def test_2D():
from proteus.Quadrature import GaussTriangle
polyOrders = [1, 2, 3]
quadOrderMax = 6
elements = [np.array([[0., 0.], [0., 1.], [1., 0.]])]
phiList = [[-1., -1., -1.], [1., 1., 1.], [-1., 1., 1.], [0., 1., 1.],
[1., 0., 0.]]
for nP in polyOrders:
for qO in range(nP, quadOrderMax):
quad = GaussTriangle(order=qO)
gf = eqp.Simplex(nSpace=2, nP=nP, nQ=len(quad.points))
for phi in phiList:
for e in elements:
b_0 = e[2, :] - e[0, :]
b_1 = e[1, :] - e[0, :]
Jac = np.array([b_0, b_1]).transpose()
dV = abs(np.linalg.det(Jac))
area = dV / 2.0
if phi[0] * phi[1] < 0.0 and phi[0] * phi[2] < 0.0:
theta0 = -phi[0] / (phi[1] - phi[0])
theta1 = -phi[0] / (phi[2] - phi[0])
x_0 = (1 - theta0) * e[0, :] + theta0 * e[1, :]
x_1 = (1 - theta1) * e[0, :] + theta1 * e[2, :]
b_0 = x_1 - e[0, :]
b_1 = x_0 - e[0, :]
Jac_0 = np.array([b_0, b_1]).transpose()
int_ImH_exact = np.linalg.det(Jac_0) / 2.0
int_H_exact = area - int_ImH_exact
int_D_exact = np.linalg.norm(x_1 - x_0)
if phi[0] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = int_H_exact
elif phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = area
int_D_exact = 0.0
elif phi[0] > 0.0:
int_H_exact = area
int_ImH_exact = 0.0
int_D_exact = 0.0
elif phi[0] == 0.0:
if phi[1] > 0.0:
int_H_exact = area
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[1] < 0.0:
int_H_exact = 0.0
int_ImH_exact = area
int_D_exact = 1.0
elif phi[1] == 0.0:
if phi[0] > 0.0:
int_H_exact = area
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = area
int_D_exact = 1.0
gf.calculate(
np.array(phi),
np.array([[e[0, 0], e[0, 1],
0.], [e[1, 0], e[1, 1], 0.],
[e[2, 0], e[2, 1], 0.]]),
np.array(quad.points))
int_H = 0.0
int_ImH = 0.0
int_D = 0.0
for k in range(len(quad.points)):
gf.set_quad(k)
int_H += quad.weights[k] * gf.H * dV
int_ImH += quad.weights[k] * gf.ImH * dV
int_D += quad.weights[k] * gf.D * dV
assert (int_H == approx(int_H_exact, 1e-15))
assert (int_ImH == approx(int_ImH_exact, 1e-15))
assert (int_D == approx(int_D_exact, 1e-15))
def test_3D():
from proteus.Quadrature import GaussTetrahedron
polyOrders = [2] #1,2,3]
quadOrderMax = 8
elements = [
np.array([[0., 0., 0.], [0., 0., 1.], [0., 1., 0.], [1., 0., 0.]]),
#np.array([[312.90104741, 109.12205319, 82.38957441],
# [371.40050898, 837.09283397, 117.87194133],
# [666.41881358, 107.49166421, 419.82032267],
# [659.82702468, 583.95327591, 217.72111178]])
]
#phiList = [[-348.3143481, -10.31124012, -2.73674249, 9.52267983]]
phiList = [[-1., -1., -1., -1.], [1., 1., 1., 1.], [-1., 1., 1., 1.],
[0., 1., 1., 1.], [1., 0., 0., 0.]]
for nP in polyOrders:
#cek hack: start at nP+1 because I think 2nd order tet rule is single precisionx
#therefore np==2 and q0 == 2 fails unless tol is reduced below
for qO in [4]: #range(nP+1,quadOrderMax):
quad = GaussTetrahedron(order=qO)
gf = eqp.Simplex(nSpace=3, nP=nP, nQ=len(quad.points))
for phi in phiList:
for e in elements:
b_0 = e[3, :] - e[0, :]
b_1 = e[2, :] - e[0, :]
b_2 = e[1, :] - e[0, :]
Jac = np.array([b_0, b_1, b_2]).transpose()
dV = abs(np.linalg.det(Jac))
volume = dV / 6.0
if phi[0] * phi[1] < 0.0 and phi[0] * phi[2] < 0.0 and phi[
0] * phi[3] < 0.0:
theta0 = -phi[0] / (phi[1] - phi[0])
theta1 = -phi[0] / (phi[2] - phi[0])
theta2 = -phi[0] / (phi[3] - phi[0])
x_0 = (1 - theta0) * e[0, :] + theta0 * e[1, :]
x_1 = (1 - theta1) * e[0, :] + theta1 * e[2, :]
x_2 = (1 - theta1) * e[0, :] + theta1 * e[3, :]
b_0 = x_2 - e[0, :]
b_1 = x_1 - e[0, :]
b_2 = x_0 - e[0, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = np.linalg.det(Jac_0) / 6.0
int_H_exact = volume - int_ImH_exact
int_D_exact = 0.5 * np.linalg.norm(
np.cross(x_2 - x_0, x_1 - x_0))
if phi[0] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = int_H_exact
elif phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = volume
int_D_exact = 0.0
elif phi[0] > 0.0:
int_H_exact = volume
int_ImH_exact = 0.0
int_D_exact = 0.0
elif phi[0] == 0.0:
if phi[1] > 0.0:
int_H_exact = volume
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[1] < 0.0:
int_H_exact = 0.0
int_ImH_exact = volume
int_D_exact = 1.0
elif phi[1] == 0.0:
if phi[0] > 0.0:
int_H_exact = volume
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = volume
int_D_exact = 1.0
gf.calculate(np.array(phi), e, np.array(quad.points))
int_H = 0.0
int_ImH = 0.0
int_D = 0.0
for k in range(len(quad.points)):
gf.set_quad(k)
int_H += quad.weights[k] * gf.H * dV
int_ImH += quad.weights[k] * gf.ImH * dV
int_D += quad.weights[k] * gf.D * dV
assert (int_H == approx(int_H_exact, 1e-15))
assert (int_ImH == approx(int_ImH_exact, 1e-15))
assert (int_D == approx(int_D_exact, 1e-15))
def test_1D():
from proteus.Quadrature import GaussEdge
polyOrders = [1, 2, 3]
quadOrderMax = 9
elements = [[0., 1.], [-2., 2.], [9., 10.]]
phiList = [[-1., -1.], [1., 1.], [-1., 1.], [0., 1.], [1., 0.]]
for nP in polyOrders:
for qO in range(nP, quadOrderMax):
quad = GaussEdge(order=qO)
gf = eqp.Simplex(nSpace=1, nP=nP, nQ=len(quad.points))
for phi in phiList:
for e in elements:
print(e, phi)
dV = e[1] - e[0]
assert (dV > 0)
if phi[0] * phi[1] < 0.0:
theta = -phi[0] / (phi[1] - phi[0])
x_0 = (1 - theta) * e[0] + theta * e[1]
int_H_exact = abs(e[1] - x_0)
int_ImH_exact = abs(x_0 - e[0])
int_D_exact = 1.0
if phi[0] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = int_H_exact
elif phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = dV
int_D_exact = 0.0
elif phi[0] > 0.0:
int_H_exact = dV
int_ImH_exact = 0.0
int_D_exact = 0.0
elif phi[0] == 0.0:
if phi[1] > 0.0:
int_H_exact = dV
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[1] < 0.0:
int_H_exact = 0.0
int_ImH_exact = dV
int_D_exact = 1.0
elif phi[1] == 0.0:
if phi[0] > 0.0:
int_H_exact = dV
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = dV
int_D_exact = 1.0
gf.calculate(np.array(phi),
np.array([[e[0], 0., 0.], [e[1], 0., 0.]]),
np.array(quad.points))
int_H = 0.0
int_ImH = 0.0
int_D = 0.0
for k in range(len(quad.points)):
gf.set_quad(k)
int_H += quad.weights[k] * gf.H * dV
int_ImH += quad.weights[k] * gf.ImH * dV
int_D += quad.weights[k] * gf.D * dV
assert (int_H == approx(int_H_exact, 1e-15))
assert (int_ImH == approx(int_ImH_exact, 1e-15))
assert (int_D == approx(int_D_exact, 1e-15))
def test_3D():
from proteus.Quadrature import GaussTetrahedron
polyOrders = [1, 2, 3]
quadOrderMax = 8
elements = [
np.array([[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]),
np.array([[659.82702468, 583.95327591, 217.72111178],
[312.90104741, 109.12205319, 82.38957441],
[371.40050898, 837.09283397, 117.87194133],
[666.41881358, 107.49166421, 419.82032267]]),
np.array([[1., 1., 0.5], [0., 0., 1.25], [0., 1., 0.5], [
0.,
0.,
0.5,
]])
]
phiList = [[-1., -1., -1., -1.], [1., 1., 1., 1.], [-1., 1., 1., 1.],
[1., -1., -1., -1.], [-1., 1., -1., -1.], [1., -1., 1., 1.],
[-1., 1., -1., -1.], [1., 1., -1., 1.], [-1., -1., 1., -1.],
[1., 1., 1., -1.], [-1., -1., -1., 1.], [-1., 1., 1., -1.],
[1., -1., -1., 1.], [-1., 1., 1., -1.], [-2., 3., 4., 5.],
[3., -2., -4., -5.], [-2., 3., -4., -5.], [3., -2., 4., 5.],
[-2., 3., -4., -5.], [3., 4., -2., 5.], [-2., -3., 4., -5.],
[3., 4., 5., -2.], [-2., -3., -4., 5.], [0., 1., 1., 1.],
[9.52267983, -348.3143481, -10.31124012, -2.73674249],
[-9.52267983, 348.3143481, -10.31124012, -2.73674249],
[-9.52267983, -348.3143481, 10.31124012, -2.73674249],
[-9.52267983, -348.3143481, -10.31124012, 2.73674249],
[0.5, -0.25, 0.5, 0.5]]
for nP in polyOrders:
for qO in range(nP, quadOrderMax):
quad = GaussTetrahedron(order=qO)
print("Simplex in ", 3, nP, len(quad.points))
gf = eqp.Simplex(nSpace=3, nP=nP, nQ=len(quad.points))
for phi in phiList:
for e in elements:
b_0 = e[3, :] - e[0, :]
b_1 = e[2, :] - e[0, :]
b_2 = e[1, :] - e[0, :]
Jac = np.array([b_0, b_1, b_2]).transpose()
dV = abs(np.linalg.det(Jac))
volume = dV / 6.0
if phi[0] < 0.0 and phi[1] > 0.0 and phi[2] > 0.0 and phi[
3] < 0.0:
print("====quad cut===== ", phi)
print("qO ", qO)
print("nP ", nP)
theta01 = 0.5 - 0.5 * (phi[1] + phi[0]) / (phi[1] -
phi[0])
theta02 = 0.5 - 0.5 * (phi[2] + phi[0]) / (phi[2] -
phi[0])
theta31 = 0.5 - 0.5 * (phi[1] + phi[3]) / (phi[1] -
phi[3])
theta32 = 0.5 - 0.5 * (phi[2] + phi[3]) / (phi[2] -
phi[3])
x_01 = (1 - theta01) * e[0, :] + theta01 * e[1, :]
x_02 = (1 - theta02) * e[0, :] + theta02 * e[2, :]
x_31 = (1 - theta31) * e[3, :] + theta31 * e[1, :]
x_32 = (1 - theta32) * e[3, :] + theta32 * e[2, :]
b_0 = x_01 - e[1, :]
b_1 = x_02 - e[1, :]
b_2 = x_31 - e[1, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = volume
int_H_exact = 0.0
int_D_exact = 0.0
int_H_exact += abs(np.linalg.det(Jac_0)) / 6.0
int_ImH_exact -= abs(np.linalg.det(Jac_0)) / 6.0
int_D_exact += 0.5 * np.linalg.norm(
np.cross(x_02 - x_01, x_32 - x_01))
b_0 = x_02 - e[2, :]
b_1 = x_32 - e[2, :]
b_2 = x_31 - e[2, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_H_exact += abs(np.linalg.det(Jac_0)) / 6.0
int_ImH_exact -= abs(np.linalg.det(Jac_0)) / 6.0
int_D_exact += 0.5 * np.linalg.norm(
np.cross(x_32 - x_01, x_31 - x_01))
b_0 = e[1, :] - x_02
b_1 = e[2, :] - x_02
b_2 = x_31 - x_02
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_H_exact += abs(np.linalg.det(Jac_0)) / 6.0
int_ImH_exact -= abs(np.linalg.det(Jac_0)) / 6.0
elif phi[0] > 0.0 and phi[1] < 0.0 and phi[
2] < 0.0 and phi[3] > 0.0:
print("====quad cut===== inside out", phi)
print("qO ", qO)
print("nP ", nP)
theta01 = 0.5 - 0.5 * (phi[1] + phi[0]) / (phi[1] -
phi[0])
theta02 = 0.5 - 0.5 * (phi[2] + phi[0]) / (phi[2] -
phi[0])
theta31 = 0.5 - 0.5 * (phi[1] + phi[3]) / (phi[1] -
phi[3])
theta32 = 0.5 - 0.5 * (phi[2] + phi[3]) / (phi[2] -
phi[3])
x_01 = (1 - theta01) * e[0, :] + theta01 * e[1, :]
x_02 = (1 - theta02) * e[0, :] + theta02 * e[2, :]
x_31 = (1 - theta31) * e[3, :] + theta31 * e[1, :]
x_32 = (1 - theta32) * e[3, :] + theta32 * e[2, :]
b_0 = x_01 - e[1, :]
b_1 = x_02 - e[1, :]
b_2 = x_31 - e[1, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = 0.0
int_H_exact = volume
int_D_exact = 0.0
int_H_exact -= abs(np.linalg.det(Jac_0)) / 6.0
int_ImH_exact += abs(np.linalg.det(Jac_0)) / 6.0
int_D_exact += 0.5 * np.linalg.norm(
np.cross(x_02 - x_01, x_32 - x_01))
b_0 = x_02 - e[2, :]
b_1 = x_32 - e[2, :]
b_2 = x_31 - e[2, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_H_exact -= abs(np.linalg.det(Jac_0)) / 6.0
int_ImH_exact += abs(np.linalg.det(Jac_0)) / 6.0
int_D_exact += 0.5 * np.linalg.norm(
np.cross(x_32 - x_01, x_31 - x_01))
b_0 = e[1, :] - x_02
b_1 = e[2, :] - x_02
b_2 = x_31 - x_02
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_H_exact -= abs(np.linalg.det(Jac_0)) / 6.0
int_ImH_exact += abs(np.linalg.det(Jac_0)) / 6.0
elif phi[0] * phi[1] < 0.0 and phi[0] * phi[
2] < 0.0 and phi[0] * phi[3] < 0.0:
theta0 = -phi[0] / (phi[1] - phi[0])
theta1 = -phi[0] / (phi[2] - phi[0])
theta2 = -phi[0] / (phi[3] - phi[0])
x_0 = (1 - theta0) * e[0, :] + theta0 * e[1, :]
x_1 = (1 - theta1) * e[0, :] + theta1 * e[2, :]
x_2 = (1 - theta2) * e[0, :] + theta2 * e[3, :]
b_0 = x_2 - e[0, :]
b_1 = x_1 - e[0, :]
b_2 = x_0 - e[0, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = abs(np.linalg.det(Jac_0)) / 6.0
int_H_exact = volume - int_ImH_exact
int_D_exact = 0.5 * np.linalg.norm(
np.cross(x_2 - x_0, x_1 - x_0))
if phi[0] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = tmp
elif phi[0] * phi[1] < 0.0 and phi[1] * phi[
2] < 0.0 and phi[1] * phi[3] < 0.0:
theta0 = -phi[1] / (phi[0] - phi[1])
theta1 = -phi[1] / (phi[2] - phi[1])
theta2 = -phi[1] / (phi[3] - phi[1])
x_0 = (1 - theta0) * e[1, :] + theta0 * e[0, :]
x_1 = (1 - theta1) * e[1, :] + theta1 * e[2, :]
x_2 = (1 - theta2) * e[1, :] + theta2 * e[3, :]
b_0 = x_2 - e[1, :]
b_1 = x_1 - e[1, :]
b_2 = x_0 - e[1, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = abs(np.linalg.det(Jac_0)) / 6.0
int_H_exact = volume - int_ImH_exact
int_D_exact = 0.5 * np.linalg.norm(
np.cross(x_2 - x_0, x_1 - x_0))
if phi[1] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = tmp
elif phi[0] * phi[2] < 0.0 and phi[1] * phi[
2] < 0.0 and phi[3] * phi[2] < 0.0:
theta0 = -phi[2] / (phi[0] - phi[2])
theta1 = -phi[2] / (phi[1] - phi[2])
theta2 = -phi[2] / (phi[3] - phi[2])
x_0 = (1 - theta0) * e[2, :] + theta0 * e[0, :]
x_1 = (1 - theta1) * e[2, :] + theta1 * e[1, :]
x_2 = (1 - theta2) * e[2, :] + theta2 * e[3, :]
b_0 = x_2 - e[2, :]
b_1 = x_1 - e[2, :]
b_2 = x_0 - e[2, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = abs(np.linalg.det(Jac_0)) / 6.0
int_H_exact = volume - int_ImH_exact
int_D_exact = 0.5 * np.linalg.norm(
np.cross(x_2 - x_0, x_1 - x_0))
if phi[2] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = tmp
elif phi[0] * phi[3] < 0.0 and phi[1] * phi[
3] < 0.0 and phi[2] * phi[3] < 0.0:
theta0 = -phi[3] / (phi[0] - phi[3])
theta1 = -phi[3] / (phi[1] - phi[3])
theta2 = -phi[3] / (phi[2] - phi[3])
x_0 = (1 - theta0) * e[3, :] + theta0 * e[0, :]
x_1 = (1 - theta1) * e[3, :] + theta1 * e[1, :]
x_2 = (1 - theta2) * e[3, :] + theta2 * e[2, :]
b_0 = x_2 - e[3, :]
b_1 = x_1 - e[3, :]
b_2 = x_0 - e[3, :]
Jac_0 = np.array([b_0, b_1, b_2]).transpose()
int_ImH_exact = abs(np.linalg.det(Jac_0)) / 6.0
int_H_exact = volume - int_ImH_exact
int_D_exact = 0.5 * np.linalg.norm(
np.cross(x_2 - x_0, x_1 - x_0))
if phi[3] > 0.0:
tmp = int_H_exact
int_H_exact = int_ImH_exact
int_ImH_exact = tmp
elif phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = volume
int_D_exact = 0.0
elif phi[0] > 0.0:
int_H_exact = volume
int_ImH_exact = 0.0
int_D_exact = 0.0
elif phi[0] == 0.0:
if phi[1] > 0.0:
int_H_exact = volume
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[1] < 0.0:
int_H_exact = 0.0
int_ImH_exact = volume
int_D_exact = 1.0
elif phi[1] == 0.0:
if phi[0] > 0.0:
int_H_exact = volume
int_ImH_exact = 0.0
int_D_exact = 0.0
if phi[0] < 0.0:
int_H_exact = 0.0
int_ImH_exact = volume
int_D_exact = 1.0
phi_in = np.array(phi)
print("phi in ", phi_in)
nodesIn = e
print("nodes in ", nodesIn)
print("quad in ", np.array(quad.points))
gf.calculate(phi_in, nodesIn, np.array(quad.points))
int_H = 0.0
int_ImH = 0.0
int_D = 0.0
for k in range(len(quad.points)):
gf.set_quad(k)
print("k ", k, gf.H, gf.ImH, gf.D)
int_H += quad.weights[k] * gf.H * dV
int_ImH += quad.weights[k] * gf.ImH * dV
int_D += quad.weights[k] * gf.D * dV
print("dV ", dV)
print(int_H, int_H_exact)
print(int_ImH, int_ImH_exact)
print(int_D, int_D_exact)
assert (int_H == approx(int_H_exact, 1e-12, 1e-12))
assert (int_ImH == approx(int_ImH_exact, 1e-12, 1e-12))
assert (int_D == approx(int_D_exact, 1e-11, 1e-11))