Applied inverse problems select contributions from the first Annual Workshop on Inverse Problems Larisa Beilina, editor

Format:

Book

Conference/Event

Contributor:

Beilina, Larisa, editor.

Conference Name:

Annual Workshop on Inverse Problems (1st : 2011 : Gothenburg, Sweden)

Workshop on Inverse Problems (2nd : 2012 : Sunne, Sweden)

Series:

Springer proceedings in mathematics & statistics volume 48

Language:

English

Subjects (All):

Inverse problems (Differential equations)--Congresses.

Inverse problems (Differential equations).

Mathematics.

Mathematical Physics.

Mathematical Applications in the Physical Sciences.

Analysis.

Local Subjects:

Mathematics.

Mathematical Physics.

Mathematical Applications in the Physical Sciences.

Analysis.

Genre:

proceedings (reports)

Conference papers and proceedings

Physical Description:

1 online resource

Other Title:

Select contributions from the first Annual Workshop on Inverse Problems

Place of Publication:

New York Springer [2013]

System Details:

PDF

text file

Summary:

This proceedings volume is based on papers presented at the First Annual Workshop on Inverse Problems whichwas heldin June 2011 at the Department of Mathematics, Chalmers University of Technology. The purpose of the workshop was to present new analytical developments and numerical methods for solutions of inverse problems. State-of-the-art and future challenges in solving inverse problems for a broad range of applications was also discussed. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area

Contents:

Theoretical and Numerical Study of Iteratively Truncated Newton's Algorithm Anatoly B. Bakushinsky, Alexandra B. Smirnova, and Hui Liu Approximate Global Convergence in Imaging of Land Mines from Backscattered Data Larisa Beilina and Michael V. Klibanov Time-adaptive FEM for Distributed Parameter Identification in Biological Models Larisa Beilina and Irina Gainova Adaptive finite element method in reconstruction of dielectrics from backscattered data Larisa Beilina, Marte P. Hatlo Andresen, Harald E. Krogstad A Posteriori Error Estimates for Fredholm Integral Equations of the First Kind N. Koshev and L. Beilina Inverse Problems in Geomechanics: Diagnostics and Prediction of the State of Rock Masses with Estimating Their Properties Larisa A. Nazarova and Leonid A. Nazarov A Globally Convergent Numerical Method for Coefficient Inverse Problems with Time-Dependent Data Aubrey Rhoden, Natee Patong, Yueming Liu, Jianzhong Su and Hanli Liu Adaptive FEM with relaxation for a hyperbolic coefficient inverse problem Larisa Beilina and Michael V. Klibanov Error Estimation in Ill-posed Problems in Special Cases Anatoly G. Yagola, Yury M. Korolev Stable numerical methods of approaching quantum mechanical molecular force fields to experimental data Gulnara Kuramshina, Igor Kochikov and Anatoly Yagola On the Alternating Method for Cauchy Problems and its Finite Element Discretisation Thouraya N. Baranger B. Tomas Johansson and Romain Rischette

Machine generated contents note: Theoretical and Numerical Study of Iteratively Truncated Newton's Algorithm Hui Liu

1. Introduction

2. Convergence Analysis: Noise-Free Data

3. Stability and Stopping Rule

4. Numerical Experiments References Approximate Global Convergence in Imaging of Land Mines from Backscattered Data Michael V. Klibanov

2. Statements of Forward and Inverse Problems with Backscattered Data

2.1. Statements of Forward and Inverse Problems

2.2. Approximately Globally Convergent Method

2.3. New Model of the Tail Function

2.4. Sequence of Equations with Respect to the Pseudo-Frequency

2.5. Approximate Globally Convergent Algorithm

2.6. Approximate Global Convergence Theorem

3. Imaging of Land Mines with Backscattered Data

3.1. Simplified Mathematical Model of Imaging of Plastic Land Mines

3.2. Numerical Results

3.3. Test1

3.4. Test2 References Time-Adaptive FEM for Distributed Parameter Identification in Biological Models Irina Gainova

2. Forward and Parameter Identification Problems in Biological Models

2.1. Statements of the Forward and Parameter Identification Problems with Applications in Biology

2.2. Tikhonov Functional

2.3. Lagrangian

3. Finite Element Method to Solve Equation (14)

4. A Posteriori Error Estimate for the Lagrangian

5. A Posteriori Error Estimate for the Tikhonov Functional

6. Relaxation Property for the Functional Eα(q)

7. Time-Mesh Refinement Recommendation and the Adaptive Algorithm References Adaptive Finite Element Method in Reconstruction of Dielectrics from Backscattered Data Harald E. Krogstad

2. Forward and Inverse Problems

3. Tikhonov Functional

4. Lagrangian and Its Frechet Derivative

5. Finite Element Method to Solve Equation (23)

6. A Posteriori Error Estimate for the Lagrangian

7. Adaptive Algorithm

7.1. Algorithm

8. Numerical Examples

8.1. Example 1

8.2. Example 2

9. Conclusions References Posteriori Error Estimates for Fredholm Integral Equations of the First Kind L. Beilina

2. Statement of the Problem

3. Finite Element Spaces

4. Finite Element Method

5. Posteriori Error Estimate for the Regularized Solution on Locally Refined Meshes

6. Posteriori Error Estimates for the Functional (44) in DG(1)

7. Posteriori Error Estimate for the Error in the Tikhonov Functional (44)

8. Adaptive Algorithm

9. Numerical Studies of the Adaptivity Technique in Microtomography References Inverse Problems in Geomechanics: Diagnostics and Prediction of the State of Rock Masses with-Estimating Their Properties Leonid A. Nazarov

2. Estimation of Rock Rheological Parameters at the Room-and-Pillar Mining System

3. Determination of Filtration Parameters and Horizontal Stresses in Coal-Rock Mass

4. Determination of Deformation Parameters of Filling Mass Under Stoping References Globally Convergent Numerical Method for Coefficient Inverse Problems with Time-Dependent Data Hanli Liu

1.1. Applications to Diffuse Optical Tomography

2. Mathematical Model

2.1. Nonlinear Integral Differential Equation

2.2. Mathematical Model of the Tail

2.3. Layer Stripping with Respect to the Frequency

2.4. Convergence

3. Numerical Methods

4. Numerical Implementations and Results

4.1. Domains

4.2. Numerical Results for Optical Tomography

5. Conclusions and Discussion References Adaptive FEM with Relaxation for a Hyperbolic Coefficient Inverse Problem Michael V. Klibanov

2. Space of Finite Elements

3. Relaxation Property for a Coefficient Inverse Problem

3.1. Coefficient Inverse Problem and Tikhonov Functional

3.2. Relaxation Property for the Functional Eα(c)

4. Mesh Refinement Recommendations

5. Adaptive Algorithm

6. Numerical Studies

6.1. Computations of Forward Problem

6.2. Results of Reconstruction Using the Approximately Globally Convergent Algorithm. Test 1

6.3. Synthesis of the Globally Convergent Algorithm with the Adaptivity. Test 2 References Error Estimation in III-Posed Problems in Special Cases Yury M. Korolev

1. Well-Posed and Ill-Posed Problems. Regularizing Algorithms

2. Priori and A Posteriori Error Estimates

2.1. Error Estimation on Compact Sets

2.2. Inverse Problems in Banach Lattices

2.3. Error Estimation for Source-wise Represented Solutions

2.4. Leonov's Scheme of A Posteriori Error Estimation

3. Conclusion References Stable Numerical Methods of Approaching Quantum Mechanical Molecular Force Fields to Experimental Data Anatoly Yagola

2. Experimental Sources of Information

3. Mathematical Formulation of the Inverse Vibrational Problem

4. Regularizing Algorithms for Solving the Inverse Vibrational Problem

5. Use of Ab Initio F0 as Tikhonov Stabilizer

6. Computer Implementation

7. Example: Predicting Vibrational Spectra of Large Molecules References On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation Romain Rischette

2. Notation and Function Spaces

3. Gap Functional and Some of Its Properties

3.1. Gap Functional

3.2. Euler-Lagrange Condition for the Functional (5)

4. Alternating Method

5. Finite Element Discretisation and Error Estimates

5.1. Finite Element Discretisation

6. Numerical Examples

7. Conclusion

Notes:

Includes bibliographical references

"In this volume articles related to the First Annual Workshop on Inverse Problems as well as to the Second Annual Workshop on Inverse Problems organized within the project "Adaptive Finite Element Methods for Solution of Inverse Problems" are collected"--Page v.

Print version record

Other Format:

Print version Applied inverse problems

ISBN:

9781461478164

1461478162

OCLC:

858626197

Access Restriction:

Restricted for use by site license