def MatrixS3D(Coords, n, Coefficients, el_type, Upwinded):
E = Element(el_type)
Se = np.zeros((len(Coords), len(Coords)))
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
weights = [1, 1]
x_0 = Coefficients[6]
r_c = Coefficients[4]
for i in range(len(x_ip)):
for j in range(len(x_ip)):
for k in range(len(x_ip)):
N = E.N(x_ip[i], x_ip[j], x_ip[k])
N_T = N.transpose()
B, Jdet, G, J_inv = E.G_ext(x_ip[i], x_ip[j], x_ip[k], Coords)
B_T = B.transpose()
x_coord = np.array([Coords[:, 0]]) @ N_T
y_coord = np.array([Coords[:, 1]]) @ N_T
z_coord = np.array([Coords[:, 2]]) @ N_T
sigma = Coefficients[3](x_coord, y_coord, z_coord, r_c, x_0)
Se += -N_T * (
sigma) * N * Jdet * weights[i] * weights[j] * weights[k]
if Upwinded == True:
delta = CalcDelta3D(Coefficients,
[x_coord, y_coord, z_coord], n)
Se += -delta * np.dot(
B_T, n.transpose()
) * sigma * N * Jdet * weights[i] * weights[j] * weights[k]
return Se
def MatrixT2D(Coords, n, Coefficients, el_type, Upwinded):
E = Element(el_type)
Te = np.zeros((len(Coords), len(Coords)))
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
weights = [1, 1]
for i in range(len(x_ip)):
for j in range(len(x_ip)):
N = E.N(x_ip[i], x_ip[j], 0)
N_T = N.transpose()
B, Jdet, G, J_inv = E.G_ext(x_ip[i], x_ip[j], 0, Coords)
B_T = B.transpose()
Te += N_T * np.dot(n, B) * Jdet * weights[i] * weights[j]
if Upwinded == True:
x_coord = np.array([Coords[:, 0]]) @ N.transpose()
y_coord = np.array([Coords[:, 1]]) @ N.transpose()
delta = CalcDelta2D(Coefficients, [x_coord, y_coord], n)
Te += delta * np.dot(B_T, n.transpose()) * np.dot(
n, B) * Jdet * weights[i] * weights[j]
return Te
def MatrixK2D(Coords, n, Coefficients, el_type, Upwinded):
E = Element(el_type)
Ke = np.zeros((len(Coords), len(Coords)))
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
weights = [1, 1]
for i in range(len(x_ip)):
for j in range(len(x_ip)):
N = E.N(x_ip[i], x_ip[j], 0)
N_T = N.transpose()
B, Jdet, G, J_inv = E.G_ext(x_ip[i], x_ip[j], 0, Coords)
B_T = B.transpose()
x_coord = np.array([Coords[:, 0]]) @ N_T
y_coord = np.array([Coords[:, 1]]) @ N_T
kappa_and_sigma = (Coefficients[0](x_coord, y_coord) +
Coefficients[3](x_coord, y_coord))
Ke += N_T * (kappa_and_sigma) * N * Jdet * weights[i] * weights[j]
if Upwinded == True:
delta = CalcDelta2D(Coefficients, [x_coord, y_coord], n)
Ke += delta * np.dot(B_T, n.transpose(
)) * kappa_and_sigma * N * Jdet * weights[i] * weights[j]
return Ke
