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Convergence estimates for the acoustic scattering problem approximated by NURBS

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Języki publikacji
EN
Abstrakty
EN
The paper contains some estimates of an approximation to the solution of the problem of acoustic waves’s scattering by an elastic obstacle in two dimensions. The problem is approximated by the isogeometric adaptive method based on the known NURBS functions. The estimates show how the error of an approximation depends on the size of intervals and the degree of functions.
Rocznik
Strony
289--307
Opis fizyczny
Bibliogr. 18 poz., wykr.
Twórcy
autor
  • Institute of Computer Science, Cracow University of Technology Warszawska 24, 31-155 Kraków, Poland
Bibliografia
  • [1] S. Amini. On the choice of the coupling parameter in boundary integral formulations of the the exterior acoustic problem. Applicable Anal., 35: 79–92, 1990.
  • [2] Y. Basilevs, L. Beirao da Veiga, J.A. Cottrell, T.J.R. Hughes, G. Sangalli. Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math. Models in Appl. Sci., 16(7): 1031–1090, 2006.
  • [3] L. Beirao da Veiga, A. Buffa, J. Rivas, G. Sangalli. Some estimates for h-p-k-refinement in isogeometric analysis. Numer. Math., 118: 271–305, 2011.
  • [4] P.G. Ciarlet, The finite element method for elliptic problems, North Holland, Amsterdam, 1978.
  • [5] L. Demkowicz, J.T. Oden, M. Ainsworth, P. Geng. Solution of elastic scattering problems in linear acoustics using h-p boundary element methods. J. Comput. Appl. Math., 36: 29–63, 1991.
  • [6] N. Heuer, E.P. Stephan. The hp-version of the boundary element method. ZAMM, 74: T511–T513, 1994.
  • [7] T.J.R. Hughes, J.A. Cottrell, Y. Basilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng., 194: 4135–4195, 2005.
  • [8] A. Karafiat, J.T. Oden, P. Geng. Variational formulations and hp boundary element approximations for hypersingular integral equations for Helmholtz exterior boundary value problems in two dimensions. Int. J. Eng. Sci., 31(4): 649–672, 1993.
  • [9] A. Karafiat. An analysis of the boundary element method for the acoustic scattering problem [in Polish]. Cracow University of Technology, Kraków, 1996.
  • [10] A. Karafiat. On hp - error estimation in the BEM for a three-dimensional Helmholtz exterior problem. Comput. Methods Appl. Mech. Eng., 150: 199–214, 1997.
  • [11] A. Karafiat. A-priori estimates of the hp-adaptive BEM in elastic scattering of acoustic waves. Comput. Assisted Mech. Eng. Sci., 7: 559–570, 2000.
  • [12] P. Kiciak. Curves and surfaces modelling [in Polish]. WNT, Warszawa, 2005.
  • [13] N.N. Lebedev. Special functions and their applications [in Russian]. Fizmatgiz, Moscow, Leningrad, 1963.
  • [14] M. Maischak, P. Mund, E.P. Stephan. Adaptive multilevel BEM for acoustic scattering. Comput. Methods Appl. Mech. Eng., 150: 351–367, 1997.
  • [15] L. Piegl, W. Tiller. The NURBS book. Springer, New York, 1997.
  • [16] F.V. Postell, E.P. Stephan. On the h, p, and h-p versions for boundary element method – numerical results. Comput. Methods Appl. Mech. Eng., 83: 69–90, 1990.
  • [17] E.P. Stephan. The h-p boundary element method for solving 2- and 3-dimensional problems. Comput. Methods Appl. Mech. Eng., 133: 183–208, 1996.
  • [18] W.L. Wendland. Boundary element methods and their asymptotic convergence. In: P. Filippi [Ed.] Theoretical acoustics and numerical treatment, CISM Courses and Lectures, pp. 135–216, Springer, Vienna, 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a665f37b-1530-4670-ae61-cc54afda9dd6
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