dolfin team mailing list archive

[Neilen Marais <nmarais@xxxxxxxxx>]

Hi,

Has the calculation of auto quadrature order changed recently?

I've set up the electromagnetic near-to-farfield transform based on
the integral of tangential electric and magnetic fields around the
boundary of the problem. I got incorrect results on a canonical test
problem and wasn't sure of the source of the error. I'm evaluating
complex integrals like:

L =   surface_integral_over_Gamma( (-n x E(r_prime) )
e^(j*k0*dot(r_prime, r_hat))ds(r_prime) )

where E is the E-field vector, r_hat is a unit vector pointing in the
far-field observation direction and r_prime is the integration
coordinate and Gamma is the closed near-to-farfield transform surface.
Since the integrals are complex, I had to split them up into several
real integrals making the whole thing quite complicated. In real
components, the complex exponential is of course broken into sin/cos
terms. Since E is a vector quantity, I also needed to take the dot
product with unit vectors, so the final forms looked like:

from dolfin import *
V = FunctionSpace(mesh, "Nedelec 1st kind H(curl)", 2)
E_r = Function(V) # real part
E_i = Function(V) # imaginary part
....
phase = k0*dot(r_prime, rhat)
n = V.cell().n
rprime = V.cell().x

# theta and phi are the far-field observation angles
import math
rhat_ = math.sin(theta)*math.cos(phi), math.sin(theta)*math.sin(phi),
math.cos(theta)])
theta_hat_ = math.cos(theta)*N.cos(phi),
math.cos(theta)*math.sin(phi), -math.sin(theta)]
rhat = Constant(rhat_)
theta_hat = Constant(theta_hat_)

M_r = -cross(n, E_r)
M_i = -cross(n, E_i)
L_r_theta =  dot(theta_hat, M_r*cos(phase) - M_i*sin(phase))*ds # real
part of Theta component of L

After some experimentation I manually specified the integration order,
and suddenlty the results seemed quite good! What is strange is that I
could not replecate the bad 'auto' order results, even by specifying
zero or first order integration. Today I upgraded my fenics
installation to the latest development version, and now the auto
results are also looking good. I realise that the inclusion of the
cos/sin terms complicate matters somewhat, but I would just like to
have a feeling for what is going on with the auto quadrature. Would it
be sensible to leave the quadrature order default at 'auto' going
forward, or should I rather be setting it explicitly?

Thanks
Neilen