.TH "integrate_option" 3rheolef "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
integrate_option \- expression integration options (rheolef-7\&.2)
.PP
    
.SH "DESCRIPTION"
.PP
This class sends options to the \fBintegrate(3)\fP function, when building a \fBform(2)\fP or a \fBfield(2)\fP\&.
.PP
Its allows one to choose the quadrature formula used during the numerical integration (Gauss, Gauss-Lobatto, etc) and the polynomial degree that is exactly integrated\&. This exactly integrated polynomial degree is called here the \fCorder\fP of the quadrature formula\&. See also \fBquadrature(1)\fP for examples of quadrature formula\&.
.PP
In addition to the customization of the quadrature formula, the present class provides some booleaan flags, e\&.g\&. computation of the inverse matrix\&.
.SH "QUADRATURE FAMILIES"
.PP
\fCgauss\fP 
.PP
.RS 4
 The Gauss formula is the default\&. 
.RE
.PP
\fCgauss_lobatto\fP 
.PP
.RS 4
 The Gauss-Lobatto formula is useful in some cases, e\&.g\&. when using the method of \fBcharacteristic(2)\fP\&. It is actually implemented for order <= 2\&. 
.RE
.PP
\fCgauss_radau\fP 
.PP
.RS 4
 The Gauss-Radau formula is another classical alternative\&. 
.RE
.PP
\fCmiddle_edge\fP 
.PP
.RS 4
 The nodes are located at the midle edge\&. This formula is useful in some special cases and its order is limited\&. 
.RE
.PP
\fCsuperconvergent\fP 
.PP
.RS 4
 Another special case, for testing superconvergence of the finite element method at some specific nodes\&. 
.RE
.PP
\fCequispaced\fP 
.PP
.RS 4
 When the solution has low regularity, e\&.g\&. is discontinuous across elements, this simple formula is also useful\&. In that case, the \fCorder\fP parameter refers to the number of nodes used and not to the degree of polynomial exactly integated\&. For instance, \fCorder=1\fP refers to the trapezoidal formulae and for the general case, there are \fCorder+1\fP nodes per edges\&. 
.RE
.PP
.SH "BOOLEAN FLAGS"
.PP
\fCinvert\fP 
.PP
.RS 4
 This flag, when set, performs a local inversion on the matrix at the element level: This procedure is allowed only when the global matrix is block diagonal, e\&.g\&. for discontinuous or bubble approximations\&. This property is true when basis functions have a compact support inside exactly one element\&. Default is \fCinvert=false\fP\&. 
.RE
.PP
\fCignore_sys_coord\fP 
.PP
.RS 4
 This flag has effects only for axisymmetric coordinate systems\&. When set, it omits the \fCr\fP weight in the \fCr dr dz\fP measure during the numerical integration performed the \fBintegrate(3)\fP function\&. This feature is useful for computing the stream function in the axisymmetric case\&. Default is \fCignore_sys_coord=false\fP\&. 
.RE
.PP
\fClump\fP 
.PP
.RS 4
 This flag, when set, performs a \fImass lumping\fP procedure on the matrix at the element level: 
.RE
.PP
a(i,i) += sum(j!=i) a(i,j)
.PP
.RS 4
 The resulting matrix is diagonal\&. This feature is useful for computing a diagonal approximation of the mass matrix for the continuous \fCP1\fP element\&. Default is \fClump=false\fP\&. 
.RE
.PP
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file fem/geo_element/integrate_option\&.h
.PP
.PP
.nf

class integrate_option {
public:
// typedefs:

  typedef size_t size_type;

  typedef enum {
        gauss           = 0,
        gauss_lobatto   = 1,
        gauss_radau     = 2,
        middle_edge     = 3,
        superconvergent = 4,
        equispaced      = 5,
        max_family      = 6
  } family_type; // update also family_name[] in quatrature\&.cc

  static const size_type   unset_order    = std::numeric_limits<size_type>::max();
  static const size_type   default_order  = unset_order;
  static const family_type default_family = gauss;

// allocators:

  integrate_option(
        family_type ft = default_family,
        size_type   k  = default_order);

  integrate_option (const std::string& name);
  integrate_option (const integrate_option& iopt);
  integrate_option& operator= (const integrate_option& iopt);

// accessors & modifiers:

  std::string    name() const;
  size_t         get_order() const;
  family_type    get_family() const;
  std::string    get_family_name() const;
  void reset (const std::string& name);
  void set_order (size_t r);
  void set_family (family_type type);
  void set_family (std::string name);

// data:

  bool invert, ignore_sys_coord, lump;

.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.