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A comparison of deterministic and Bayesian inverse with application in micromechanics

Radim Blaheta, Michal Béreš, Simona Domesová, Pengzhi Pan (2018)

Applications of Mathematics

The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities...

A modified quasi-boundary value method for the backward time-fractional diffusion problem

Ting Wei, Jun-Gang Wang (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an a priori regularization parameter...

A symbolic algorithm for the approximate solution of an inverse problem for liner kinetic equation.

Yildiz, Mustafa (2009)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

An alternative method for solving direct and inverse Stokes problems.

Curteanu, Anca E., Elliott, Lionel, Ingham, Derek B., Lesnic, Daniel (2005)

Acta Universitatis Apulensis. Mathematics - Informatics

An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in Lp-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov...