Publisher selected to publication Recovery of multiple coefficients in a reaction-diffusion equation Recovery of multiple coefficients in a reaction-diffusion equation (2019) B. Kaltenbacher, W. Rundell Journal of Mathematical Analysis and Applications No Publisher selected to publication On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs (2018) B. Kaltenbacher, A. Klassen Inverse Problems No Publisher selected to publication Identifying conductivity in electrical impedance tomography with total variation regularization. Identifying conductivity in electrical impedance tomography with total variation regularization. (2017) M. Hinze, B. Kaltenbacher, T. Quyen Numerische Mathematik No Publisher selected to publication Lavrentiev's regularization method in Hilbert spaces revisited Lavrentiev's regularization method in Hilbert spaces revisited (2016) B. Hofmann, B. Kaltenbacher, E. Resmerita Inverse Problems and Imaging (IPI) No Publisher selected to publication Functional error estimators for the adaptive discretization of inverse problems Functional error estimators for the adaptive discretization of inverse problems (2016) C. Clason, B. Kaltenbacher, W. Daniel Inverse Problems No Publisher selected to publication The least error method for sparse solution reconstruction The least error method for sparse solution reconstruction (2016) B. Kristian, B. Kaltenbacher, E. Resmerita Inverse Problems No Publisher selected to publication The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius (2019) B. Kaltenbacher, A. Klassen, M. Previatti de Souza Journal of Inverse and Ill-Posed Problems No Publisher selected to publication Regularization of a backwards parabolic equation by fractional operators Regularization of a backwards parabolic equation by fractional operators (2019) B. Kaltenbacher, W. Rundell Inverse Problems and Imaging (IPI) No Publisher selected to publication On an inverse potential problem for a fractional reaction-diffusion equation On an inverse potential problem for a fractional reaction-diffusion equation (2019) B. Kaltenbacher, W. Rundell Inverse Problems No Publisher selected to publication
Events	No related events
Lectures	Nonlinear acoustic waves: modeling, numerics, optimization Nonlinear acoustic waves: modeling, numerics, optimization B. Kaltenbacher since 05.04.2019 To Lecture Iterative regularization of time-dependent inverse problems Iterative regularization of time-dependent inverse problems B. Kaltenbacher since 10.01.2019 To Lecture Regularization of backwards diffusion by fractional time derivatives Regularization of backwards diffusion by fractional time derivatives B. Kaltenbacher since 09.07.2019 To Lecture All-at-once versus reduced formulations of inverse problems and their regularization All-at-once versus reduced formulations of inverse problems and their regularization B. Kaltenbacher since 12.04.2019 To Lecture Regularization of backwards diffusion by fractional time derivatives Regularization of backwards diffusion by fractional time derivatives B. Kaltenbacher since 25.06.2019 To Lecture Regularization of backwards diffusion by fractional time derivatives Regularization of backwards diffusion by fractional time derivatives B. Kaltenbacher since 02.10.2019 To Lecture Regularization of backwards diffusion by fractional time derivatives Regularization of backwards diffusion by fractional time derivatives B. Kaltenbacher since 29.10.2019 To Lecture Iterative solution methods for all-at-once and reduced formulations of inverse problems Iterative solution methods for all-at-once and reduced formulations of inverse problems B. Kaltenbacher since 08.07.2019 To Lecture Parameter identification in PDEs via box constrained minimization Parameter identification in PDEs via box constrained minimization B. Kaltenbacher since 27.09.2018 To Lecture Mathematics of nonlinear acoustics: modeling, numerics, optimization Mathematics of nonlinear acoustics: modeling, numerics, optimization B. Kaltenbacher since 13.10.2018 To Lecture Integration based profile likelihood calculation for parameter estimation in PDEs Integration based profile likelihood calculation for parameter estimation in PDEs B. Kaltenbacher since 25.07.2018 To Lecture Adaptive discretization of inverse problems based on functional error estimators Adaptive discretization of inverse problems based on functional error estimators B. Kaltenbacher since 28.06.2018 To Lecture Minimization Based Formulation and Regularization of Inverse Problems Minimization Based Formulation and Regularization of Inverse Problems B. Kaltenbacher since 07.02.2018 To Lecture