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High-accuracy discretization methods for solid mechanics

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Novel high-accuracy computational techniques for solid mechanics problems are presented. They include fourth-order and arbitrary-order finite difference methods based on Pade-type differencing formulas and a meshless method which uses radial basis functions in a "finite difference'' mode. Some results illustrating high performance of the suggested numerical methods are displayed.
Rocznik
Strony
531--553
Opis fizyczny
Bibliogr. 29 poz., rys., wykr.
Twórcy
  • Computing Center of Russian Academy of Sciences, Vavilova str. 40, 119991 Moscow, Russia
  • Computing Center of Russian Academy of Sciences, Vavilova str. 40, 119991 Moscow, Russia
  • Computing Center of Russian Academy of Sciences, Vavilova str. 40, 119991 Moscow, Russia
Bibliografia
  • 1. A. A. SAMARSKII, V. B . ANDREEV, Finite difference methods for elliptic equatims (In Russian), Izd. Nauka, Moscow 1976.
  • 2. A. 1. TOLSTYKH, Muitioperator high-order compact upwind methods for CFD ptraLLel calculations, [in:] Parallel Computational Fluid Dynamics, D. R. Emerson, A. Ecer,J . Periaux and N. Satofuka [Eds.]' 383- 390, Elsevier, Amsterdam 1998.
  • 3. A. 1. TOLSTYKH, On pr'escribed order integro-interpolation schemes, J. Compllt. Math and Math. Phys. (trans!. from Russian), to appear in 2002.
  • 4. T . LIZKA, J. ORKITZ, The finite difference method at arbitrary irregular grids md its application in applied mechanics, Comput. Struct. , 11,83- 95, 1980.
  • 5. J. J. MONAGHAN, Why particle methods work, SIAM J. Sci. Stat. Comput., 3, 42!- 433, 1982.
  • 6. T. BELYTCHKO, Y. KRONGAUS, D . ORGAN, M. FLEMING, P . KRYSL, Meshless mdhods: An overview and recent developments, Compo Meth. App!. Eng., 139, 3- 47, 1996.
  • 7. E. J. KANSA, R. E. CARLSON, Radial basis function: a class of grid-free scatterel data approximations, Comput. Fluid Dynamics J., 3 , 479- 496, 1995.
  • 8. G. FASSHAUER, Solving partial differential equations with collocation with radia basis functions, [in :] Chamonix proceedings, A. Le Mehaute, C. Robut and L. L. Shunaker [Eds.], 1- 8, Vanderbilt University Press, Nashville TN 1996.
  • 9. C. FRANKE, R. SCHABACK, Solving partial differential equations by collocation Rusing radial basis functions, Appl. Math. Comput., 93, 73- 82, 1998.
  • 10. M. A. ZERROUKAT, Fast boundary element algorithm for time-dependent potentia/problems, Appl.. Math. Modelling, 22, 183- 196, 1998.
  • 11. M. D. BUHMANN, Radial functions on compact support. Proc. Edinburg Math. Soc , 41, 33- 46, 1998.
  • 12. H. WENDLAND, Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree, Adv. Comput. Math. , 4, 386- 396, 1995.
  • 13. Z. Wu, Compactly supported positive definite radial functions, Adv. Comput. Mah., 4, 283-292, 1995.
  • 14. R. K. BEATSON, J. B. CHERRIE, C. T. MONAL, Fast fitting of radial basis funrtions. Methods based on preconditioned GMRES iteration, Adv. in Comput. Math., 11,251- 270, 1999.
  • 15. S. M. WONG, Y. C. HON, T. S. LI, S . L. CHUG, E. J. KANSA, Multizone decomplsition of time dependent problems using the multi quadric scheme, Comput. Math. Appl., 31, 23- 45, 1999.
  • 16. A. I. TOLSTYKH, On using RBF-based differencing formulas for unstructured and mixed structured-unstructured grid calculations, [in:] Proceedings of 16th IMACS World Congress, Lausanne 2000.
  • 17. E. J. KANSA, Multyquadrics - a scattered data approximation scheme with applications to fluid dynamics - II: Solutions to parabolic, hyper'bolic and elliptic partial differentia equations, Comput. Math. App!., 19, 147- 161, 1990.
  • 18. E . J. KANSA, Y. C. HON, Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations, Cornput. Math. App!. 39, 123- 137, 2000.
  • 19. G. I. MARCHUK, V. 1. AGOSHKOV, Introduction to projective-difference methods (in Russian), Izd. Nauka, Moscow 1981.
  • 20. L BABUSKA, T. SCAPOLLA, Benchmark computation and performance evai1wtion for a rhombic plate bending problem, Int. J. Num. Meth. Eng., 28,155- 179, 1989.
  • 21. L. S. D. MORLEY Skew plates and Str'Uctures. International Series of Monographs In Aeronautics, MclCmillan, New York 1963.
  • 22. V. I. VLASOV, D. B. VOLKOV, Multypole methodfol' solving Poisson equation in Romains with rounded angles, Zh . Vychis!. Mat. Mat. Fiz., 35, 6, 867- 872, 1995.
  • 23. X. ZHANG, K . Z. SONG, M. W. Lu, X. LIU, Meshless methods based on collocation with radial basis functions, Comput. Mech., 26, 333- 343, 2000.
  • 24. S. P. TIMOSHENKO, S . N. GOODIER, Theory of elastisity, McGraw-Hill, New York 1970.
  • 25. W. R. MADYCH, S. A. NELSON, Error bounds for multiqltadric interpolation, [in:] Approximation theory VI, C. K. CHUl, L . L. SHUMAKER, J. W. WARDS [Eds.], Academic Press, New York 1989.
  • 26. M. D. BUHMANN, Multivariate car'dinal interpolation with radial-basis functions, Constructive approximations, 6 , 225- 255, 1990.
  • 27. A. GEORGE, J. W-H LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, New Jercey 1981.
  • 28. E. I. GRIGOLUK, V. I. MAMAI, Nonlinear deformation of thin-wall construction [in Russian], Izd. Nauka Fizmatlit, Moscow 1997.
  • 29. V. G. MAZJA, S. A. NAZAROV, Paradoxes of the solutions of boundary value problem on the smooth domain approximated by polygons, Izv. Aka.d. Nauk USSR, Ser. Mat., 50, 1156- 1177, 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0002-0113
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