NAME

       integrate_option - expression integration options (rheolef-7.2)

DESCRIPTION

       This class sends options to the integrate(3) function, when building a form(2) or a
       field(2).

       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 order of the quadrature formula.
       See also quadrature(1) for examples of quadrature formula.

       In addition to the customization of the quadrature formula, the present class provides
       some booleaan flags, e.g. computation of the inverse matrix.

QUADRATURE FAMILIES

       gauss

           The Gauss formula is the default.

       gauss_lobatto

           The Gauss-Lobatto formula is useful in some cases, e.g. when using the method of
           characteristic(2). It is actually implemented for order <= 2.

       gauss_radau

           The Gauss-Radau formula is another classical alternative.

       middle_edge

           The nodes are located at the midle edge. This formula is useful in some special cases
           and its order is limited.

       superconvergent

           Another special case, for testing superconvergence of the finite element method at
           some specific nodes.

       equispaced

           When the solution has low regularity, e.g. is discontinuous across elements, this
           simple formula is also useful. In that case, the order parameter refers to the number
           of nodes used and not to the degree of polynomial exactly integated. For instance,
           order=1 refers to the trapezoidal formulae and for the general case, there are order+1
           nodes per edges.

BOOLEAN FLAGS

       invert

           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 invert=false.

       ignore_sys_coord

           This flag has effects only for axisymmetric coordinate systems. When set, it omits the
           r weight in the r dr dz measure during the numerical integration performed the
           integrate(3) function. This feature is useful for computing the stream function in the
           axisymmetric case. Default is ignore_sys_coord=false.

       lump

           This flag, when set, performs a mass lumping procedure on the matrix at the element
           level:

       a(i,i) += sum(j!=i) a(i,j)

           The resulting matrix is diagonal. This feature is useful for computing a diagonal
           approximation of the mass matrix for the continuous P1 element. Default is lump=false.

IMPLEMENTATION

       This documentation has been generated from file fem/geo_element/integrate_option.h

       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;

       };

AUTHOR

       Pierre  Saramito  <Pierre.Saramito@imag.fr>

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.