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Projection
1. Nodal Projection
An important keyword is project which allows to compute the
interpolant of an expression with respect to a nodal function space over a part of the mesh or the whole mesh. The interface is as follows
project( _space=<nodal function space in which the interpolant lives>
_range=<domain range iterators>,
_expr=<expression to be interpolated>, .... )Here are some examples:
typedef FunctionSpace<Mesh<Simplex<$d$>,
bases<Lagrange<1,Vectorial> > > Xhv_type;
auto Xhv = Xhv_type::New( mesh );
// build a piecewise $\P_1$ vectorial function in Xhv containing the
// coordinates of the vertices the mesh.
auto coord = project( _space=Xhv, _range=elements(mesh), _expr=P() );
// compute the x derivative of the coord function
auto dx_coord = project( _space=Xhv, _range=elements(mesh), _expr=dxv(coord) );
auto dy_coord = project( _space=Xhv, _range=elements(mesh), _expr=dyv(coord) );