.TH "band" 2rheolef "Sat Mar 13 2021" "Version 7.1" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
band \- banded level set method (rheolef-7\&.1)
.PP
.SH "DESCRIPTION"
.PP
Let \fCfh\fP be a finite element function defined on a geometric domain \fCLambda\fP\&. Then, the set of elements intersecting the zero level set is defined by \fC{x in Lambda, fh(x) = 0}\fP and is called a \fIband\fP\&. This class represents such a band: it is used for solving problems defined on a surface, when the surface itself is implicitly defined by a \fBlevel_set(3)\fP function\&.
.SH "ACESSORS"
.PP
Each side in the surface mesh, as returned by the \fClevel_set\fP member function, is included into an element of the band mesh, as returned by the \fCband\fP member function\&. Moreover, in the distributed memory environment, this correspondence is on the same local memory, so local indexes can be used for this correspondence: it is provided by the \fCsid_ie2bnd_ie\fP member function\&.
.SH "TOPOLOGY AND DOMAINS"
.PP
For the direct resolution of systems posed on the band, the mesh returned by the \fCband()\fP member function provides some domains of vertices\&. The \fC'zero'\fP vertex domain lists all vertices \fCxi\fP such that \fCfh(xi)=0\fP\&. The \fC'isolated'\fP vertex domain lists all vertices \fCxi\fP such that \fCfh(xi)!=0\fP and \fCxi\fP is contained by only one element \fCK\fP and all vertices \fCxj!=xi\fP of \fCK\fP satisfies \fCfh(xj)=0\fP\&. Others vertices of the band, separated by the zero and isolated ones, are organized by connected components: the \fCn_connex_component\fP member function returns its number\&. Corresponding vertex domains of the band are named \fC'cci'\fP where \fIi\fP should be replaced by any number between 0 and \fCn_connex_component-1\fP, e\&.g\&. \fCcc0\fP, \fCcc1\fP, etc\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file main/lib/band\&.h
.PP
The \fCband\fP class is simply an alias to the \fC\fBband_basic\fP\fP class
.PP
.PP
.nf
typedef band_basic<Float> band;
.fi
.PP
\fB\fP
.RS 4
.RE
.PP
The \fC\fBband_basic\fP\fP class provides an interface, via the \fBsmart_pointer(7)\fP class family, to a mesh container:
.PP
.PP
.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& opt = level_set_option());

// 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; }
.fi
.PP
.PP
.nf
};
.fi
.PP

.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH COPYRIGHT
Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr>
GPLv3+: GNU GPL version 3 or later  <http://gnu.org/licenses/gpl.html>.
This  is  free  software:  you  are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.