NAME

       integrate - integrate a function or an expression

DESCRIPTION

       Integrate an expression over a domain by using a quadrature formulae.  There are three main usages of the
       integrate  function,  depending  upon the type of the expression.  (i) When the expression is a numerical
       one, it leads to a numerical value.  (ii) When the  expression  involves  a  symbolic  test-function  see
       test(2), the result is a linear form, represented by the field class.  (iii) When the expression involves
       both   symbolic  trial- and test-functions see test(2), the result is a bilinear form, represented by the
       field class.

SYNOPSYS

        template <class T, class M, class Expr>
        T integrate (const geo_basic<T,M>& omega, Expr expr,
          quadrature_option_type qopt)

        template <class T, class M, class Expr>
        field integrate (const geo_basic<T,M>& omega, VFExpr expr,
          quadrature_option_type qopt)

        template <class T, class M, class Expr>
        form integrate (const geo_basic<T,M>& omega, VFExpr expr,
          form_option_type fopt)

EXAMPLE

         Float f (const point& x);
         ...
         quadrature_option_type qopt;
         Float value = integrate (omega, f, qopt);
         field lh = integrate (omega, f*v, qopt);

       The last argument specifies the quadrature formulae used  for  the  computation  of  the  integral.   The
       expression can be any function, classs-function or any linear or nonlinear field expression see field(2).

DEFAULT ARGUMENTS

       In  the case of a linear form, the domain is optional: by default it is the full domain definition of the
       test function.

         field l1h = integrate (f*v, qopt);

       When the integration is perfomed on a subdomain, this subdomain simply replace the first argument  and  a
       domain name could also be used:

         field l2h = integrate (omega["boundary"], f*v, qopt);
         field l3h = integrate ("boundary", f*v, qopt);

       The  quadrature  formulae  is  required,  except  when  a  test  and/or trial function is provided in the
       expression to integrate.  In that case, the quadrature formulae is deduced from the space containing  the
       test  (or  trial)  function.   When a test function is suppied, let k be its polynomial degree.  Then the
       default quadrature is choosen to be exact at least for 2*k+1  polynoms.   When  both  a  test  and  trial
       functions are suppied, let k1 and k2 be their polynomial degrees.  Then the default quadrature is choosen
       to  be  exact  at  least  for  k1+k2+1 polynoms.  Also, when the expression is a constant, the quadrature
       function is optional: in that case, the constant is also optional and the following call:

         Float meas = integrate (omega);

       is valid and returns the measure of the domain.

SEE ALSO

       test(2), test(2), field(2)

rheolef-6.5                                        rheolef-6.5                               integrate(4rheolef)