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# band - compute the band arround a level set

 band(2rheolef) rheolef-6.7 band(2rheolef)

## NAME

band - compute the band arround a level set

## DESCRIPTION

Given a function fh defined in a domain Lambda, 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)).

## ACCESSORS

Each side in the surface mesh, as returned by the level_set member function, is included into an element of the band mesh, as returned by the band 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 sid_ie2bnd_ie member functions.

## BAND TOPOLOGY AND DOMAINS

For the direct resolution of systems posed on the band, the mesh returned by the band() provides some domains of vertices. The "zero" vertex domain lists all vertices xi such that fh(xi)=0. The "isolated" vertex domain lists all vertices xi such that fh(xi)!=0 and xi is contained by only one element K and all vertices xj!=xi of K satifies fh(xj)=0. Others vertices of the band, separated by the zero and isolated ones, are organizd by connected components: the n_connex_component member function returns its number. Corresponding vertex domains of the band are named "cc<i>" where <i> should be replaced by any number between 0 and n_connex_component-1.

## IMPLEMENTATION

```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;

```