Experimental design for outflow experiments based on a multi-level identification method for material laws

Inverse Problems

Volumn 19, Issue 5, 2003, Pages 1011-1030

  Bitterlich, Sandro ^a   Knabner, Peter ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS; PROBLEM SOLVING;

MATERIAL LAWS;

INVERSE PROBLEMS;

EID: 0142030494     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/19/5/302     Document Type: Article

References (25)

1. Bandemer H and Bellmann A 1979 Statistische Versuchsplanung (Leipzig: Teubner)
2. Bitterlich S and Knabner P 2001 Formfree and cascadic identification of material laws in (un)saturated fluid flow from column experiments Z. Angew. Math. Mech. 81 (suppl. 1) 13
3. Bitterlich S and Knabner P 2002 An efficient method for solving an inverse problem for the Richards equation J. Comput. Appl. Math. 147 153
4. Chavent G, Zhang J and Chardaire-Riviere C 1994 Estimation of mobilities and capillary pressure from centrifuge experiments Inverse Problems in Engineering Mechanics ed H D Bui, M Tanaka, M Bonnet, H Maigre, E Luzzato and M Reynier (Rotterdam: Balkema) p 265
5. Cramér H 1966 Mathematical Methods of Statistics (Princeton, NJ: Princeton University Press)
6. DuChateau P 1997 An inverse problem for the hydraulic properties of porous media SIAM J. Math. Anal. 28 611
7. Durner W and Zurmühl T 1998 Determination of parameters for bimodal hydraulic functions by inverse modeling Soil Sci. Soc. Am. J. 62 874
8. Durner W, Priesack E, Vogel H-J and Zurmühl T 1999a Determination of parameters for flexible hydraulic functions by inverse modeling Proc. Int. Workshop on Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media ed M Th van Genuchten, F J Leij and L Wu (Riverside, CA: University of California Press) p 817
9. Durner W, Schultze B and Zurmühl T 1999b State-of-the-art in inverse modeling of inflow/outflow experiments Proc. Int. Workshop on Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media ed M Th van Genuchten, F J Leij and L Wu (Riverside, CA: University of California Press) p 661
10. Gribb M M 1996 Parameter estimation for determining hydraulic properties of a fine sand from transient flow measurements Water Resour. Res. 32 1965
11. Hanke M, Neubauer A and Scherzer O 1995 A convergence analysis of the Landweber iteration for nonlinear ill-posed problems Numer. Math. 72 21
12. Hansen P C 2001 The L-curve and its use in the numerical treatment of inverse problems Computational Inverse Problems in Electrocardiology ed P Johnston (Southampton: WIT Press) p 119
13. Igler B A 1998 Identification of nonlinear coefficient functions in reactive transport through porous media PhD Thesis University of Erlangen-Nuremberg
14. Igler B A and Knabner P 2000 Structural Identification of Nonlinear Coefficient Functions in Transport Processes through Porous Media (Springer Lectures on Applied Mathematics) (Berlin: Springer) p 157
15. Isakov V 1998 Inverse Problems for Partial Differential Equations (Berlin: Springer)
16. Katayama K and Narihisa H 2001 Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem Eur. J. Oper. Res. 134 103
17. Kirkpatrick S, Gelatt C D Jr and Vecchi M P 1983 Optimization by simulated annealing Science 220 671
18. Kuhn H 1992 Heuristische Suchverfahren mit simulierter Abkühlung Wirtschaftswissenschaftliches Studium 8 387
19. Louis A K 1989 Inverse und schlecht gestellte Probleme (Stuttgart: Teubner)
20. Scherzer O 1998 An iterative multi level algorithm for solving nonlinear ill-posed problems Numer. Math. 80 579
21. Schittkowski K 1988 Solving constrained nonlinear least squares problems by a general purpose sqp-method Trends in Mathematical Optimization vol 83, ed K-H Hoffmann, J-B Hiriart-Urruty, C Lemarechal and J Zowe (Basle: Birkhäuser)
22. Schneid E 2000 Hybrid-gemischte finite-elemente-diskretisierung der Richards-Gleichung PhD Thesis University of Erlangen-Nuremberg
23. Tarantola A 1987 Inverse Problem Theory (Amsterdam: Elsevier)
24. van Genuchten M Th 1980 A closed-form equation for predicting the hydraulic conductivity of unsaturated soils Soil Sci. Soc. Am. J. 44 892
25. Vogel C R 1996 Non-convergence of the L-curve regularization parameter selection method Inverse Problems 12 535