Galerkin formulation and singularity subtraction for spectral solutions of boundary integral equations

Michael, Ofer; Barbone, Paul E.

doi:10.1002/(sici)1097-0207(19980115)41:1<95::aid-nme275>3.3.co;2-p

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“…Γu = Γ, Γp = ∅), the discretized displacement and traction are related by the following matrix equation, which comes directly from Eq. (23) and the regularized expressions (115), (116):…”

Section: Coupling Of Bem With Femmentioning

confidence: 99%

Symmetric Galerkin Boundary Element Method

Bonnet

Maier²,

Polizzotto³

2008

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This review concerns a methodology for solving numerically, to engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form; the discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager's sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions, some quadratic forms have a clear energy meaning, variational properties characterize the solutions and other results, invalid in traditional boundary element methods, enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, computer implementations. Areas and aspects which at present require further research are identified and comparative assessments are attempted with respect to traditional boundary integral-element methods.

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Section: Coupling Of Bem With Femmentioning

confidence: 99%