Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem

Rodrigues, F. A.; Orlande, Helcio R. B.; Dulikravich, George S.

doi:10.1016/j.matcom.2004.02.005

Cited by 33 publications

(22 citation statements)

References 21 publications

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“…The superscript q in equation (5) denotes the iteration number where a restarting strategy is applied to the iterative procedure of the conjugate gradient method. Different versions of the conjugate gradient method can be found in the literature depending on the form used for the computation of the direction of descent given by equation (5) [3][4][5][19][20][21][22].…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…Powell [19] suggested the following expressions for the conjugation coefficients, which gives the so-called Powell-Beale's version of the conjugate gradient method [19][20][21][22]:…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…Restarting is performed by making k ¼ 0 in equation (5). For more details on the restarting strategy see references [19][20][21][22].…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…The effects of the use of temperature and moisture content measurements on the inverse analysis are examined, by using simulated measured data with random errors. In addition, different versions of the conjugate gradient method are compared, as applied to the solution of the present inverse problem [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous estimation of the spacewise and timewise variations of mass and heat transfer coefficients in drying

Saker

Orlande

Huang

et al. 2006

Inverse Problems in Science and Engineering

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In this article, the conjugate gradient method with adjoint problem is applied for the identification of the heat and mass transfer coefficients at the surface of drying capillary-porous bodies. The unknown functions are supposed to vary in time and along the surface open to the surrounding environment. The inverse problem is solved by considering either the heat or the mass transfer coefficients as unknown, as well as by considering simultaneously both functions as unknown. The effects of temperature and moisture content measurements on the inverse analysis are examined. A comparison of different versions of the conjugate gradient method is also presented as applied to the inverse problem under study.

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Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…Powell [19] suggested the following expressions for the conjugation coefficients, which gives the so-called Powell-Beale's version of the conjugate gradient method [19][20][21][22]:…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…Restarting is performed by making k ¼ 0 in equation (5). For more details on the restarting strategy see references [19][20][21][22].…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simultaneous estimation of the spacewise and timewise variations of mass and heat transfer coefficients in drying

Saker

Orlande

Huang

et al. 2006

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

show abstract

“…There is an extensive literature about inverse method, namely about inverse heat transfer (Beck, Blackwell, & St. Clair, 1985;Lin, Chen, & Yang, 2004;Rodrigues, Orlande, & Dulikravich, 2004;Zueco, Alhama, & González Fernández, 2004). The objective of the present paper is double.…”

Section: Introductionmentioning

confidence: 96%

Model-free estimation of mass fluxes based on concentration profiles. I. Presentation of the method and of a sensitivity analysis

Lucas¹,

Bohuon

2005

Journal of Food Engineering

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A three‐dimensional numerical internal tidal model involving adjoint method

Chen

Miao

2011

Numerical Methods in Fluids

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SUMMARY A three‐dimensional internal tidal model involving the adjoint method is constructed based on the nonlinear, time‐dependent, free‐surface hydrodynamic equations in spherical coordinates horizontally, and isopycnic coordinates vertically, subject to the hydrostatic approximations. This model consists of two submodels: the forward model is used for the simulation of internal tides, while the adjoint model is used for optimization of modal parameters. Mode splitting technique is employed in both forward and adjoint models. In this model, the adjoint method is employed to estimate model parameters by assimilating the interior observations. As a preliminary feasibility study, a set of ideal experiments with the model‐generated pseudo‐observations of surface currents are performed to invert the open boundary conditions (OBCs). In the ideal experiments, 14 kinds of bottom topographies and six kinds of predetermined distributions of OBCs are considered to examine their influence on experiment results. The inversion obtained satisfying results and all the predetermined distributions were successfully inverted. Analysis of results suggests the following: in the case where the spatial variation of the OBC distribution is great or the open boundary is close to a rough topography, the results will be comparatively poor, but still satisfactory; both the tidal elevations and currents can be simulated very accurately with the surface currents at several observation points; the assimilation precision could be reliable and able to reflect both of the inversion and simulation results in the whole field. The performance and results of ideal experiments give a preliminary indication that the construction of this model is successful. Copyright © 2011 John Wiley & Sons, Ltd.

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Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem

Cited by 33 publications

References 21 publications

Simultaneous estimation of the spacewise and timewise variations of mass and heat transfer coefficients in drying

Simultaneous estimation of the spacewise and timewise variations of mass and heat transfer coefficients in drying

Model-free estimation of mass fluxes based on concentration profiles. I. Presentation of the method and of a sensitivity analysis

A three‐dimensional numerical internal tidal model involving adjoint method

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