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NEW NUMERICAL INTEGRATION SCHEMES FOR APPLICATIONS OF GALERKIN BEM TO 2‐D PROBLEMS
Author(s) -
AIMI A.,
DILIGENTI M.,
MONEGATO G.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970615)40:11<1977::aid-nme150>3.0.co;2-o
Subject(s) - mathematics , galerkin method , piecewise , boundary element method , boundary value problem , integration by parts , integral equation , boundary (topology) , numerical integration , numerical analysis , polynomial , mathematical analysis , finite element method , physics , thermodynamics
We consider hypersingular integral formulation of some elasticity and potential boundary value problems on 2‐D domains. In particular, we consider all integrals whose evaluation is required when the equations are solved by a Galerkin BEM based on piecewise polynomial approximants of arbitrary local degrees. In order to compute these integrals, we use very efficient formulas recently proposed, which require the user to define a mesh, not necessarily uniform, on the boundary and specify the local degrees of the approximant. These rules are quite suitable for the construction of h – p version of the BEM. Implementation of h −, p − and h – p methods are applied to some classical problems and several numerical results are presented. © 1997 by John Wiley & Sons, Ltd.