Page 1 Next

Displaying 1 – 20 of 27

Showing per page

A Numerical Approach of the sentinel method for distributed parameter systems

Aboubakari Traore, Benjamin Mampassi, Bisso Saley (2007)

Open Mathematics

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.

An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations

Larisa Beilina, Samar Hosseinzadegan (2016)

Applications of Mathematics

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments...

Computational approaches to some inverse problems from engineering practice

Vala, Jiří (2015)

Programs and Algorithms of Numerical Mathematics

Development of engineering structures and technologies frequently works with advanced materials, whose properties, because of their complicated microstructure, cannot be predicted from experience, unlike traditional materials. The quality of computational modelling of relevant physical processes, based mostly on the principles of classical thermomechanics, is conditioned by the reliability of constitutive relations, coming from simplified experiments. The paper demonstrates some possibilities of...

Global superconvergence of finite element methods for parabolic inverse problems

Hossein Azari, Shu Hua Zhang (2009)

Applications of Mathematics

In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.

Heating source localization in a reduced time

Sara Beddiaf, Laurent Autrique, Laetitia Perez, Jean-Claude Jolly (2016)

International Journal of Applied Mathematics and Computer Science

Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this...

Numerical treatment of a time dependent inverse problem in photon transport

S. Pieraccini, R. Riganti, A. Belleni-Morante (2005)

Bollettino dell'Unione Matematica Italiana

The time-dependent intensity of a UV-photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.

On the optimization of initial conditions for a model parameter estimation

Matonoha, Ctirad, Papáček, Štěpán, Kindermann, Stefan (2017)

Programs and Algorithms of Numerical Mathematics

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence...

On the solution of inverse problems for generalized oxygen consumption

Denis Constales, Jozef Kačur (2001)

Applications of Mathematics

We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.

Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates

Marián Slodička (2003)

Applications of Mathematics

In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain Ω N , with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant α ( t ) , accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution u and...

Solvability and numerical algorithms for a class of variational data assimilation problems

Guri Marchuk, Victor Shutyaev (2002)

ESAIM: Control, Optimisation and Calculus of Variations

A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.

Solvability and numerical algorithms for a class of variational data assimilation problems

Guri Marchuk, Victor Shutyaev (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.

Static hedging of barrier options with a smile : an inverse problem

Claude Bardos, Raphaël Douady, Andrei Fursikov (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Let L be a parabolic second order differential operator on the domain Π ¯ = 0 , T × . Given a function u ^ : R and x ^ > 0 such that the support of u ^ is contained in ( - , - x ^ ] , we let y ^ : Π ¯ be the solution to the equation: L y ^ = 0 , y ^ | { 0 } × = u ^ . Given positive bounds 0 < x 0 < x 1 , we seek a function u with support in x 0 , x 1 such that the corresponding solution y satisfies: y ( t , 0 ) = y ^ ( t , 0 ) t 0 , T . We prove in this article that, under some regularity conditions on the coefficients of L , continuous solutions are unique and dense in the sense that y ^ | [ 0 , T ] × { 0 } can be C 0 -approximated, but an exact solution does not...

Currently displaying 1 – 20 of 27

Page 1 Next