Provided by: librheolef-dev_7.0-3_amd64 #### 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.

```

#### SYNOPSIS

```        Float integrate (geo domain);
Float integrate (geo domain, quadrature_option qopt);
Value integrate (geo domain, Expression, quadrature_option qopt);

field integrate (Expression);
field integrate (geo domain, Expression);
field integrate (geo domain, Expression, quadrature_option qopt);

form integrate (Expression);
form integrate (Expression, integrate_option qopt);
form integrate (geo domain, Expression);
form integrate (geo domain, Expression, integrate_option qopt);

```

#### EXAMPLE

```       For computing the measure of a domain:

Float meas_omega = integrate (omega);

For computing the integral of a function:

Float f (const point& x);
...
qopt.set_order (3);
Float int_f = integrate (omega, f, qopt);

the computation of the integral.   The  function  can  be  replaced  by  any  field-valued
expression  (see  field(2)).  For computing a right-hand-side of a variational formulation
with the previous function f:

space Xh (omega, "P1");
test v (Xh);
field lh = integrate (f*v);

For computing a bilinear form:

trial u (Xh);
test v (Xh);
form m = integrate (u*v);

The expression u*v can be replaced by any bilinear expression (see field(2)).

```

#### DEFAULTARGUMENTS

```       In the case of a linear or bilinear form, the domain is optional: by  default  it  is  the
full  domain  definition of the test function.  Also, the quadrature formulae is optional:
by default, its order is 2*k+1 where k is the polynomial degree of the Xh space associated
to the test function v.  When both a test u and trial v functions are supplied, let k1 and
k2 be their polynomial degrees.  Then the default quadrature is  chosen  to  be  exact  at
least  for  k1+k2+1  polynoms.   When  the  integration  is performed 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);
field l3h = integrate ("boundary", f*v);

For convenience, only the domain name can be supplied.

```

#### SEEALSO

```       test(2), test(2), quadrature_option(2), field(2), field(2)

```

```       Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL  version