Parametric stitching for smooth coupling of subdomains with non-matching discretizations

Abstract

Incompatible parametric subdomains are common in computer-aided design (CAD) and in computer-aided engineering (CAE). In this paper, we present a unified formulation to smoothly couple non-matching parametric domains for both geometric modeling and analysis of behavior. The key concept used to accomplish the coupling is a “parametric stitching” or p-stitching interface between the incompatible patches. Specifically, p-stitching permits independently varying fields with assured, arbitrary smoothness at the interface between the coupled subdomains. The developed procedure enables modular construction of coupling problems with compatible interfaces as well as the ability to characterize sharp changes in gradient, as at dissimilar material interfaces. Fundamental to the developed methodology is enriched field approximations. The base approximations in the subdomains are enriched by the interfacial fields constructed as a function of distance from the coupling interfaces. The proposed method is argued to be the smooth extension of the dual–primal method such as the localized version of the Lagrange multiplier method. In the present paper, non-uniform rational B-splines (NURBS) are chosen for discretizing the parametric subdomains. The developed procedure though is valid for other representations of subdomains whose basis functions obey partition of unity. We validate the proposed method through patch tests and demonstrate the approach on several two- and three-dimensional elastostatic as well as heat conduction numerical examples.