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Feng, Tao
Publications (9 of 9) Show all publications
Feng, T., Gulliksson, M. & Liu, W. (2009). Adaptive finite element methods for parameter estimation problems in linear elasticity. International Journal of Numerical Analysis & Modeling, 6(1), 17-32
Open this publication in new window or tab >>Adaptive finite element methods for parameter estimation problems in linear elasticity
2009 (English)In: International Journal of Numerical Analysis & Modeling, ISSN 1705-5105, Vol. 6, no 1, p. 17-32Article in journal (Refereed) Published
Abstract [en]

In this paper, the Lame coefficients in the linear elasticity problem are estimated by using the measurements of displacement. Some a posteriori error estimators for the approximation error of the parameters are derived, and then adaptive finite element schemes are developed for the discretization of the parameter estimation problem, based on the error estimators. The Gauss-Newton method is employed to solve the discretized nonlinear least-squares problem. Some numerical results are presented.

Keywords
finite element methods, inverse problems, paramater estimation
National Category
Mathematics Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-8788 (URN)000264008000002 ()2-s2.0-62749179686 (Scopus ID)
Available from: 2009-04-15 Created: 2009-04-15 Last updated: 2017-12-13Bibliographically approved
Feng, T., Yan, N. & Liu, W. (2008). Adaptive finite element methods for the identification of distributed parameters in elliptic equation. Advances in Computational Mathematics, 29(1), 27-53
Open this publication in new window or tab >>Adaptive finite element methods for the identification of distributed parameters in elliptic equation
2008 (English)In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 29, no 1, p. 27-53Article in journal (Refereed) Published
Abstract [en]

In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments

Keywords
Parameter identification - Finite element approximation - Adaptive finite element methods - Least-squares - Gauss–Newton
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-3422 (URN)10.1007/s10444-007-9035-6 (DOI)3407 (Local ID)3407 (Archive number)3407 (OAI)
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2017-12-12Bibliographically approved
Feng, T., Gulliksson, M. & Liu, W. (2007). A Posteriori Error Estimators of Recovery Type for Parameter Estimation Problem in Linear Elastic Problem. In: Free and Moving Boundaries: Analysis, Simulation and Control (pp. 395-410). Boca Raton: CRC Press
Open this publication in new window or tab >>A Posteriori Error Estimators of Recovery Type for Parameter Estimation Problem in Linear Elastic Problem
2007 (English)In: Free and Moving Boundaries: Analysis, Simulation and Control, Boca Raton: CRC Press, 2007, p. 395-410Chapter in book (Other academic)
Place, publisher, year, edition, pages
Boca Raton: CRC Press, 2007
Series
Lecture notes in pure and applied mathematics ; 252
Keywords
finite element, parameter estimation
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-3421 (URN)3406 (Local ID)9781584886068 (ISBN)3406 (Archive number)3406 (OAI)
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-12-22Bibliographically approved
Feng, T., Edström, P. & Gulliksson, M. (2007). Levenberg-Marquardt Methods for Parameter Estimation Problems in the Radiative Transfer Equation. Inverse Problems, 23(3), 879-891, Article ID 002.
Open this publication in new window or tab >>Levenberg-Marquardt Methods for Parameter Estimation Problems in the Radiative Transfer Equation
2007 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 23, no 3, p. 879-891, article id 002Article in journal (Refereed) Published
Abstract [en]

A discrete ordinate method is developed for solving the radiative transfer equation, and the corresponding parameter estimation problem is given a least-squares formulation. Two Levenberg-Marquardt methods, a feasible-path approach and an SQP type method, are analyzed and compared. A sensitivity analysis is given, and it is shown how it can be used for designing measurements with minimal impact of measurement noise. Numerical experiments are performed to exemplify the usefulness of the theory.

Keywords
Radiative transfer, parameter estimation
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-4111 (URN)10.1088/0266-5611/23/3/002 (DOI)000246789100002 ()2-s2.0-34249701208 (Scopus ID)4718 (Local ID)4718 (Archive number)4718 (OAI)
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2017-12-12Bibliographically approved
Feng, T., Gulliksson, M. & Liu, W. (2006). Adaptive finite element methods for the identification of elastic constants. Journal of Scientific Computing, 26(2), 217-235
Open this publication in new window or tab >>Adaptive finite element methods for the identification of elastic constants
2006 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 26, no 2, p. 217-235Article in journal (Refereed) Published
Abstract [en]

In this paper, the elastic constants of a material are recovered from measured displacements where the model is the equilibrium equations for the orthotropic case. The finite element method is used for the discretization of the state equation and the Gauss–Newton method is used to solve the nonlinear least squares problem attained from the parameter estimation problem. A posteriori error estimators are derived and used to improve the accuracy by an appropriate mesh refinement. A numerical experiment is presented to show the applicability of the approach.

Keywords
Parameter estimation, finite element approximation, adaptive finite element methods, least squares, Gauss–Newton
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-3242 (URN)10.1007/s10915-004-4935-9 (DOI)000235445800004 ()2-s2.0-32944461738 (Scopus ID)3196 (Local ID)3196 (Archive number)3196 (OAI)
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2017-12-12Bibliographically approved
Feng, T. (2005). Adaptive finite element methods for parameter estimation problems in partial differential equations. (Doctoral dissertation). Sundsvall: Mittuniversitetet
Open this publication in new window or tab >>Adaptive finite element methods for parameter estimation problems in partial differential equations
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Physical and chemical phenomena are often described by a system of partial di®erential equations. These equations usually involve unknown parameters, which cannot be measured directly but which can be adjusted to make the model predictions match the observed data. The process of ¯tting these para- meters to laboratory or plant data is called parameter estimation. In order to recover these parameters, the well-known output least squares formulation is of- ten utilized. To solve the optimization problem governed by partial di®erential equations, the in¯nite-dimensional problem must be approximated by introduc- ing discretizations such as a ¯nite elements or di®erences. It is clear that the e±ciency of the numerical methods dealt with here will be in°uenced by the discretization scheme. The goal of this thesis is to develop e±cient numerical methods for the parameter estimation problems governed by partial di®erential equations, based on adaptive ¯nite element methods. This work was initiated by an investigation into an a posteriori error esti- mator of residual type for parameter estimation problems with a ¯nite number of unknown parameters. It appears that an adaptive ¯nite element algorithm guided by the derived a posteriori error estimator produces a sequence of eco- nomical, locally re¯ned meshes. The methods are then applied to the identi¯ca- tion of elastic constants in paper from measured displacements. Further, some a posteriori error estimators of gradient recovery type are derived for the error in parameters due to the discretization. The main advantages of using error estimators of this type are the simplicity of their implementation and their cost e®ectiveness. Often, the unknown parameters are functions, which also need to be dis- cretized. Adaptive ¯nite element method is developed for the estimation of distributed parameters in elliptic equations with multi-mesh techniques. Finally, a goal-oriented adaptive method, dual weighted residual methods (DWR methods) are employed determining the elastic constants in paper from measured displacements.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2005. p. 30
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 4
Keywords
parameter estimation, ¯nite element approximation, adaptive ¯nite element methods, a posteriori error estimates, least squares.
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-8866 (URN)
Public defence
2005-10-22, 00:00 (English)
Available from: 2009-05-06 Created: 2009-05-06 Last updated: 2009-09-21Bibliographically approved
Feng, T. (2002). Mixed Finite Elements Methods with Finite Difference Streamline-Diffusion Method for Miscible Displacement in Porous Media. Journal of Shandong University. Natural Science. Shandong Daxue Xuebao. Lixue Ban, 37(5), 391-395
Open this publication in new window or tab >>Mixed Finite Elements Methods with Finite Difference Streamline-Diffusion Method for Miscible Displacement in Porous Media
2002 (English)In: Journal of Shandong University. Natural Science. Shandong Daxue Xuebao. Lixue Ban, ISSN 1671-9352, Vol. 37, no 5, p. 391-395Article in journal (Refereed) Published
Keywords
Mixed Finite Elements Methods, Streamline-Diffusion
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-3241 (URN)3195 (Local ID)3195 (Archive number)3195 (OAI)
Available from: 2008-09-30 Created: 2008-09-30Bibliographically approved
Vexler, B., Feng, T. & Gulliksson, M.Adaptive finite element methods for determining the elastic constants of paper from measured displacements.
Open this publication in new window or tab >>Adaptive finite element methods for determining the elastic constants of paper from measured displacements
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-9368 (URN)
Available from: 2009-07-13 Created: 2009-07-13 Last updated: 2010-01-14Bibliographically approved
Feng, T., Gulliksson, M. & Liu, W. Mesh Adaptation and Optimal Design of the Measurement Points for Parameter Estimation Problem.
Open this publication in new window or tab >>Mesh Adaptation and Optimal Design of the Measurement Points for Parameter Estimation Problem
(English)Manuscript (Other academic)
Keywords
Parameter Estimation, Inverse Problems, Optimal Design, Optimization
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-6349 (URN)4407 (Local ID)4407 (Archive number)4407 (OAI)
Available from: 2009-02-18 Created: 2009-02-18 Last updated: 2010-01-14Bibliographically approved
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