Boundary integral tolerance too large

[SteinStoter]

Hi,

I'm working on a case where I have pretty widely varying coefficients (space on micro-scale and field values at unit scale). This is giving me some tolerance issues for creating the 'constraint' vector. Here a MWE:

from nutils.expression_v2 import Namespace
import numpy as np

# Immersed grid parameters
height = 10E-6
width = 50E-6
nelems = 80
rotation = 0.24680893346957228

# Construct the rotated immersed domain
ambient_domain, geometry = mesh.rectilinear([np.linspace(-width/2, width/2, nelems+1)]*2)
R = np.mat( [[np.cos(rotation),-np.sin(rotation)],[np.sin(rotation),np.cos(rotation)]] )
geometry = function.matmul(R,geometry)
ns = Namespace()
ns.x = geometry
trimfunc =  f"{height/2} - abs( x_1 )"
domain = ambient_domain.trim(trimfunc@ns, maxrefine=3)
ns.define_for('x', gradient='∇', normal='n', jacobians=('dV', 'dS'))

# Construct function space for the potential field
ns.basis = domain.basis('spline', degree=3, continuity=2)
ns.φ = function.dotarg('φ', ns.basis)

# Project linear function on domain boundaries
sqr = domain.boundary["left"].integral('(φ - 2E5 x_1)^2 dS' @ ns, degree=2)
cons = solver.optimize(('φ',), sqr, droptol=1e-15)
cons['φ'] = np.nan_to_num(cons['φ'])

# Checks
length_L = domain.boundary["left"].integrate('1 dS'@ns, degree=2)
phi_int_L = domain.boundary["left"].integrate('φ dS'@ns, arguments=cons, degree=2)
print("Error in height:", length_L - height/np.cos(rotation)) # Should be 0
print("Error in integral:", phi_int_L) # Should be 0
print("Error coefficients:", sum(cons['φ'])) # Should be 0?

When you run that, you'll see that the integral of phi on the left boundary is ~E-10. I really need to push this down at least some orders of magnitude to avoid numerical artifacts.

Any thoughts on how to do that?

Best,
Stein