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Conventionally, piecewise polynomials have been used in the boundary elementsmethod (BEM) to approximate unknown boundary values. Since infinitely smoothradial basis functions (RBFs) are more stable and accurate than the polynomialsfor high dimensional domains, the unknown values are approximated by the RBFsin this paper. Therefore, a new formulation of BEM, called radial BEM, isobtained. To calculate singular boundary integrals of the new method, wepropose a new distribution for boundary source points that removes singularityfrom the integrals. Therefore, the boundary integrals are calculated preciselyby the standard Gaussian quadrature rule (GQR) with n = 16 quadrature nodes.Several numerical examples are presented to check the efficiency of the radialBEM versus standard BEM and RBF collocation method for solving partialdifferential equations (PDEs). Analytical and numerical studies presented inthis paper admit the radial BEM as a perfect version of BEM which will enrichthe contribution of BEM and RBFs in solving PDEs, impressively.

Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently