.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
..
.TH band 2rheolef "rheolef-6.7" "rheolef-6.7" "rheolef-6.7"
.\" label: /*Class:
.SH NAME
\fBband\fP - compute the band arround a level set
.\" skip: @findex  level_set
.\" skip: @clindex field
.\" skip: @clindex geo
.PP
.SH DESCRIPTION

Given a function \fBfh\fP defined in a domain \fBLambda\fP,
compute the band of elements intersecting the
level set defined by {x in Lambda, fh(x) = 0}.
This class is used for solving problems defined on a
surface described by a level set function (See level_set(4)).
.PP
.SH ACCESSORS

Each side in the surface mesh, as returned by the \fBlevel_set\fP member
function, is included into an element of the band mesh, as returned by the
\fBband\fP member function. Moreover, in the distributed memory environment,
this correspondance is on the same process, so local indexes can be used
for this correspondance: this is the \fBsid_ie2bnd_ie\fP member functions.
.PP
.SH BAND TOPOLOGY AND DOMAINS

For the direct resolution of systems posed on the band, the mesh returned
by the \fBband()\fP provides some domains of vertices.
The \fB"zero"\fP vertex domain lists all vertices \fBxi\fP such that \fBfh(xi)=0\fP.
The \fB"isolated"\fP vertex domain lists all vertices \fBxi\fP
such that \fBfh(xi)!=0\fP and \fBxi\fP is contained by only one element \fBK\fP
and all vertices \fBxj!=xi\fP of \fBK\fP satifies \fBfh(xj)=0\fP.
Others vertices of the band, separated by the zero and isolated ones,
are organizd by connected components:
the \fBn_connex_component\fP member function returns its number.
Corresponding vertex domains of the band are named \fB"cc<i>"\fP
where \fB<i>\fP should be replaced
by any number between 0 and \fBn_connex_component-1\fP.
.\" END
.SH IMPLEMENTATION
.\" begin_example
.Sp
.nf
template <class T, class M = rheo_default_memory_model>
class band_basic {
public:

  typedef typename geo_basic<T,M>::size_type size_type;

// allocators:

  band_basic();
  band_basic(const field_basic<T,M>& fh,
    const level_set_option_type& opt = level_set_option_type());

/// accessors:

  const geo_basic<T,M>& band() const { return _band; }
  const geo_basic<T,M>& level_set() const { return _gamma; }
  size_type sid_ie2bnd_ie (size_type sid_ie) const { return _sid_ie2bnd_ie [sid_ie]; }
  size_type n_connected_component() const { return _ncc; }

// data:
protected:
  geo_basic<T,M>        _gamma;
  geo_basic<T,M>        _band;
  disarray<size_type,M> _sid_ie2bnd_ie;
  size_type             _ncc;
};
typedef band_basic<Float> band;
.Sp
.fi
.\" end_example

.\" LENGTH = 1
.SH SEE ALSO
level_set(4)