def test_fast_stiffness_geo_2d():
kv = bspline.make_knots(3, 0.0, 1.0, 15)
geo = geometry.bspline_quarter_annulus()
A = stiffness_fast((kv,kv), geo, verbose=0)
A_ref = read_sparse_matrix(os.path.join(os.path.dirname(__file__),
"poisson_neu_d2_p3_n15_stiff.mtx.gz"))
assert abs(A - A_ref).max() < 1e-9
def test_mass_geo_2d():
kv = bspline.make_knots(3, 0.0, 1.0, 15)
geo = geometry.bspline_quarter_annulus()
M = mass((kv,kv), geo)
M_ref = read_sparse_matrix(os.path.join(os.path.dirname(__file__),
"poisson_neu_d2_p3_n15_mass.mtx.gz"))
assert abs(M - M_ref).max() < 1e-14
def test_animate_field():
kvs = 2 * (bspline.make_knots(2, 0.0, 1.0, 5),)
fields = [ bspline.BSplineFunc(kvs,
approx.interpolate(kvs, lambda x,y: np.sin(t+x) * np.exp(y)))
for t in range(3) ]
anim = animate_field(fields, geo=geometry.bspline_quarter_annulus(), res=10)
anim.to_jshtml()
def test_divdiv_geo_2d():
kv = bspline.make_knots(3, 0.0, 1.0, 15)
geo = geometry.bspline_quarter_annulus()
A = divdiv((kv,kv), geo, layout='packed')
# construct divergence-free function
from pyiga.approx import interpolate
u = interpolate((kv,kv), lambda x,y: (x,-y), geo=geo).ravel()
assert abs(A.dot(u)).max() < 1e-12
def test_compare_intproj():
f = lambda x,y: np.cos(x)*np.exp(y)
kvs = 2 * (bspline.make_knots(3, 0.0, 1.0, 50),)
x1 = interpolate(kvs, f)
x2 = project_L2(kvs, f)
assert abs(x1-x2).max() < 1e-5
geo = geometry.bspline_quarter_annulus()
x1 = interpolate(kvs, f, geo=geo)
x2 = project_L2(kvs, f, f_physical=True, geo=geo)
assert abs(x1-x2).max() < 1e-5
def test_divdiv_geo_2d():
kv = bspline.make_knots(3, 0.0, 1.0, 15)
geo = geometry.bspline_quarter_annulus()
A = divdiv((kv,kv), geo, layout='packed', format='bsr')
# construct divergence-free function
u = interpolate((kv,kv), lambda x,y: (x,-y), geo=geo)
assert abs(A.dot(u.ravel())).max() < 1e-12
# test blocked layout
A = divdiv((kv,kv), geo, layout='blocked')
u_blocked = np.moveaxis(u, -1, 0) # move last axis to the front
assert abs(A.dot(u_blocked.ravel())).max() < 1e-12
def test_hierarchical_assemble():
hs = create_example_hspace(p=4, dim=2, n0=4, disparity=1, num_levels=3)
geo = geometry.bspline_quarter_annulus()
hdiscr = HDiscretization(hs, vform.stiffness_vf(dim=2), {'geo': geo})
A = hdiscr.assemble_matrix()
# compute matrix on the finest level for comparison
A_fine = assemble.stiffness(hs.knotvectors(-1), geo=geo)
I_hb = hs.represent_fine()
A_hb = (I_hb.T @ A_fine @ I_hb)
assert np.allclose(A.A, A_hb.A)
#
A3 = assemble.assemble(vform.stiffness_vf(dim=2), hs, geo=geo)
assert np.allclose(A.A, A3.A)
#
def f(x, y):
return np.cos(x) * np.exp(y)
f_hb = assemble.inner_products(
hs.knotvectors(-1), f, f_physical=True, geo=geo).ravel() @ I_hb
f2 = assemble.assemble('f * v * dx', hs, f=f, geo=geo)
assert np.allclose(f_hb, f2)