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The Almansi method of fundamental solutions for solving biharmonic problems
Author(s) -
Karageorghis Andreas,
Fairweather Graeme
Publication year - 1988
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.1620260714
Subject(s) - biharmonic equation , representation (politics) , mathematics , laplace transform , method of fundamental solutions , mathematical analysis , laplace's equation , boundary value problem , boundary (topology) , plane (geometry) , function (biology) , moving least squares , geometry , singular boundary method , finite element method , boundary element method , structural engineering , engineering , evolutionary biology , politics , political science , law , biology
A new fundamental solutions method for the numerical solution of two‐dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the approximate solution is expressed in terms of fundamental solutions of Laplace's equation, and is determined by a least squares fit of the boundary conditions. The results of numerical experiments which demonstrate the efficacy of the method are presented.