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Volumn 206, Issue 2, 2007, Pages 774-795

Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains

Author keywords

Cauchy Navier equations; Circulant matrices; Elliptic systems; Fast algorithms; Fast Fourier transform; Method of fundamental solutions; Thermo elastostatics

Indexed keywords

CAUCHY-NAVIER EQUATIONS; CIRCULANT MATRICES; ELLIPTIC SYSTEMS; METHOD OF FUNDAMENTAL SOLUTIONS; THERMOELASTOSTATICS;

EID: 34249826933     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.08.037     Document Type: Article
Times cited : (31)

References (49)
  • 1
    • 34249814100 scopus 로고    scopus 로고
    • M. A. Aleksidze, Fundamentalnye funktsii v priblizhennykh resheniyakh granichnykh zadach [Fundamental functions in approximate solutions of boundary value problems], Spravochnaya Matematicheskaya Biblioteka [Mathematical Reference Library], "Nauka", Moscow, 1991. (in Russian); (with an English summary.).
  • 2
    • 0035546639 scopus 로고    scopus 로고
    • The method of fundamental solutions for layered elastic materials
    • Berger J.R., and Karageorghis A. The method of fundamental solutions for layered elastic materials. Eng. Anal. Bound. Elem. 25 (2001) 877-886
    • (2001) Eng. Anal. Bound. Elem. , vol.25 , pp. 877-886
    • Berger, J.R.1    Karageorghis, A.2
  • 3
    • 34249804863 scopus 로고    scopus 로고
    • J.R. Berger, A. Karageorghis, P.A. Martin, Stress intensity factor computation using the method of fundamental solutions: mixed-mode problems, Internat. J. Numer. Methods Eng., to appear.
  • 4
    • 38249002591 scopus 로고
    • Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions
    • Bialecki B., and Fairweather G. Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. J. Comput. Appl. Math. 46 (1993) 369-386
    • (1993) J. Comput. Appl. Math. , vol.46 , pp. 369-386
    • Bialecki, B.1    Fairweather, G.2
  • 5
    • 0035281751 scopus 로고    scopus 로고
    • Orthogonal spline collocation methods for partial differential equations
    • Numerical Analysis 2000, vol. VII, Partial Differential Equations
    • Bialecki B., and Fairweather G. Orthogonal spline collocation methods for partial differential equations. J. Comput. Appl. Math. 128 (2001) 55-82 Numerical Analysis 2000, vol. VII, Partial Differential Equations
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 55-82
    • Bialecki, B.1    Fairweather, G.2
  • 6
    • 0022107918 scopus 로고
    • Fundamental solutions method for elliptic boundary value problems
    • Bogomolny A. Fundamental solutions method for elliptic boundary value problems. SIAM J. Numer. Anal. 22 (1985) 644-669
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 644-669
    • Bogomolny, A.1
  • 7
    • 34249794640 scopus 로고    scopus 로고
    • C.A. Brebbia, S. Walker, E. Alarcón, A. Martin, F. Paris, F. Hartmann, J.C.F. Telles, L.C. Wrobel, J. Dominguez, M. Margulies, W.L. Wendland, Progress in Boundary Element Methods, vol. 1, Wiley, New York, 1981, Edited and with a preface by A. Brebbia, Halsted Press Book, New York.
  • 8
    • 0021574589 scopus 로고
    • A comparison of the boundary element and superposition methods
    • Burgess G., and Maharejin E. A comparison of the boundary element and superposition methods. Comput. & Structures 19 (1984) 697-705
    • (1984) Comput. & Structures , vol.19 , pp. 697-705
    • Burgess, G.1    Maharejin, E.2
  • 9
    • 34249779623 scopus 로고    scopus 로고
    • P.J. Davis, Circulant Matrices, Wiley, New York, Chichester, Brisbane, 1979, A Wiley-Interscience Publication, Pure and Applied Mathematics.
  • 10
    • 0032344733 scopus 로고    scopus 로고
    • The method of fundamental solutions for elliptic boundary value problems. Numerical treatment of boundary integral equations
    • Fairweather G., and Karageorghis A. The method of fundamental solutions for elliptic boundary value problems. Numerical treatment of boundary integral equations. Adv. Comput. Math. 9 (1998) 69-95
    • (1998) Adv. Comput. Math. , vol.9 , pp. 69-95
    • Fairweather, G.1    Karageorghis, A.2
  • 11
    • 16244362691 scopus 로고    scopus 로고
    • A matrix decomposition MFS algorithm for axisymmetric biharmonic problems
    • Fairweather G., Karageorghis A., and Smyrlis Y.-S. A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Adv. Comput. Math. 23 (2005) 55-71
    • (2005) Adv. Comput. Math. , vol.23 , pp. 55-71
    • Fairweather, G.1    Karageorghis, A.2    Smyrlis, Y.-S.3
  • 12
    • 0035736355 scopus 로고    scopus 로고
    • A force supersition approach to plane elastic stress and strain analysis
    • Fenner R.T. A force supersition approach to plane elastic stress and strain analysis. J. Strain Anal. 36 (2001) 517-529
    • (2001) J. Strain Anal. , vol.36 , pp. 517-529
    • Fenner, R.T.1
  • 13
    • 0346201627 scopus 로고
    • Il teorema del massimo modulo per l'equazione dell'elastostatica tridimensionale
    • Fichera G. Il teorema del massimo modulo per l'equazione dell'elastostatica tridimensionale. Arch. Rational Mech. Anal. 7 (1961) 373-387
    • (1961) Arch. Rational Mech. Anal. , vol.7 , pp. 373-387
    • Fichera, G.1
  • 15
    • 34249799360 scopus 로고    scopus 로고
    • M.A. Golberg, C.S. Chen, The method of fundamental solutions for potential, Helmholtz and diffusion problems, in: Boundary Integral Methods: Numerical and Mathematical Aspects, Computational Engineering, vol. 1, WIT Press/Computational Mechanics Publications, Boston, MA, 1999, pp. 103-176.
  • 16
    • 34249803369 scopus 로고    scopus 로고
    • A. Karageorghis, C.S. Chen, Y.-S. Smyrlis, A matrix decomposition RBF algorithm: approximation of functions and their derivatives, Appl. Numer. Math., to appear.
  • 17
    • 0033687730 scopus 로고    scopus 로고
    • The method of fundamental solutions for axisymmetric elasticity problems
    • Karageorghis A., and Fairweather G. The method of fundamental solutions for axisymmetric elasticity problems. Comput. Mech. 25 (2000) 524-532
    • (2000) Comput. Mech. , vol.25 , pp. 524-532
    • Karageorghis, A.1    Fairweather, G.2
  • 18
    • 32144448188 scopus 로고    scopus 로고
    • Stress intensity factor computation using the method of fundamental solutions
    • Karageorghis A., Poullikkas A., and Berger J.R. Stress intensity factor computation using the method of fundamental solutions. Comput. Mech. 37 (2006) 445-454
    • (2006) Comput. Mech. , vol.37 , pp. 445-454
    • Karageorghis, A.1    Poullikkas, A.2    Berger, J.R.3
  • 19
    • 36148994005 scopus 로고    scopus 로고
    • A. Karageorghis, Y.-S. Smyrlis, Matrix decomposition MFS algorithms, in: Boundary elements and other mesh reduction methods, XXVIII (Skiathos, 2006), International Series on Advances in Boundary Elements, vol. 42, WIT Press, Southampton, 2006, pp. 61-68.
  • 20
    • 34249827949 scopus 로고    scopus 로고
    • A. Karageorghis, Y.-S. Smyrlis, T. Tsangaris, A matrix decomposition MFS algorithm for certain linear elasticity problems, Numer. Algorithms, to appear.
  • 21
    • 0000969707 scopus 로고
    • On the numerical stability of the method of fundamental solution applied to the Dirichlet problem
    • Kitagawa T. On the numerical stability of the method of fundamental solution applied to the Dirichlet problem. Japan J. Appl. Math. 5 (1988) 123-133
    • (1988) Japan J. Appl. Math. , vol.5 , pp. 123-133
    • Kitagawa, T.1
  • 22
    • 0023541981 scopus 로고
    • Review of applications of the boundary collocation methods in mechanics of continuous media
    • Kołodziej J.A. Review of applications of the boundary collocation methods in mechanics of continuous media. Solid Mech. Arch. 12 (1987) 187-231
    • (1987) Solid Mech. Arch. , vol.12 , pp. 187-231
    • Kołodziej, J.A.1
  • 23
    • 34249797077 scopus 로고    scopus 로고
    • J.A. Kołodziej, Zastosowanie metody kollokacji brzegowej w zagadnieniach mechaniki [Applications of the Boundary Collocation Method in Applied Mechanics], Wydawnictwo Politechniki Poznańskiej, Poznań, 2001 (in Polish).
  • 24
    • 0000485806 scopus 로고
    • On a method of solving approximately the limiting problems of mathematical physics
    • Kupradze V.D. On a method of solving approximately the limiting problems of mathematical physics. Ž. Vyčisl. Mat. i Mat. Fiz. 4 (1964) 1118-1121
    • (1964) Ž. Vyčisl. Mat. i Mat. Fiz. , vol.4 , pp. 1118-1121
    • Kupradze, V.D.1
  • 25
    • 0012460960 scopus 로고
    • An approximate method of solving certain boundary-value problems
    • (in Russian)
    • Kupradze V.D., and Aleksidze M.A. An approximate method of solving certain boundary-value problems. Soobšč. Akad. Nauk Gruzin. SSR 30 (1963) 529-536 (in Russian)
    • (1963) Soobšč. Akad. Nauk Gruzin. SSR , vol.30 , pp. 529-536
    • Kupradze, V.D.1    Aleksidze, M.A.2
  • 26
    • 33748444430 scopus 로고
    • The method of functional equations for the approximate solution of certain boundary value problems
    • Kupradze V.D., and Aleksidze M.A. The method of functional equations for the approximate solution of certain boundary value problems. Comput. Methods Math. Phys. 4 (1964) 82-126
    • (1964) Comput. Methods Math. Phys. , vol.4 , pp. 82-126
    • Kupradze, V.D.1    Aleksidze, M.A.2
  • 27
    • 34249777611 scopus 로고    scopus 로고
    • V.D. Kupradze, T.G. Gegelia, M.O. Basheleshvili, T.V. Burchuladze, Trekhmernye zadachi matematicheskoi teorii uprugosti i termouprugosti [Three-dimensional problems in the mathematical theory of elasticity and thermoelasticity.], Izdat. "Nauka", Moscow, 1976 (in Russian).
  • 30
    • 0021902595 scopus 로고
    • An extension of the superposition method for plane anisotropic elastic bodies
    • Maharejin E. An extension of the superposition method for plane anisotropic elastic bodies. Comput. & Structures 21 (1985) 953-958
    • (1985) Comput. & Structures , vol.21 , pp. 953-958
    • Maharejin, E.1
  • 31
    • 2342463081 scopus 로고    scopus 로고
    • The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity
    • Marin L., and Lesnic D. The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity. International J. Solids Structure 41 (2004) 3425-3438
    • (2004) International J. Solids Structure , vol.41 , pp. 3425-3438
    • Marin, L.1    Lesnic, D.2
  • 32
    • 0025457920 scopus 로고
    • An effective direct solution method for certain boundary element equations in 3D
    • Meyer A., and Rjasanow S. An effective direct solution method for certain boundary element equations in 3D. Math. Methods Appl. Sci. 13 (1990) 43-53
    • (1990) Math. Methods Appl. Sci. , vol.13 , pp. 43-53
    • Meyer, A.1    Rjasanow, S.2
  • 34
    • 0036465594 scopus 로고    scopus 로고
    • The method of fundamental solutions for three-dimensional elastostatics problems
    • Poullikkas A., Karageorghis A., and Georgiou G. The method of fundamental solutions for three-dimensional elastostatics problems. Comput. & Structures 80 (2002) 365-370
    • (2002) Comput. & Structures , vol.80 , pp. 365-370
    • Poullikkas, A.1    Karageorghis, A.2    Georgiou, G.3
  • 35
    • 0030234658 scopus 로고    scopus 로고
    • Analysis of composite using charge simulation method
    • Raamachandran J., and Rajamohan C. Analysis of composite using charge simulation method. Eng. Anal. Bound. Elem. 18 (1996) 131-135
    • (1996) Eng. Anal. Bound. Elem. , vol.18 , pp. 131-135
    • Raamachandran, J.1    Rajamohan, C.2
  • 36
    • 0020194553 scopus 로고
    • Fundamental solutions for the collocation method in planar elastostatics
    • Redekop D. Fundamental solutions for the collocation method in planar elastostatics. Appl. Math. Modelling 6 (1982) 390-393
    • (1982) Appl. Math. Modelling , vol.6 , pp. 390-393
    • Redekop, D.1
  • 37
    • 0023174506 scopus 로고
    • Fundamental solutions for the collocation method in three-dimensional elastostatics
    • Redekop D., and Cheung R.S.W. Fundamental solutions for the collocation method in three-dimensional elastostatics. Comput. & Structures 26 (1987) 703-707
    • (1987) Comput. & Structures , vol.26 , pp. 703-707
    • Redekop, D.1    Cheung, R.S.W.2
  • 38
    • 0020607273 scopus 로고
    • Use of fundamental solutions in the collocation method in axisymmetric elastostatics
    • Redekop D., and Thompson J.C. Use of fundamental solutions in the collocation method in axisymmetric elastostatics. Comput. & Structures 17 (1983) 485-490
    • (1983) Comput. & Structures , vol.17 , pp. 485-490
    • Redekop, D.1    Thompson, J.C.2
  • 39
    • 38149147298 scopus 로고
    • Effective algorithms with circulant-block matrices
    • Rjasanow S. Effective algorithms with circulant-block matrices. Linear Algebra Appl. 202 (1994) 55-69
    • (1994) Linear Algebra Appl. , vol.202 , pp. 55-69
    • Rjasanow, S.1
  • 40
    • 84988148096 scopus 로고
    • Optimal preconditioner for boundary element formulation of the Dirichlet problem in elasticity
    • Rjasanow S. Optimal preconditioner for boundary element formulation of the Dirichlet problem in elasticity. Math. Methods Appl. Sci. 18 (1995) 603-613
    • (1995) Math. Methods Appl. Sci. , vol.18 , pp. 603-613
    • Rjasanow, S.1
  • 41
    • 0032392501 scopus 로고    scopus 로고
    • The structure of the boundary element matrix for the three-dimensional Dirichlet problem in elasticity
    • Rjasanow S. The structure of the boundary element matrix for the three-dimensional Dirichlet problem in elasticity. Numer. Linear Algebra Appl. 5 (1998) 203-217
    • (1998) Numer. Linear Algebra Appl. , vol.5 , pp. 203-217
    • Rjasanow, S.1
  • 42
    • 34249779304 scopus 로고    scopus 로고
    • Y.-S. Smyrlis, Applicability and applications of the method of fundamental solutions, Technical Report TR-03-2006, Department of Mathematics and Statistics, University of Cyprus, February 2006.
  • 43
    • 0041950033 scopus 로고    scopus 로고
    • Some aspects of the method of fundamental solutions for certain harmonic problems
    • Smyrlis Y.-S., and Karageorghis A. Some aspects of the method of fundamental solutions for certain harmonic problems. J. Sci. Comput. 16 (2001) 341-371
    • (2001) J. Sci. Comput. , vol.16 , pp. 341-371
    • Smyrlis, Y.-S.1    Karageorghis, A.2
  • 44
    • 8344281356 scopus 로고    scopus 로고
    • Some aspects of the method of fundamental solutions for certain biharmonic problems
    • Smyrlis Y.-S., and Karageorghis A. Some aspects of the method of fundamental solutions for certain biharmonic problems. CMES Comput. Model. Eng. Sci. 4 (2003) 535-550
    • (2003) CMES Comput. Model. Eng. Sci. , vol.4 , pp. 535-550
    • Smyrlis, Y.-S.1    Karageorghis, A.2
  • 45
    • 1842832046 scopus 로고    scopus 로고
    • A matrix decomposition MFS algorithm for axisymmetric potential problems
    • Smyrlis Y.-S., and Karageorghis A. A matrix decomposition MFS algorithm for axisymmetric potential problems. Eng. Anal. Bound. Elem. 28 (2004) 463-474
    • (2004) Eng. Anal. Bound. Elem. , vol.28 , pp. 463-474
    • Smyrlis, Y.-S.1    Karageorghis, A.2
  • 46
    • 3142703789 scopus 로고    scopus 로고
    • Numerical analysis of the MFS for certain harmonic problems
    • Smyrlis Y.-S., and Karageorghis A. Numerical analysis of the MFS for certain harmonic problems. M2AN Math. Model. Numer. Anal. 38 (2004) 495-517
    • (2004) M2AN Math. Model. Numer. Anal. , vol.38 , pp. 495-517
    • Smyrlis, Y.-S.1    Karageorghis, A.2
  • 47
    • 33746594581 scopus 로고    scopus 로고
    • A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains
    • Tsangaris T., Smyrlis Y.-S., and Karageorghis A. A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains. J. Sci. Comput. 28 (2006) 31-50
    • (2006) J. Sci. Comput. , vol.28 , pp. 31-50
    • Tsangaris, T.1    Smyrlis, Y.-S.2    Karageorghis, A.3
  • 48
    • 34249792985 scopus 로고    scopus 로고
    • D.-L. Young, C.L. Chiu, C.M. Fan, C.C. Tsai, Y.C. Lin, Method of fundamental solutions for multidimensional stokes equations by the dual-potential formulation, Eur. J. Mech. B Fluids, to appear.
  • 49
    • 25444438222 scopus 로고    scopus 로고
    • The method of fundamental solutions for 2d and 3d stokes problems
    • (Short note)
    • Young D.-L., Jane S.J., Fan C.M., Murugesan K., and Tsai C.C. The method of fundamental solutions for 2d and 3d stokes problems. J. Comput. Phys. 211 (2006) 1-8 (Short note)
    • (2006) J. Comput. Phys. , vol.211 , pp. 1-8
    • Young, D.-L.1    Jane, S.J.2    Fan, C.M.3    Murugesan, K.4    Tsai, C.C.5


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