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Engineering with Computers
Erschienen in: Engineering with Computers 3/2018

25.11.2017 | Original Article

Numerical techniques for solving system of nonlinear inverse problem

verfasst von: Reza Pourgholi, S. Hashem Tabasi, Hamed Zeidabadi

Erschienen in: Engineering with Computers | Ausgabe 3/2018

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Abstract

In this paper, based on the cubic B-spline finite element (CBSFE) and the radial basis functions (RBFs) methods, the inverse problems of finding the nonlinear source term for system of reaction–diffusion equations are studied. The approach of the proposed methods are to approximate unknown coefficients by a polynomial function whose coefficients are determined from the solution of minimization problem based on the overspecified data. In fact, this work considers a comparative study between the cubic B-spline finite element method and radial basis functions method. The stability and convergence analysis for these problems are investigated and some examples are given to illustrate the results.
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Literatur
1.
Beck JV, Blackwell B, Haji-sheikh A (1996) Comparison of some inverse heat conduction methods using experimental data. Int J Heat Mass Transf 3:3649–3657CrossRef
2.
Pourgholi R, Azizi N, Gasimov YS, Aliev F, Khalafi HK (2009) Removal of numerical instability in the solution of an inverse heat conduction problem. Commun Nonlinear Sci Numer Simul 14(6):2664–2669MathSciNetCrossRefMATH
3.
Pourgholi R, Dana H, Tabasi SH (2014) Solving an inverse heat conduction problem using genetic algorithm: sequential and multi-core parallelization approach. Appl Math Model 38(7):1948–1958MathSciNetCrossRef
4.
Shenefelt JR, Luck R, Taylor RP, Berry JT (2002) Solution to inverse heat conduction problems employing singular value decomposition and model-reduction. Int J Heat Mass Transf 45:67–74CrossRefMATH
5.
Tikhonov AN, Arsenin VY (1977) Solution of ill-posed problems. V.H. Winston and Sons, WashingtonMATH
6.
7.
Pourgholi R, Rostamian M (2010) A numerical technique for solving IHCPs using Tikhonov regularization method. Appl Math Model 34(8):2102–2110MathSciNetCrossRefMATH
8.
Beck JV, Blackwell B, St CR (1985) Clair, inverse heat conduction: ill posed problems. Wiley, New York
9.
Duchateau P, Rundell W (1985) Unicity in an inverse problem for an unknown reaction term in a reaction diffusion equation. J Differ Equ 59(2):155–164
10.
Muzylev NV (1980) Uniqueness theorems for some convergence problems of heat conduction. USSR Comput Math Phys 20(2):120–134
11.
Pilant MS, Rundell W (1986) An inverse problem for a nonlinear parabolic equation. Commun Partial Differ Equ 11(4):445–457
12.
Pilant MS, Rundell W (1988) Fixed point methods for a nonlinear parabolic inverse coefcient problem. Commun Partial Differ Equ 13(4):469–549
13.
Anger G (1990) Inverse problems in differential equations. Plenum, New YorkMATH
14.
Nanda A, Das PC (2000) Determination of the non-linear reaction term in a coupled reaction–diffusion system. Numer Funct Anal Optim 21(3&4):489–508
15.
16.
Bangerth W, Joshi A (2009) Adaptive finite element methods for nonlinear inverse problems. In: Proceedings of the 2009 ACM symposium on Applied Computing, pp 1002–1006
17.
Beilina L, Johnson C (2001) A hybrid FEM/FDM method for an inverse scattering problem. In: Numerical Mathematics and Advanced Applications - ENUMATH 2001. Springer-Verlag, Berlin, pp 545–556
18.
Beilina L (2003) Adaptive finite element/difference method for inverse elastic scattering waves. Appl Comput Math 2:119–134MathSciNetMATH
19.
Ling X, Keanini RG, Cherukuri HP (2003) A non-iterative finite element method for inverse heat conduction problems. Int J Numer Methods Eng 56:1315–1334CrossRefMATH
20.
Kansa EJ (1990) Multiquadricsa scattered data approximation scheme with applications to computational fluid dynamics—I. Comput Math Appl 19:127–145MathSciNetCrossRefMATH
21.
Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76:1905–1915CrossRef
22.
Hon YC, Mao XZ (1998) An efficient numerical scheme for Burgers equation. Appl Math Comput 95:37–50MathSciNetMATH
23.
Hon YC, Cheung KF, Mao XZ, Kansa EJ (1999) Multiquadric solution for shallow water equations. J Hydraul Eng 125:524–533CrossRef
24.
Zerroukat M, Power H, Chen CS (1992) A numerical method for heat transfer problem using collocation and radial basis functions. Int J Numer Methods Eng 42:1263–1278CrossRefMATH
25.
Hon YC, Mao XZ (1999) A radial basis function method for solving options pricing model. Financ Eng 8(1):31–49
26.
Marcozzi M, Choi S, Chen CS (2001) On the use of boundary conditions for variational formulations arising in financial mathematics. Appl Math Comput 124:197–214MathSciNetMATH
27.
Fasshauer GE (2007) Meshfree Approximation Methods with Matlab: (With CD-ROM), vol 6. World Scientific Publishing Co Inc
28.
Hon YC, Wu Z (2000) A numerical computation for inverse boundary determination problem. Eng Anal Bound Elem 24:599–606CrossRefMATH
29.
30.
Li J (2005) Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems. Commun Numer Methods Eng 21:169–182MathSciNetCrossRefMATH
31.
Cheng AH-D, Cabral JJSP (2005) Direct solution of ill-posed boundary value problems by radial basis function collocation method. Int J Numer Methods Eng 64:45–64MathSciNetCrossRefMATH
32.
Ma L, Wu Z (2011) Radial basis functions method for parabolic inverse problem. Int J Comput Math 88(2):384–395MathSciNetMATH
33.
Bayona V, Moscoso M, Carretero M, Kindelan M (2010) RBF-FD formulas and convergence properties. J Comput Phys 229:8281–8295CrossRefMATH
34.
35.
Tikhonov AN, Arsenin VY (1977) On the solution of ill-posed problems. Wiley, New YorkMATH
36.
37.
38.
Elden L (1984) A note on the computation of the generalized cross-validation function for ill-conditioned least squares problems. BIT 24:467–472MathSciNetCrossRefMATH
39.
Golub GH, Heath M, Wahba G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21:215–223MathSciNetCrossRefMATH
40.
Wahba G (1990) Spline models for observational data. SIAM, Philadelphia
41.
Martin L, Elliott L, Heggs PJ, Ingham DB, Lesnic D, Wen X (2006) Dual reciprocity boundary element method solution of the Cauchy problem for Helmholtz-type equations with variable coefficients. J. Sound Vib 297:89–105CrossRefMATH
42.
Dehghan M, Tatari M (2006) Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions. Mathematical and Computer Modelling 44:1160–1168MathSciNetCrossRefMATH
43.
Cabeza JMG, Garcia JAM, Rodriguez AC (2005) A Sequential Algorithm of Inverse Heat Conduction Problems Using Singular Value Decomposition. International Journal of Thermal Sciences 44:235–244CrossRef
Metadaten
Titel
Numerical techniques for solving system of nonlinear inverse problem
verfasst von
Reza Pourgholi
S. Hashem Tabasi
Hamed Zeidabadi
Publikationsdatum
25.11.2017
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 3/2018
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-017-0554-6

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