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 (Expression, quadrature_option qopt);
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);
...
quadrature_option qopt;
qopt.set_order (3);
Float int_f = integrate (omega, f, qopt);
The last argument specifies the quadrature formulae (see quadrature_option(2))
used for 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)).
DEFAULT ARGUMENTS¶
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.
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.