The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis

Abstract

In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. IN-TERNODES is an interpolation-based method that, on each interface of the configuration, exploits two independent interpolation operators to enforce the continuity of the traces and of the normal derivatives. INTERNODES easily handles both parametric and geometric NURBS non-conformity. We specify how to set up the interpolation matrices on non-conforming interfaces, how to enforce the continuity of the normal derivatives and we give special attention to implementation aspects. The numerical results show that INTERNODES exhibits optimal convergence rate with respect to the mesh size of the NURBS spaces an that it is robust with respect to jumping coefficients.

Conservation of Forces and Total Work at the Interface Using the Internodes Method

“…If the meshes are conforming at the interface, then the interpolation matrices P 12 and P 21 are in fact the identity matrix and M Γ 2 = M Γ 1 . It follows that the Internodes method (15) reduces to…”

“…Its analysis for 2D and 3D second-order elliptic equations has been carried out in [ 16 ] and its generalization to decompositions with more than two subdomains is presented in [ 16 , 19 ]. The Internodes method has also been applied in the context of Isogeometric Analysis [ 15 ] to deal with non-conforming multi-patch geometries. For what concerns the theoretical analysis, it has been proved in [ 16 ] that, when the mesh sizes h 1 and h 2 of the two subdomains vanish with the same rate and the local polynomial degree p (the same in both subdomain) grows up, the Internodes method features the same convergence order of the Mortar method in the H 1 -broken norm error.…”