Current events
2013-11-04 - 2013-11-12
A. Yagola will give a special course at the Department of Mathematical Sciences at Chalmers University of Technology and GU, Introduction to the theory, numerical methods and applications of ill-posed problems.
2013-11-04 - 2013-11-12
G. Kuramshina will give a special course at the Department of Mathematical Sciences at Chalmers University of Technology and GU, Inverse problems of vibrational spectroscopy.
Past Events
2013-08-01 - 2013-08-31
Participants of the project G.Kuramshina, A. Yagola and A. Bakushinskiy visited the Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
2013-03-05
Vladimir Sharafutdinov, Local audibility of a hyperbolic metric The Spectral Analysis seminar, Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
Abstract:
The subject of the talk relates to the famous question by M. Cac: can one hear the shape of a drum? In particular, to which extent is a compact Riemannian manifold (M,g) determined by the eigenvalue
spectrum of the Laplacian Delta_g? A Riemannian manifold (M,g) is said to be locally audible if the following statement holds for every metric g' on M which is sufficiently close to g: if the Laplacians Delta_g and Delta_g' are isospectral, then the metrics are isometric. We prove local audibility of a compact locally symmetric Riemannian manifold of negative sectional curvature. Alongwise with the proof, I will try to give you some flavour of spetral geometry. In particular, I will discuss how the spectrum of the Laplacian relates to lengths of closed geodesics and how heat invariants can be used for proving the pre-compactness of an isospectral family of metrics.
2013-03-06
Vladimir Sharafutdinov, The linearized problem of magneto-photoelasticity,
CAM seminar, Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University
Abstract:
The idea of using the Faraday rotation in photoelasticity was proposed by Aben in 1970. He introduced the term "magneto-photoelasticity". The idea remained to be a hypothetic method till the last decade. Recently, a measurement instruments were designed which combined an optical polariscope and solenoidal coils. The mathematical nature of the problem is still not well understood. Moreover, the mathematical foundation of general photoelasticity, as presented in Aben's book, is also not quite irreproachable mathematically. The resulting equations are okey, but some arguments used in their derivation seem to be not quite correct. As many good engineers before him, Aben rather divines equations than derives them.
In the first part of our talk, we use the quasi-isotropic approximation of geometric optics for deriving the equations of magneto-photoelasticity in the case of a nonhomogeneous background medium and of a variable exterior magnetic field. Our arguments are as rigorous mathematically as geometric optics is. We actually demonstrate that equations of magneto-photoelasticity coincide with the Rytov law for quasi-isotropic gyrotropic media. In the case of a homogeneous background medium and of a constant exterior magnetic field our equations coincide with Aben's ones.
In the general case, the solution to Aben's equations depends on equation coefficients in a very complicated way. To simplify the analysis of the solution, we assume the variable coefficients to be sufficiently small such that higher order terms can be ignored. We derive an explicit linearized formula for the solution to Aben's equations.
Finally, we consider the inverse problem of recovering the medium anisotropy (stresses in particular) from the results of polarization measurements that are known for several values of the intensity of the exterior magnetic field.
The linearized version of the problem turns out to be very easy in virtue of our explicit formula. Actually, if values of the intensity of the exterior magnetic field are chosen in an appropriate way, the measurements give us Fourier coefficients of sought functions.
2013-03-03 - 2013-03-06
Vladimir Sharafutdinov, Sobolev Institute of Mathematics, Novosibirsk, Russia, visited Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
2013-01-30
Anatoly Yagola, Piecewise convex approximation of solutions of ill-posed problems,
CAM seminar, Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University
Abstract:
In this presentation we propose to solve ill-posed problems on compact sets of piecewise convex-concave functions using so called inflection points method. The method gives a possibility to calculate a posteriori error estimates of the approximate solution. We discuss the determination of the aerosol particle size distribution function using the particle spectrum extinction equation. This is an ill-posed integral equation of the first kind. Using a priori information, we apply the inflection points regularization method and develop a conjugate gradient projection method for solving the corresponding optimization problem. The regularization parameter can be considered as the number of inflection points and their positions. Algorithms for constructing an approximate solution are described. Error estimates are also presented. Our numerical tests are given to show the efficiency and feasibility of the proposed algorithm.
2013-01-26 - 2013.02.02.
Participants of the project G.Kuramshina and A. Yagola visited the Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
2013-01-09
Larisa Beilina, Approximate Global Convergence and Adaptive Finite Element Method in imaging of buried targets.
CAM seminar, Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University
Abstract:
We will present new model of an approximately globally convergent numerical method and adaptive finite element method applied to the solution of a Coefficient Inverse Problem for a hyperbolic equation. We consider the data which are generated by either a single location of the point source or by a single direction of the incident plane wave. This is special case of interest in military applications or airport security.
We will present two-stage numerical procedure: on the first stage we apply an approximate globally convergent algorithm, which rigorous guarantee of obtaining at least one point in a small neighborhood of the exact solution without any advanced knowledge of that neighborhood. On the second stage this approximation is taken as the starting point for iterations of a locally convergent adaptive finite element method.
We will present results of reconstruction using simulated and experimental data in 2d and 3d including the one for imaging of explosives hidden in belts worn by humans.
2012-12-01 - 2013.02.01.
Participant of the project Irina Gaynova visited the Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
2012-05-02 - 2012-05-06 Second Annual Workshop on Inverse Problems at Selma Spa+.
This worksop is continuation of a series of workshops on Inverse problems supported by the Swedish Institute, Visby Program.
First annual workshop on Inverse Problems within the Visby Program was held at 02.06-03.06. 2011 at the Department of Mathematics, Chalmers University of Technology and Gothenburg University, Gothenburg, Sweden.
2011-?-26 - 2012-02-26 Participant of the project Irina Gaynova visited the Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
Wednesday December 7, 13.15-14.15, room MV:L14
Presentation:Valeriy Gubatenko, Department of Geophysics, Saratov State University
"The setting of the inverse problem of electrical prospecting"
Abstract:. It is shown how the classical formulation of the inverse problem of electromagnetic sounding for sufficiently smooth frequency dispersion of electrical conductivity and magnetic permeability can be reduced to finding the electric field intensity in a geological medium. The problem of uniqueness of the solution of this problem was investigated. Nonuniqueness of finding the frequency-dispersed conductivity in the one-dimensional magnetotelluric sounding is illustrated by an example.
2011-12-03 - 2011-12-13
Participant of the project Professor Valeriy Gubatenko visited the Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University.
2011-12-01 - 2012-02-01
Participant of the project Vladimir Timonov visited the Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
2011-11-24
Larisa Beilina is visitting Department of Mathematics, KTH. Presentation
Abstract: In this talk we will summarize results of our research group during 2007-2011 on the approximate globally convergent numerical method with combination of the adaptivity technique for solution of hyperbolic coefficient inverse problems, which we call two-stage numerical procedure. We will also briefly discuss the framework of the functional analysis for the adaptivity technique. At the end of the talk we will present verification of the two-stage numerical procedure on the experimental data.
2011-09-27 - 2011-09-29
Conference "Inverse Problems and Applications" at Centre de Mathématiques Appliquées, École Polytechnique (Palaiseau)
Presentation:
L. BEILINA, Chalmers University of Technology and Gothenburg University.
Title: Approximate globally convergent numerical method and adaptivity technique for inverse problems with experimental data.
Abstract: In this talk we will summarize results of our research group during 2007- 2011 on the approximate globally convergent numerical method with combination of the adaptivity technique for solution of hyperbolic coefficient inverse problems , which we call two-stage numerical procedure. We will also briefly discuss the framework of the functional analysis for the adaptivity technique. At the end of the talk we will present verification of the two-stage numerical procedure on the experimental data.
Fall Semester 2011
Course at the Department of Mathematical Sciences: Electromagnetic Fields and Waves: mathematical models and numerical methods
2011-07-01 - 2011-08-01
Participants of the project Professor Anatolii Yagola and Gulnara Kuramshina visited the Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University
2011-06-02 - 2011-06-03
Annual Workshop on Inverse Problems
Department of Mathematics, Chalmers University of Technology and GU
2011-06-01 - 2011-09-01 Participant of the project Professor Anatolii Bakushinskij visited the Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University.
2011-05-01 - 2011-09-01
Participant of the project Senior Researcher Irina Gainova visited the Department of Mathematical Sciences, Chalmers University of Technology and Gotheburg University.
2011-04-27 Mini-workshop on Inverse Problems at Moscow State University, Russia, consisting of 2 talks:
L.Beilina, Approximate global convergence and adaptivity forsolutions of inverse problems.
M.V. Klibanov, Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattered data.
2011-03-01 - 2011-10-01 Participant of the project PhD student Nikolay Koshev visited the Department of Mathematical Sciences, Chalmers University of Technology and Gotheburg University
2011-02-10
d'Alambert seminar at UPMC, Paris 6, France.
L.Beilina, Chalmers University of Technology and Gothenburg University, Sweden
Globally convergent numerical method with adaptivity for inverse problems with experimental data.
Abstract:In this talk we will summarize results of our research group during 2007- 2010 on the globally convergent numerical method and adaptivity technique for solution of inverse problems - two-stage numerical procedure. We will also briefly discuss the framework of the functional analysis for the adaptivity technique. At the end of the talk we will present verification of the two-stage numerical procedure on the experimental data.
2011-02-07- 2011-02-13
Research visits to UPMC, Paris 6, Ecole Polytechnique, University de Cergy-Pointoise
2010-10-27- 2010-11-04
Participant of the project Prof.Roman Novikov visited Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
2010-10-30
Spectral and computational methods for Maxwell's equations
2010-09-18
Session Recent advances in numerical methods for inverse problems resolution.