On adaptive refinement analysis for the coupled boundary element method : reproducing kernel particle method

An adaptive refinement procedure for the coupled boundary element-reproducing kernel particle method (coupled BE-RKPM) is suggested. The procedure is developed by combining a h-adaptive BEM refinement scheme based on the residual approach and an adaptive RKPM refinement scheme based on an extraction type a posteriori error estimator. During the adaptive refinement process for the coupled analysis, the displacement compatibility condition along the interface boundary of the BEM and the RKPM domains is maintained by using a penalty approach and a simple node spacing adjustment procedure. Thus, no specially formulated finite element is required along the interface boundary between the RKPM and the BEM domains. Numerical examples show that the suggested procedure significantly reduces the effect of singularity and nearly optimal convergence rate is obtained.Accepted versio