def post_loop(self, d_idx, d_gradv, d_invtt, d_divv):
tt, invtt, idmat, gradv = declare('matrix(9)', 4)
augtt = declare('matrix(18)')
start_indx, row, col, rowcol, drowcol, dim = declare('int', 6)
dim = self.dim
start_indx = 9 * d_idx
identity(idmat, 3)
identity(tt, 3)
for row in range(3):
for col in range(3):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
gradv[rowcol] = d_gradv[drowcol]
for row in range(dim):
for col in range(dim):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
tt[rowcol] = d_invtt[drowcol]
augmented_matrix(tt, idmat, 3, 3, 3, augtt)
gj_solve(augtt, 3, 3, invtt)
gradvls = declare('matrix(9)')
mat_mult(gradv, invtt, 3, gradvls)
for row in range(dim):
d_divv[d_idx] += gradvls[row * 3 + row]
for col in range(dim):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
d_gradv[drowcol] = gradvls[rowcol]
def loop_all(self, d_idx, d_x, d_y, d_z, d_h, s_x, s_y, s_z, s_h, s_m,
s_rho, SPH_KERNEL, NBRS, N_NBRS, d_ai, d_gradai, d_bi, s_V,
d_gradbi):
x = d_x[d_idx]
y = d_y[d_idx]
z = d_z[d_idx]
h = d_h[d_idx]
i, j, k, s_idx, d, d2 = declare('int', 6)
alp, bet, gam, phi, psi = declare('int', 5)
xij = declare('matrix(3)')
dwij = declare('matrix(3)')
d = self.dim
d2 = d * d
m0 = 0.0
m1 = declare('matrix(3)')
m2 = declare('matrix(9)')
temp_vec = declare('matrix(3)')
temp_aug_m2 = declare('matrix(18)')
m2inv = declare('matrix(9)')
grad_m0 = declare('matrix(3)')
grad_m1 = declare('matrix(9)')
grad_m2 = declare('matrix(27)')
ai = 0.0
bi = declare('matrix(3)')
grad_ai = declare('matrix(3)')
grad_bi = declare('matrix(9)')
for i in range(3):
m1[i] = 0.0
grad_m0[i] = 0.0
bi[i] = 0.0
grad_ai[i] = 0.0
for j in range(3):
m2[3 * i + j] = 0.0
grad_m1[3 * i + j] = 0.0
grad_bi[3 * i + j] = 0.0
for k in range(3):
grad_m2[9 * i + 3 * j + k] = 0.0
for i in range(N_NBRS):
s_idx = NBRS[i]
xij[0] = x - s_x[s_idx]
xij[1] = y - s_y[s_idx]
xij[2] = z - s_z[s_idx]
hij = (h + s_h[s_idx]) * 0.5
rij = sqrt(xij[0] * xij[0] + xij[1] * xij[1] + xij[2] * xij[2])
wij = SPH_KERNEL.kernel(xij, rij, hij)
SPH_KERNEL.gradient(xij, rij, hij, dwij)
V = 1.0 / s_V[s_idx]
m0 += V * wij
for alp in range(d):
m1[alp] += V * wij * xij[alp]
for bet in range(d):
m2[d * alp + bet] += V * wij * xij[alp] * xij[bet]
for gam in range(d):
grad_m0[gam] += V * dwij[gam]
for alp in range(d):
fac = 1.0 if alp == gam else 0.0
temp = (xij[alp] * dwij[gam] + fac * wij)
grad_m1[d * gam + alp] += V * temp
for bet in range(d):
fac2 = 1.0 if bet == gam else 0.0
temp = xij[alp] * fac2 + xij[bet] * fac
temp2 = (xij[alp] * xij[bet] * dwij[gam] + temp * wij)
grad_m2[d2 * gam + d * alp + bet] += V * temp2
identity(m2inv, d)
augmented_matrix(m2, m2inv, d, d, d, temp_aug_m2)
# If is_singular > 0 then matrix was singular
is_singular = gj_solve(temp_aug_m2, d, d, m2inv)
if is_singular > 0.0:
# Cannot do much if the matrix is singular. Perhaps later
# we can tag such particles to see if the user can do something.
pass
else:
mat_vec_mult(m2inv, m1, d, temp_vec)
# Eq. 12.
ai = 1.0 / (m0 - dot(temp_vec, m1, d))
# Eq. 13.
mat_vec_mult(m2inv, m1, d, bi)
for gam in range(d):
bi[gam] = -bi[gam]
# Eq. 14. and 15.
for gam in range(d):
temp1 = grad_m0[gam]
for alp in range(d):
temp2 = 0.0
for bet in range(d):
temp1 -= m2inv[d * alp + bet] * (
m1[bet] * grad_m1[d * gam + alp] +
m1[alp] * grad_m1[d * gam + bet])
temp2 -= (m2inv[d * alp + bet] *
grad_m1[d * gam + bet])
for phi in range(d):
for psi in range(d):
temp1 += (m2inv[d * alp + phi] *
m2inv[d * psi + bet] *
grad_m2[d2 * gam + d * phi + psi] *
m1[bet] * m1[alp])
temp2 += (m2inv[d * alp + phi] *
m2inv[d * psi + bet] *
grad_m2[d2 * gam + d * phi + psi] *
m1[bet])
grad_bi[d * gam + alp] = temp2
grad_ai[gam] = -ai * ai * temp1
if N_NBRS < 2 or is_singular > 0.0:
d_ai[d_idx] = 1.0
for i in range(d):
d_gradai[d * d_idx + i] = 0.0
d_bi[d * d_idx + i] = 0.0
for j in range(d):
d_gradbi[d2 * d_idx + d * i + j] = 0.0
else:
d_ai[d_idx] = ai
for i in range(d):
d_gradai[d * d_idx + i] = grad_ai[i]
d_bi[d * d_idx + i] = bi[i]
for j in range(d):
d_gradbi[d2 * d_idx + d * i + j] = grad_bi[d * i + j]
def post_loop(self, d_idx, d_gradv, d_invtt, d_divv, d_grada, d_adivv,
d_ss, d_trssdsst):
tt = declare('matrix(9)')
invtt = declare('matrix(9)')
augtt = declare('matrix(18)')
idmat = declare('matrix(9)')
gradv = declare('matrix(9)')
grada = declare('matrix(9)')
start_indx, row, col, rowcol, drowcol, dim, colrow = declare('int', 7)
ltstart_indx, dltrowcol = declare('int', 2)
dim = self.dim
start_indx = 9 * d_idx
identity(idmat, 3)
identity(tt, 3)
for row in range(3):
for col in range(3):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
gradv[rowcol] = d_gradv[drowcol]
grada[rowcol] = d_grada[drowcol]
for row in range(dim):
for col in range(dim):
rowcol = row * 3 + col
drowcol = start_indx + rowcol
tt[rowcol] = d_invtt[drowcol]
augmented_matrix(tt, idmat, 3, 3, 3, augtt)
gj_solve(augtt, 3, 3, invtt)
gradvls = declare('matrix(9)')
gradals = declare('matrix(9)')
mat_mult(gradv, invtt, 3, gradvls)
mat_mult(grada, invtt, 3, gradals)
for row in range(dim):
d_divv[d_idx] += gradvls[row * 3 + row]
d_adivv[d_idx] += gradals[row * 3 + row]
for col in range(dim):
rowcol = row * 3 + col
colrow = row + col * 3
drowcol = start_indx + rowcol
d_gradv[drowcol] = gradvls[rowcol]
d_grada[drowcol] = gradals[rowcol]
d_adivv[d_idx] -= gradals[rowcol] * gradals[colrow]
# Traceless Symmetric Strain Rate
divvbydim = d_divv[d_idx] / dim
start_indx = d_idx * 9
ltstart_indx = d_idx * 6
for row in range(dim):
col = row
rowcol = start_indx + row * 3 + col
dltrowcol = ltstart_indx + (row * (row + 1)) / 2 + col
d_ss[dltrowcol] = d_gradv[rowcol] - divvbydim
for row in range(1, dim):
for col in range(row):
rowcol = row * 3 + col
colrow = row + col * 3
dltrowcol = ltstart_indx + (row * (row + 1)) / 2 + col
d_ss[dltrowcol] = 0.5 * (gradvls[rowcol] + gradvls[colrow])
# Trace ( S dot transpose(S) )
for row in range(dim):
for col in range(dim):
dltrowcol = ltstart_indx + (row * (row + 1)) / 2 + col
d_trssdsst[d_idx] += d_ss[dltrowcol] * d_ss[dltrowcol]