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A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and nonlinear boundary value problems. (English) Zbl 0957.74077
From the summary: We present a meshless method for solving linear and nonlinear boundary value problems, based on the local boundary integral equation method (LBIE) and the moving least squares approximation. The implementation of the LBIE formulation is described for linear and nonlinear problems with the linear part of differential operator being of Helmholtz-type. For nonlinear problems, we give additionally the total formulation and a rate formulation. The present method is a true meshless one, as it does not need domain and boundary elements to deal with the volume and boundary integrals. Numerical examples are presented for several linear and nonlinear problems, for which exact solutions are available.

##### MSC:
 74S15 Boundary element methods applied to problems in solid mechanics 65N38 Boundary element methods for boundary value problems involving PDEs
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