Engineering analysis with CAD-based macroelements

Older and contemporary CAD-based interpolations, either for surfaces or for volume blocks, are capable of creating sets of basis functions on which finite-element (Galerkin–Ritz) and global collocation procedures can be supported. For some of these interpolations, this paper investigates the quality of the relevant numerical solution in several 2D and 3D engineering problems. It is shown that the global character of all these CAD interpolations ensures excellent numerical solution, although somewhere the boundary may be slightly violated. The study deals with several benchmark tests that span a large part in the spectrum of engineering analysis, from potential problems (Poisson equation-electrostatics and acoustics) to elasticity ones (beam in torsion, plate bending: statics and dynamics).