The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction

International Journal for Numerical Methods in Engineering

Volumn 69, Issue 8, 2007, Pages 1570-1589

  Jin, Bangti ^a   Marin, Liviu ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Inverse source problem; Method of fundamental solutions; Steady state heat conduction; Truncated singular value decomposition

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTER SIMULATION; INVERSE PROBLEMS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; SENSITIVITY ANALYSIS; TEMPERATURE;

INVERSE SOURCE PROBLEM; METHOD OF FUNDAMENTAL SOLUTIONS; STEADY-STATE HEAT CONDUCTION; TRUNCATED SINGULAR VALUE DECOMPOSITION;

HEAT CONDUCTION;

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTER SIMULATION; HEAT CONDUCTION; INVERSE PROBLEMS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; SENSITIVITY ANALYSIS; TEMPERATURE;

EID: 33846990077     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1826     Document Type: Article

References (45)

1. Isakov V. Inverse Source Problems. American Mathematical Society: Providence, Rhode-Island; 1989.
2. El Badia A, Ha Duong T. Some remarks on the problem of source identification from boundary measurements. Inverse Problems 1998; 14(4):883-891.
3. El Badia A. Inverse source problem in an anisotropic medium by boundary measurements. Inverse Problems 2005; 21(5):1487-1506.
4. Ling L, Hon YC, Yamamoto M. Inverse source identification for Poisson equation. Inverse Problems in Science and Engineering 2005; 13(4):433-447.
5. Kagawa Y, Sun Y, Matsumoto O. Inverse solution of Poisson equation using DRM boundary element model - Identification of space charge distribution. Inverse Problems in Engineering 1995; 1(2):247-265.
6. Sun Y, Kagawa Y. Identification of electric charge distribution using dual reciprocity boundary element models. IEEE Transactions on Magnetics 1997; 33(2):1970-1973.
7. Trlep M, Hamler A, Hribernik B. The use of DRM for inverse problems of Poisson's equation. IEEE Transactions on Magnetics 2000; 36(4):1649-1652.
8. Matsumoto T, Tanaka M, Tsukamoto T. Source identification using boundary element method with dual reciprocity method. In Advances in Boundary Element Techniques IV, Gallego R, Aliabadi MH (eds). University of London: Queen Mary, 2003; 177-182.
9. Matsumoto T, Tanaka M, Tsukamoto T. Identifications of source distributions using BEM with dual reciprocity method. In Inverse Problems in Engineering Mechanics IV, Tanaka M (ed.). Elsevier Science: Amsterdam, New York, 2003; 127-135.
10. Farcas A, Elliott L, Ingham DB, Lesnic D, Mera NS. A dual reciprocity boundary element method for the regularized numerical solution of the inverse source problem associated to the Poisson equation. Inverse Problems in Engineering 2003; 11(2):123-139.
11. El Badia A, Ha Duong T, Moutazaim F. Numerical solution for the identification of source terms from boundary measurements. Inverse Problems in Engineering 2000; 8(4):345-364.
12. Golberg MA, Chen CS. The method of fundamental solution for potential, Helmholtz and diffusion problems. In Boundary Integral Methods - Numerical and Mathematical Aspects, Golberg MA (ed.). Computational Mechanics Publications: Southampton, 1998; 103-176.
13. Fairweather G, Karageorghis A. The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics 1998; 9(1-2):69-95.
14. Cho HA, Golberg MA, Muleshkov AS, Li X. Trefftz methods for time-dependent partial differential equations. Computers, Materials and Continua 2004; 1(1):1-37.
15. Marin L, Lesnic D. The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations. Computers and Structures 2005; 83(4-5):267-278.
16. Marin L. A meshless method for the numerical solution of the Cauchy problem associated with three-dimensional Helmholtz-type equations. Applied Mathematics and Computation 2005; 165(2):355-374.
17. Jin B, Zheng Y. A meshless method for some inverse problems associated with the Helmholtz equation. Computer Methods in Applied Mechanics and Engineering 2006; 195(19-22):2270-2288.
18. Jin B, Zheng Y Marin L. The method of fundamental solutions for some inverse boundary value problems associated with steady-state anisotropic heat conduction. International Journal for Numerical Methods in Engineering 2006; 65(11):1865-1891.
19. Marin L, Lesnic D. The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity. International Journal of Solids and Structures 2004; 41(13):3425-3438.
20. Marin L. A meshless method for solving the Cauchy problem in three-dimensional elastostatics. Computers and Mathematics with Applications 2005; 50(1-2):73-92.
21. Hon YC, Wei T. A fundamental solution method for inverse heat conduction problem. Engineering Analysis with Boundary Elements 2004; 28(5):489-495.
22. Hon YC, Wei T. The method of fundamental solutions for solving multidimensional inverse heat conduction problems. CMES - Computer Modeling in Engineering and Science 2005; 7(2):119-132.
23. El Badia A, Ha-Duong T. An inverse source problem in potential analysis. Inverse Problems 2000; 16(3):651-663.
24. Sober E. The principle of parsimony. British Journal of Philosophy Science 1981; 32(2):145-156.
25. Wood AS, Tupholme GE, Bhatti MIH, Heggs PJ. Steady-state heat transfer through extended plane surfaces. International Communications in Heat and Mass Transfer 1995; 22(1):99-109.
26. Kupradze VD, Aleksidze MA. The method of functional equations for the approximate solution of certain boundary value problems. USSR Computational Mathematics and Mathematical Physics 1964; 4(1):82-126.
27. Mathon R, Johnston RL. The approximate solution of elliptic boundary-value problems by fundamental solutions. SIAM Journal on Numerical Analysis 1977; 14(4):638-650.
28. Fairweather G, Karageorghis A, Martin PA. The method of fundamental solutions for scattering and radiation problems. Engineering Analysis with Boundary Elements 2003; 27(7):759-769.
29. Kythe PK. Fundamental Solutions for Differential Operators and Applications. Birkhäuser: Boston, 1996.
30. Cheng AH-D, Antes H, Ortner N. Fundamental solutions of products of Helmholtz and polyharmonic operators. Engineering Analysis with Boundary Elements 1994; 14(2):187-191.
31. Poullikkas A, Karageorghis A, Georgiou G. Method of fundamental solutions for harmonic and biharmonic boundary value problems. Computational Mechanics 1998; 21(4-5):416-423.
32. Mitic P, Rashed YF. Convergence and stability of the method of meshless fundamental solutions using an array of randomly distributed source. Engineering Analysis with Boundary Elements 2004; 28(2):143-153.
33. Hansen PC. Rank-deficient and Discrete III-posed Problems: Numerical Aspects of Linear Inversion. SIAM: Philadelphia, 1998.
34. Hansen PC, O'Leary DP. The use of the L-curve in the regularization of discrete ill-ppsed problems. SIAM Journal on Scientific Computing 1993; 14(6):1487-1503.
35. Chen LY, Chen JT, Hong HK, Chen CH. Application of Cesàro mean and the L-curve for the deconvolution problem. Soil Dynamics and Earthquake Engineering 1995; 14(5):361-373.
36. Hanke M. Limitations of the L-curve method in ill-posed problems. BIT Numerical Mathematics 1996; 36(2): 287-301.
37. Vogel CR. Non-convergence of the L-curve regularization parameter selection method. Inverse Problems 1996; 12(4):535-547.
38. Guerra V, Hernandez V. Numerical aspects in locating the corner of the L-curve. In Approximation, Optimization and Mathematical Economics, Lassonde M (ed.). Springer-Verlag: Heidelberg, 2001; 121-131.
39. Kaufman L, Neumaier A. PET regularization by envelope guided conjugate gradients. IEEE Transactions on Medical Imaging 1996; 15(3):385-389.
40. Castellanos JL, Gomez S, Guerra V. The triangle method for finding the corner of the L-curve. Applied Numerical Mathematics 2002; 43(4):359-373.
41. Ramachandran PA. Method of fundamental solutions: singular value decomposition analysis. Communications in Numerical Methods in Engineering 2002; 18(11):789-801.
42. Jin B. A meshless method for the Laplace and biharmonic equations subjected to noisy boundary data. CMES - Computer Modeling in Engineering and Science 2004; 6(3):253-261.
43. Karageorghis A. Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities. Numerical Methods for Partial Differential Equations 1992; 8(1):1-19.
44. Marengo EA, Devaney AJ, Ziolkowski RW. Inverse source problem and minimum energy sources. Journal of Optical Society of America 2000; 17(1):34-45.
45. Hanke M, Hansen PC. Regularization methods for large-scale problems. Surveys on Mathematics for Industry 1993; 3(4):253-315.