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Tytuł artykułu

Weighted least-squares algorithms of the method of fundamental solutions

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Warianty tytułu
Konferencja
Symposium Vibrations in Physical Systems (XXI ; 26-29.05.2004 ; Poznań-Kierz, Polska)
Języki publikacji
EN
Abstrakty
EN
We Study the Method of Fundamental Solutions (MPS) for the solution of certain elliptic boundary value problems. We propose least squares algorithms, when the number of collocation points is larger the number of singularities as well as in "the case in which the number of singularities is larger than the number of collocation points.
Rocznik
Tom
Strony
339--348
Opis fizyczny
Bibliogr. 16 poz., wz.
Twórcy
  • Departament of Mathematics & Statistics, University of Cyprus
  • Departament of Mathematics & Statistics, University of Cyprus
Bibliografia
  • |1| R.A. ADAMS AND J.J. F. FOURNIER. Sobolev Spaces. 2nd edition, Academic Press, 2003.
  • |2| P.J. DAVIS, Circulant Matrices, John Wiley & Sons. New York. 1979.
  • |3| G. FAIRWEATHER AND A. KARAGEORGHIS, The method of fundamental solutions for elliptic boundary value problems. Adv. Comput. Math., 9, 69, 95, 1998.
  • |4| G. FAIRWEATHER, A. KARAGEORGHIS AND P. A. MARTIN, The method of fundamental solutions for scattering and radiation problems, Engng. Analysis with Boundary Elements. 27, 759 769, 2003.
  • |5| M.A. GOLBERG AND C.S. CHEN. Discrete Projection Methods for Integral Equations, Computational Mechanics Publications. Southampton, 1990.
  • |6| M.A. GOLBERG AND C.S. CHEN, The method of fundamental solutions for potential. Helmholtz and diffusion problems, in: Boundary Integral Methods and Mathematical Aspects, ed. M. A. Golberg, WIT Press/Computational Mechanics Publications, Boston, 103 170, 1999.
  • |7| I.S. GRADSHTEYN AND I.M. RYZHIK, Table of Integrals, Series, and Products, 6th edition, Academic Press, London. 2000.
  • |8| M. KATSURADA, A mathematical study of the charge stimulation method II, J. Fac. Sci., Univ. of Tokyo, Sect. 1A, Math. 36, 135, 162, 1989.
  • |9| M. KATSURADA AND H. OKAMOTO, A mathematical study of the charge stimulation method I, J. Fac. Sci., Univ. of Tokyo. Sect. 1A. Math. 35, 507 518, 1988.
  • |10| J.A. KOLODZIEJ, Review of applications of the boundary collocation methods m mechanics of continuous media, Solid Mech. Arch., 12, 187 231, 1987.
  • |11| J.A. KOLODZIEJ, Applications of the Boundary Collocation Method in Applied Mechanics, Wydawnictwo Politechniki Poznańskiej, Poznań, 2001. (In Polish).
  • |12| P.A. RAMACHANDRAN, Method of fundamental solutions: singular value decomposition analysts, Commun. Numer. Moth. Engng., 18, 789 801, 2002.
  • |13| Y.S. SMYRLIS AND A. KARAGEORGHIS, Some aspects of the method of fundamental solutions for certain harmonic problems, .1. Sci. Comput., 16, 341 371, 2001.
  • |14| Y.S. SMYRLIS AND A. KARAGEORGHIS. Numerical analysts of the MFS for certain harmonic problems, RAIRO Model. Math. Anal. Numer., to appear.
  • |15| Y.S. SMYRLIS AND A. KARAGEORGHIS, A Linear least squares MFS for certain elliptic problems. Num. Alg.. 35, 29 44, 2004.
  • |16| Y.S. SMYRLIS, Aspects of the least squares MFS for certain elliptic BVP, in preparation.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c2b35e9a-3a26-40aa-9445-7a525eab6005
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