Making the boundary element method less sensitive to changes or errors in the input data

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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. Copyright © 1987 John Wiley & Sons, Ltd

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International Journal for Numerical Methods in Engineering