Identification problems with given material interfaces

Haslinger, Jaroslav; Blaheta, Radim; Hrtus, Rostislav

doi:10.1016/j.cam.2016.06.023

Cited by 9 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where w > 0 are suitable weights. The same approach has been used to a closely related problem in [6]. In the rest of the paper we assume w = 1, = 1, ..., L.…”

Section: Numerical Realizationmentioning

confidence: 99%

Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals

Haslinger

Blaheta

Mäkinen

2021

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

“…where w > 0 are suitable weights. The same approach has been used to a closely related problem in [6]. In the rest of the paper we assume w = 1, = 1, ..., L.…”

Section: Numerical Realizationmentioning

confidence: 99%

Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals

Haslinger

Blaheta

Mäkinen

2021

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

“…where R E i ((E, ν), w) = I (K 1 (E)) E i w + (K 3 ((E, ν), w)) E i w, This, together with (41), defines the components of the gradient J with respect to E and ν. For detailed information we refer to [9,21]. axial load, we computed the values of deflection of the beam at the given points and to these values we added the white noise from standard normal distribution.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…For this purpose, an optimal control approach can be used. The similar idea for the identification of coefficients in scalar elliptical differential equations was used in [9], where a steady state groundwater flow problem was considered as a numerical example and a coefficient of hydraulic conductivity was identified.…”

Section: Introductionmentioning

confidence: 99%

Identification Problem for Nonlinear Gao Beam

2020

View full text Add to dashboard Cite

This paper deals with the identification of coefficients in the nonlinear beam model which was first introduced by D. Y. Gao in 1996. For the identification of coefficients, an optimal control approach is used. The unknown coefficients are material parameters of the beam and play the role of the control variables. The existence of at least one solution of the optimal control problem is proved. For the studied problem the finite element approximation is provided. Finally some illustrative examples are introduced.

show abstract

“…We concentrate here on the data for the flow model, as we consider these data most uncertain and hardly predictable. The determination of hydraulic conductivity is not easy even for heterogeneous porous materials without fractures, see, e.g., [3,19]. Moreover, the use of deterministic inverse model parameter identification methods is difficult as a noise in the observed data disturbs the identification and/or excludes to get reasonable result without regularization.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inversion for steady flow in fractured porous media with contact on fractures and hydro-mechanical coupling

et al. 2020

Self Cite

View full text Add to dashboard Cite

The paper is motivated by a strong interest in numerical analysis of flow in fractured porous media, e.g., rocks in geoengineering applications. It follows the conception of porous media as a continuum with fractures which are represented as lower dimensional objects. In the paper, the finite element discretization of the flow in coupled continuum and fractures is used; fluid pressures serve as the basic unknowns. In many applications, the flow is connected with deformations of the porous matrix; therefore, the hydro-mechanical coupling is also considered. The fluid pressure is transferred to the mechanical load in both pores and fractures and the considered mechanical model involves elastic deformations of the porous matrix and opening/closing of the fractures with the non-penetration constraint. The mechanical model with this constraint is implemented via the technique of the Lagrange multipliers, duality formulation, and combination with a suitable domain decomposition method. There is usually lack of information about problem parameters and they undergo many uncertainties coming e.g. from the heterogeneity of rock formations and complicated realization of experiments for parameter identification. These experiments rarely provide some of the asked parameters directly but require solving inverse problems. The stochastic (Bayesian) inversion is natural due to the mentioned uncertainties. In this paper, the implementation of the Bayesian inversion is realized via Metropolis-Hastings Markov chain Monte Carlo approach. For the reduction of computational demands, the sampling procedure uses the delayed acceptance of samples based on a surrogate model which is constructed during a preliminary sampling process. The developed hydro-mechanical model and the implemented Bayesian inversion are tested on two types of model inverse problems. KeywordsPorous media with fractures • Coupled hydro-mechanics • Bayesian inversion • Multi-dimensional flow model • Contact mechanics on fractures Mathematics Subject Classification (2010) 86-08 • 82-08 • 65N21 • 65C60 • 60-0 • 74G15

show abstract

Identification problems with given material interfaces

Cited by 9 publications

References 8 publications

Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals

Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals

Identification Problem for Nonlinear Gao Beam

Bayesian inversion for steady flow in fractured porous media with contact on fractures and hydro-mechanical coupling

Contact Info

Product

Resources

About