In this paper, general interpolating isogeometric boundary node method (IIBNM) and isogeometric boundary element method (IBEM) based on parameter space are proposed for 2D elasticity problems. In both methods, the integral cells and elements are defined in parameter space, which can reproduce the geometry exactly at all the stages. In IIBNM, the improved interpolating moving leastsquare method (IIMLS) is applied for field approximation and the shape functions have the delta function property.

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... e Lagrangian basis functions are used for field approximation in IBEM. Thus, the boundary conditions can be imposed directly in both methods. The shape functions are defined in 1D parameter space and no curve length needs to be computed. Besides, most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly. Numerical examples have demonstrated the accuracy of the proposed methods.