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Isoparametric, finite element, variational solution of integral equations for three‐dimensional fields
Author(s) -
Jeng G.,
Wexler A.
Publication year - 1977
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.1620110909
Subject(s) - mathematics , integral equation , fredholm integral equation , mathematical analysis , discretization , finite element method , electric field integral equation , boundary element method , physics , thermodynamics
An improved numerical method, based on a variational approach with isoparametric finite elements, is presented for the solution of the boundary integral equation formulation of three‐dimensional fields. The technique provides higher‐order approximation of the unknown function over a bounding surface described by two‐parameter, non‐planar elements. The integral equation is discretized through the Rayleigh–Ritz procedure. Convergence to the solution for operators having a positive‐definite component is guaranteed. Kernel singularities are treated by removing them from the relevant integrals and dealing with them analytically. A successive element iterative process, which produces the solution of the large dense matrix of the complete structure, is described. The discretization and equation solution take place one element at a time resulting in storage and computational savings. Results obtained for classical test models, involving scalar electrostatic potential and vector elastostatic displacement fields, demonstrate the technique for the solution of the Fredholm integral equation of the first kind. Solution of the Fredholm equation of the second kind is to be reported subsequently.