A sub-domain RPIM with condensation of degree of freedom

A sub-domain radial point interpolation method is proposed to simulate problem of linear elasticity. In present method, the problem domain is firstly divided into sub-domains with arbitrary shape, and then, nodes without connectivity are imbedded in every sub-domain. The local variational weak formulation is established over sub-domains, in which nodes within the sub-domain are used for approximation. Local discrete equations of weak form are simplified by condensation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on sub-domains. Compatibility of displacement in adjacent sub-domains and convergence of present method are discussed. And displacements and its gradient are continuous in the entire problem domain. In contrast to an early formulation of RPIM based on Galerkin weak form, which is proposed by Liu and coworkers, certain modifications are presented to increase its computational efficiency in this paper. Numerical examples show that computational efficiency of present method is higher than that of standard RPIM based on Galerkin weak form, and good accuracy, high convergence can also be obtained.