## Linux and UNIX Man Pages

Test Your Knowledge in Computers #219
Difficulty: Easy
When a data packet comes in to a port on a router, the router reads the network address information in the packet footer to determine the ultimate destination.
True or False?

# curl(3rheolef) [debian man page]

```curl(3rheolef)							    rheolef-6.1 						    curl(3rheolef)

NAME
curl -- curl operator

SYNOPSIS
form(const space V, const space& M, "curl");

DESCRIPTION
Assembly the form associated to the curl operator on finite element space.  In three dimensions, both V and M are vector-valued:

/
|
b(u,q) = |  curl(u).q dx
|
/ Omega

In  two	dimensions, only V is vector-valued.  The V space may be a either P2 finite element space, while the M space may be P1d.  See also
form(2) and space(2).

EXAMPLE
The following piece of code build the divergence form associated to the P2 approximation for a three dimensional geometry:

geo omega("cube");
space V(omega, "P2",  "vector");
space M(omega, "P1d", "vector");
form b(V, M, "curl");

while this code becomes in two dimension:

geo omega("square");
space V(omega, "P2",  "vector");
space M(omega, "P1d");
form b(V, M, "curl");

form(2), space(2)

rheolef-6.1							    rheolef-6.1 						    curl(3rheolef)```

## Check Out this Related Man Page

```s_grad_grad(3rheolef)						    rheolef-6.1 					     s_grad_grad(3rheolef)

NAME

SYNOPSIS

DESCRIPTION
Assembly  the  form associated to the -div(grad) variant operator on a finite element space V.  The V space may be a either P1 or P2 finite

/
|
|
/ Omega

The stream function on tri-dimensionnal cartesian coordinate systems is such that

u = curl psi
div psi = 0

where u is the velocity field. Taking the curl of the first relation, using the identity:

and using the div(psi)=0 relation leads to:

In  the	axisymmetric  case, the stream function psi is scalar ans is defined from the velocity field u=(ur,uz) by (see Batchelor, 6th ed.,
1967, p 543):

d psi			    d psi
uz = (1/r) -----	 and   ur = - (1/r) -----
d r			     d r

See also http://en.wikipedia.org/wiki/Stokes_stream_function .  Multiplying by rot(xi)=(d xi/dr, -d xi/dz), and integrating with r  dr  dz,
we get a well-posed variationnal problem:

a(psi,xi) = b(xi,u)

with

/
| (d psi d xi	 d psi d xi)
a(psi,xi) = | (----- ---- + ----- ----) dr dz
| ( d r  d r	  d z  d z )
/ Omega

and

/
| (d xi	    d xi   )
b(xi,u) = | (---- ur - ---- uz) r dr dz
| (d z	    d r    )
/ Omega

Notice  that  a	is  symmetric definite positive, but without the 'r' weight as is is usual for axisymmetric standard forms.  The b form is
named "s_curl", for the Stokes curl variant of the "curl" operator (see s_curl(3)) as it is closely related to  the  "curl"  operator,  but
differs by the r and 1/r factors, as:

(	  d (r xi)     d xi )
curl(xi) = ( (1/r) -------- ; - -----)
(	    d r        d z  )

while

( d xi       d xi )
s_curl(xi) = ( ----  ;  - ---- )
( d r        d z  )

EXAMPLE
The following piece of code build the form associated to the P1 approximation:

geo g("square");
space V(g, "P1");