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 _______________________________________________ Mailing list: https://launchpad.net/~dolfin Post to : [email protected] Unsubscribe : https://launchpad.net/~dolfin More help : https://help.launchpad.net/ListHelp
