Provided by:
librheolefdev_6.61build2_amd64 NAME
characteristic  the LagrangeGalerkin method implemented
SYNOPSYS
The class characteristic implements the LagrangeGalerkin method:
It is the extension of the method of characteristic from the finite
difference to the finite element context.
EXAMPLE
Consider the bilinear form lh defined by
/

lh(x) =  uh(x+dh(x)) v(x) dx

/ Omega
where dh is a deformation vector field.
The characteristic is defined by X(x)=x+dh(x)
and the previous integral writes equivalently:
/

lh(x) =  uh(X(x)) v(x) dx

/ Omega
For instance, in LagrangeGalerkin methods,
the deformation field dh(x)=dt*uh(x)
where uh is the advection field and dt a time step.
The following code implements the computation of lh:
field dh = ...;
field uh = ...;
characteristic X (dh);
test v (Xh);
field lh = integrate (compose(uh, X)*v, qopt);
The GaussLobatto quadrature formule is recommended for
LagrangeGalerkin methods.
The order equal to the polynomial order of Xh
(order 1: trapeze, order 2: simpson, etc).
Recall that this choice of quadrature formulae guaranties inconditional
stability at any polynomial order.
Alternative quadrature formulae or order can be used by using the
additional quadrature option argument to the integrate function see integrate(4).
IMPLEMENTATION
template<class T, class M = rheo_default_memory_model>
class characteristic_basic : public smart_pointer<characteristic_rep<T,M> > {
public:
typedef characteristic_rep<T,M> rep;
typedef smart_pointer<rep> base;
// allocator:
characteristic_basic(const field_basic<T,M>& dh);
// accesors:
const field_basic<T,M>& get_displacement() const;
const characteristic_on_quadrature<T,M>&
get_pre_computed (
const space_basic<T,M>& Xh,
const field_basic<T,M>& dh,
const quadrature_option_type& qopt) const;
};
typedef characteristic_basic<Float> characteristic;
SEE ALSO
integrate(4)