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

Published New York : Springer, [2013] ©2013

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Description 1 online resource (xiii, 197 pages) Series Springer proceedings in mathematics & statistics ; volume 48 Springer proceedings in mathematics & statistics ; volume 48. Contents 880-01 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 880-01/(S 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 -- 1. Introduction -- 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 -- 1. Introduction -- 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 -- 1. Introduction -- 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 -- 1. Introduction -- 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 -- 1. Introduction -- 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. Introduction -- 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 -- 1. Introduction -- 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 -- 1. Introduction -- 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 -- 1. Introduction -- 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 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 Analysis mathematische natuurkunde mathematical physics wiskunde mathematics analyse analysis Mathematics (General) Wiskunde (algemeen) Bibliography Includes bibliographical references Notes "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 Subject Inverse problems (Differential equations) -- Congresses MATHEMATICS -- Calculus. MATHEMATICS -- Mathematical Analysis. Inverse problems (Differential equations) Genre/Form proceedings (reports) Conference papers and proceedings Conference papers and proceedings. Actes de congrès. Form Electronic book Author Beilina, Larisa, editor Workshop on Inverse Problems (2nd : 2012 : Sunne, Sweden) ISBN 9781461478164 1461478162

Other Titles Select contributions from the first Annual Workshop on Inverse Problems

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