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Non‐singular boundary integral representation of potential field gradients
Author(s) -
Sladek V.,
Sladek J.
Publication year - 1992
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.1620330606
Subject(s) - mathematics , singular integral , discretization , boundary (topology) , representation (politics) , singular boundary method , mathematical analysis , field (mathematics) , singular point of a curve , singular solution , boundary value problem , point (geometry) , numerical analysis , regular singular point , integral equation , geometry , boundary element method , pure mathematics , finite element method , physics , politics , political science , law , thermodynamics
In this paper we derive the non‐singular boundary integral representation of the field gradients for two‐dimensional problems of classical potential field theory. Numerical implementation of this representation is developed too. The proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary. Since the integrands in this new method are finite at any internal point, accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary. Two test problems are analysed in which the numerical results computed by strongly singular, weakly singular and non‐singular integral representations are compared mutually and with exact solutions.