def test_dofs():
line = ufc_simplex(1)
T = ufc_simplex(2)
T.vertices = np.asarray([(0.0, 0.0), (1.0, 0.25), (-0.75, 1.1)])
MTW = MardalTaiWinther(T, 3)
Qline = make_quadrature(line, 6)
linebfs = expansions.LineExpansionSet(line)
linevals = linebfs.tabulate(1, Qline.pts)
for ed in range(3):
n = T.compute_scaled_normal(ed)
wts = np.asarray(Qline.wts)
vals = MTW.tabulate(0, Qline.pts, (1, ed))[(0, 0)]
nvals = np.dot(np.transpose(vals, (0, 2, 1)), n)
normal_moments = np.zeros((9, 2))
for bf in range(9):
for k in range(len(Qline.wts)):
for m in (0, 1):
normal_moments[bf,
m] += wts[k] * nvals[bf, k] * linevals[m, k]
right = np.zeros((9, 2))
right[3 * ed, 0] = 1.0
right[3 * ed + 2, 1] = 1.0
assert np.allclose(normal_moments, right)
for ed in range(3):
t = T.compute_edge_tangent(ed)
wts = np.asarray(Qline.wts)
vals = MTW.tabulate(0, Qline.pts, (1, ed))[(0, 0)]
tvals = np.dot(np.transpose(vals, (0, 2, 1)), t)
tangent_moments = np.zeros(9)
for bf in range(9):
for k in range(len(Qline.wts)):
tangent_moments[bf] += wts[k] * tvals[bf, k] * linevals[0, k]
right = np.zeros(9)
right[3 * ed + 1] = 1.0
assert np.allclose(tangent_moments, right)
def test_dofs():
line = ufc_simplex(1)
T = ufc_simplex(2)
T.vertices = np.random.rand(3, 2)
AW = ArnoldWinther(T, 3)
# check Kronecker property at vertices
bases = [[[1, 0], [0, 0]], [[0, 1], [1, 0]], [[0, 0], [0, 1]]]
vert_vals = AW.tabulate(0, T.vertices)[(0, 0)]
for i in range(3):
for j in range(3):
assert np.allclose(vert_vals[3*i+j, :, :, i], bases[j])
for k in (1, 2):
assert np.allclose(vert_vals[3*i+j, :, :, (i+k) % 3], np.zeros((2, 2)))
# check edge moments
Qline = make_quadrature(line, 6)
linebfs = expansions.LineExpansionSet(line)
linevals = linebfs.tabulate(1, Qline.pts)
# n, n moments
for ed in range(3):
n = T.compute_scaled_normal(ed)
wts = np.asarray(Qline.wts)
nqpline = len(wts)
vals = AW.tabulate(0, Qline.pts, (1, ed))[(0, 0)]
nnvals = np.zeros((30, nqpline))
for i in range(30):
for j in range(len(wts)):
nnvals[i, j] = n @ vals[i, :, :, j] @ n
nnmoments = np.zeros((30, 2))
for bf in range(30):
for k in range(nqpline):
for m in (0, 1):
nnmoments[bf, m] += wts[k] * nnvals[bf, k] * linevals[m, k]
for bf in range(30):
if bf != AW.dual.entity_ids[1][ed][0] and bf != AW.dual.entity_ids[1][ed][2]:
assert np.allclose(nnmoments[bf, :], np.zeros(2))
# n, t moments
for ed in range(3):
n = T.compute_scaled_normal(ed)
t = T.compute_edge_tangent(ed)
wts = np.asarray(Qline.wts)
nqpline = len(wts)
vals = AW.tabulate(0, Qline.pts, (1, ed))[(0, 0)]
ntvals = np.zeros((30, nqpline))
for i in range(30):
for j in range(len(wts)):
ntvals[i, j] = n @ vals[i, :, :, j] @ t
ntmoments = np.zeros((30, 2))
for bf in range(30):
for k in range(nqpline):
for m in (0, 1):
ntmoments[bf, m] += wts[k] * ntvals[bf, k] * linevals[m, k]
for bf in range(30):
if bf != AW.dual.entity_ids[1][ed][1] and bf != AW.dual.entity_ids[1][ed][3]:
assert np.allclose(ntmoments[bf, :], np.zeros(2))
# check internal dofs
Q = make_quadrature(T, 6)
qpvals = AW.tabulate(0, Q.pts)[(0, 0)]
const_moms = qpvals @ Q.wts
assert np.allclose(const_moms[:21], np.zeros((21, 2, 2)))
assert np.allclose(const_moms[24:], np.zeros((6, 2, 2)))
assert np.allclose(const_moms[21:24, 0, 0], np.asarray([1, 0, 0]))
assert np.allclose(const_moms[21:24, 0, 1], np.asarray([0, 1, 0]))
assert np.allclose(const_moms[21:24, 1, 0], np.asarray([0, 1, 0]))
assert np.allclose(const_moms[21:24, 1, 1], np.asarray([0, 0, 1]))
def test_dofs():
line = ufc_simplex(1)
T = ufc_simplex(2)
T.vertices = np.asarray([(0.0, 0.0), (1.0, 0.25), (-0.75, 1.1)])
AW = ArnoldWintherNC(T, 2)
Qline = make_quadrature(line, 6)
linebfs = expansions.LineExpansionSet(line)
linevals = linebfs.tabulate(1, Qline.pts)
# n, n moments
for ed in range(3):
n = T.compute_scaled_normal(ed)
wts = np.asarray(Qline.wts)
nqpline = len(wts)
vals = AW.tabulate(0, Qline.pts, (1, ed))[(0, 0)]
nnvals = np.zeros((18, nqpline))
for i in range(18):
for j in range(len(wts)):
nnvals[i, j] = n @ vals[i, :, :, j] @ n
nnmoments = np.zeros((18, 2))
for bf in range(18):
for k in range(nqpline):
for m in (0, 1):
nnmoments[bf, m] += wts[k] * nnvals[bf, k] * linevals[m, k]
for bf in range(18):
if bf != AW.dual.entity_ids[1][ed][0] and bf != AW.dual.entity_ids[
1][ed][2]:
assert np.allclose(nnmoments[bf, :], np.zeros(2))
# n, t moments
for ed in range(3):
n = T.compute_scaled_normal(ed)
t = T.compute_edge_tangent(ed)
wts = np.asarray(Qline.wts)
nqpline = len(wts)
vals = AW.tabulate(0, Qline.pts, (1, ed))[(0, 0)]
ntvals = np.zeros((18, nqpline))
for i in range(18):
for j in range(len(wts)):
ntvals[i, j] = n @ vals[i, :, :, j] @ t
ntmoments = np.zeros((18, 2))
for bf in range(18):
for k in range(nqpline):
for m in (0, 1):
ntmoments[bf, m] += wts[k] * ntvals[bf, k] * linevals[m, k]
for bf in range(18):
if bf != AW.dual.entity_ids[1][ed][1] and bf != AW.dual.entity_ids[
1][ed][3]:
assert np.allclose(ntmoments[bf, :], np.zeros(2), atol=1.e-7)
# check internal dofs
Q = make_quadrature(T, 6)
qpvals = AW.tabulate(0, Q.pts)[(0, 0)]
const_moms = qpvals @ Q.wts
assert np.allclose(const_moms[:12], np.zeros((12, 2, 2)))
assert np.allclose(const_moms[15:], np.zeros((3, 2, 2)))
assert np.allclose(const_moms[12:15, 0, 0], np.asarray([1, 0, 0]))
assert np.allclose(const_moms[12:15, 0, 1], np.asarray([0, 1, 0]))
assert np.allclose(const_moms[12:15, 1, 0], np.asarray([0, 1, 0]))
assert np.allclose(const_moms[12:15, 1, 1], np.asarray([0, 0, 1]))