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Making the boundary element method less sensitive to changes or errors in the input data
Author(s) -
Vable Madhukar
Publication year - 1987
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.1620240809
Subject(s) - boundary element method , discretization , mathematics , method of fundamental solutions , boundary knot method , singular boundary method , matrix (chemical analysis) , mathematical analysis , algebraic equation , boundary (topology) , boundary value problem , block matrix , finite element method , eigenvalues and eigenvectors , physics , structural engineering , engineering , nonlinear system , materials science , quantum mechanics , composite material
To solve a problem by the boundary element method requires a solution of an integral equation. By discretizing the boundary, the integral equation is reduced to a set of linear algebraic equations. If the matrix in algebraic equation is not diagonal dominant or more precisely, poorly conditioned, then the accuracy of the numerical solution becomes very sensitive to small changes in the input data. Small errors in the input data or changes in the mesh description can change the solution drastically. In this paper a scheme is described which improves the condition of the matrix. Furthermore, it also reduces the sensitivity of the condition of the matrix to changes in the mesh description. The ideas described are applicable to any boundary element formulation. However, the numerical examples are from two‐dimensional elastostatics solved by the indirect version of the boundary element method.