  This paper presents a novel method for solving partial differential equations
on three-dimensional CAD geometries by means of immersed isogeometric
discretizations that do not require quadrature schemes. It relies on a new
developed technique for the evaluation of polynomial integrals over spline
boundary representations that is exclusively based on analytical computations.
First, through a consistent polynomial approximation step, the finite element
operators of the Galerkin method are transformed into integrals involving only
polynomial integrands. Then, by successive applications of the divergence
theorem, those integrals over B-Reps are transformed into first surface and
then line integrals with polynomials integrands. Eventually these line
integrals are evaluated analytically with machine precision accuracy. The
performance of the proposed method is demonstrated by means of numerical
experiments in the context of 2D and 3D elliptic problems, retrieving optimal
error convergence order in all cases. Finally, the methodology is illustrated
for 3D CAD models with an industrial level of complexity.

Numerical Analysis;Graphics;Numerical Analysis