A coupled IGA-Meshfree discretization of arbitrary order of accuracy and without global geometry parameterization

This article presents a novel approach for coupling of Isogeometric Analysis (IGA) and Meshfree discretizations. Taking advantage of the strengths of both techniques, we make IGA responsible for the representation of the exact geometry of the problem domain boundary, while the Reproducing Kernel Particle Method (RKPM) discretization is employed in the interior of the domain. The coupling procedure relies on the higher-order consistency or reproducing conditions that are directly imposed in the physical domain. The resulting IGA-RKPM coupling technique preserves the geometric exactness of IGA while circumventing the need for global volumetric parameterization of the problem domain, and achieves arbitrary-order approximation accuracy while maintaining higher-order smoothness of the discretization. Numerical examples demonstrate the optimal convergence properties of the coupled IGA-RKPM formulation, and show its effectiveness in constructing volumetric discretizations for complex-geometry objects.