## A boundary element-free method (BEFM) for two-dimensional potential problems.(English)Zbl 1160.65348

Summary: Combining the boundary integral equation (BIE) method and improved moving least-squares (IMLS) approximation, a direct meshless BIE method, which is called the boundary element-free method (BEFM), for two-dimensional potential problems is discussed in this paper. In the IMLS approximation, the weighted orthogonal functions are used as the basis functions; then the system of linear equations is not ill-conditioned and can be solved without obtaining the inverse matrix. Based on the IMLS approximation and the BIE for two-dimensional potential problems, the formulae of the BEFM are given. The BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily; thus, it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.

### MSC:

 65N38 Boundary element methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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### References:

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