NURBS Miniapps
These miniapps demonstrate the use of NURBSbased Isogeometric analysis^{1},^{2}.
NURBS Ex 1: Laplace problem
This example code solves a simple Laplace problem
\begin{align}
\Delta u = 1
\end{align}
with
homogeneous Dirichlet boundary conditions.
For implementation see miniapps/nurbs/nurbs__ex1
.
NURBS Ex 3: Maxwell problem
This example code solves a simple 3D electromagnetic diffusion problem corresponding to the second order definite Maxwell equation \begin{align} \nabla\times\nabla\times\, E + E = f \end{align} with boundary condition $ E \times n $ = "given tangential field". Here, we use a given exact solution $E$ and compute the corresponding r.h.s. $f$. We discretize with Nedelec finite elements in 2D or 3D.
The example demonstrates the use of $H(curl)$ finite element
spaces with the curlcurl and the (vector finite element) mass
bilinear form, as well as the computation of discretization
error when the exact solution is known. Static condensation is
also illustrated.
For implementation see miniapps/nurbs/nurbs__ex1
.
NURBS Ex 5: Darcy problem
This example code solves a simple 2D/3D mixed Darcy problem
corresponding to the saddle point system
\begin{align}
\begin{array}{rcl}
k\,{\bf u} + {\rm grad}\,p &=& f \\
{\rm div}\,{\bf u} &=& g
\end{array}
\end{align}
with natural boundary condition $p = $ "given pressure".
Here we use a given exact solution $({\bf u},p)$ and compute the
corresponding right hand side $(f, g)$. We discretize with RaviartThomas
finite elements (velocity $\bf u$) and piecewise discontinuous
polynomials (pressure $p$).
For implementation see miniapps/nurbs/nurbs__ex5
.

T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs: "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Computer Methods in Applied Mechanics and Engineering, Elsevier, 2005, 194 (3941), pp.41354195. ↩

T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs: "Isogeometric analysis: toward integration of CAD and FEA", Wiley&Sons 2009 ↩