Blending NURBS and Lagrangian representations in isogeometric analysis

This article introduces a method for blending NURBS with Lagrangian representations in isogeometric analysis. In the blended representation, selected boundary edges or surfaces of a multivariate NURBS patch are parameterized in (rational) Lagrangian form. Lagrangian parameters are obtained by transforming the NURBS representation. The transformation, by construction, exactly preserves the original geometry. The transformation method is described in detail. In analysis, the blended form is useful for interfacing NURBS domains to finite element domains, or for imposing essential boundary conditions. The application is demonstrated using numerical examples.