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Galerkin boundary integral analysis for the axisymmetric Laplace equation
Author(s) -
Gray L. J.,
Garzon Maria,
Mantič Vladislav,
Graciani Enrique
Publication year - 2006
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/nme.1613
Subject(s) - mathematics , galerkin method , singularity , mathematical analysis , integral equation , laplace's equation , rotational symmetry , laplace transform , logarithm , symmetry (geometry) , boundary value problem , boundary (topology) , weight function , geometry , physics , finite element method , thermodynamics
The boundary integral equation for the axisymmetric Laplace equation is solved by employing modified Galerkin weight functions. The alternative weights smooth out the singularity of the Green's function at the symmetry axis, and restore symmetry to the formulation. As a consequence, special treatment of the axis equations is avoided, and a symmetric‐Galerkin formulation would be possible. For the singular integration, the integrals containing a logarithmic singularity are converted to a non‐singular form and evaluated partially analytically and partially numerically. The modified weight functions, together with a boundary limit definition, also result in a simple algorithm for the post‐processing of the surface gradient. Published in 2005 by John Wiley & Sons, Ltd.