def calculate_phir(phi, dphi, s, xq, K_fine, eps, LorY, kappa):
phir = 0
for i in range(len(s.triangle)):
panel = s.vertex[s.triangle[i]]
K, V = gaussIntegration_fine(xq, panel, s.normal[i], s.Area[i], K_fine, kappa, LorY, eps)
phir += (-K*phi[i] + V*dphi[i])/(4*pi)
return phir
def calculate_phir(phi, dphi, s, xq, K_fine, eps, LorY, kappa, E, m_E, m_a, infty):
phir = 0
dummy = array([[0,0,0]])
for i in range(len(s.triangle)):
panel = s.vertex[s.triangle[i]]
K, V, Kp = gaussIntegration_fine(xq, panel, s.normal[i], s.Area[i], dummy, K_fine, kappa, E, m_E, m_a, LorY, eps, infty)
# s.normal is dummy: needed for Kp, which we don't use here.
phir += (-K*phi[i] + V*dphi[i])/(4*pi)
return phir
def calculate_phir(phi, dphi, s, xq, K_fine, eps, LorY, kappa):
phir = 0
dummy = array([[0,0,0]])
for i in range(len(s.triangle)):
panel = s.vertex[s.triangle[i]]
K, V, Kp = gaussIntegration_fine(xq, panel, s.normal[i], s.Area[i], dummy, K_fine, kappa, LorY, eps)
# s.normal is dummy: needed for Kp, which we don't use here.
phir += (-K*phi[i] + V*dphi[i])/(4*pi)
return phir
def blockMatrix(tar, src, WK, kappa, threshold, LorY, xk, wk, K_fine, eps):
Ns = len(src.xi)
Nt = len(tar.xi)
K = len(WK)
dx = transpose(ones((Ns * K, Nt)) * tar.xi) - src.xj
dy = transpose(ones((Ns * K, Nt)) * tar.yi) - src.yj
dz = transpose(ones((Ns * K, Nt)) * tar.zi) - src.zj
r = sqrt(dx * dx + dy * dy + dz * dz + eps * eps)
dx = reshape(dx, (Nt, Ns, K))
dy = reshape(dy, (Nt, Ns, K))
dz = reshape(dz, (Nt, Ns, K))
r = reshape(r, (Nt, Ns, K))
if LorY == 1: # if Laplace
# Double layer
K_lyr = src.Area * (sum(WK / r**3 * dx, axis=2) * src.normal[:, 0] +
sum(WK / r**3 * dy, axis=2) * src.normal[:, 1] +
sum(WK / r**3 * dz, axis=2) * src.normal[:, 2])
# Single layer
V_lyr = src.Area * sum(WK / r, axis=2)
# Adjoint double layer
Kp_lyr = -src.Area * (
transpose(
transpose(sum(WK / r**3 * dx, axis=2)) * tar.normal[:, 0]) +
transpose(
transpose(sum(WK / r**3 * dy, axis=2)) * tar.normal[:, 1]) +
transpose(
transpose(sum(WK / r**3 * dz, axis=2)) * tar.normal[:, 2]))
else: # if Yukawa
# Double layer
K_lyr = src.Area * (
sum(WK / r**2 * exp(-kappa * r) *
(kappa + 1 / r) * dx, axis=2) * src.normal[:, 0] +
sum(WK / r**2 * exp(-kappa * r) *
(kappa + 1 / r) * dy, axis=2) * src.normal[:, 1] +
sum(WK / r**2 * exp(-kappa * r) *
(kappa + 1 / r) * dz, axis=2) * src.normal[:, 2])
# Single layer
V_lyr = src.Area * sum(WK * exp(-kappa * r) / r, axis=2)
# Adjoint double layer
Kp_lyr = zeros(shape(K_lyr)) #TO BE IMPLEMENTED
same = zeros((Nt, Ns), dtype=int32)
if abs(src.xi[0] - tar.xi[0]) < 1e-10:
for i in range(Nt):
same[i, i] = 1
tri_ctr = average(src.vertex[src.triangle[:]], axis=1)
dx = transpose(ones((Ns, Nt)) * tar.xi) - tri_ctr[:, 0]
dy = transpose(ones((Ns, Nt)) * tar.yi) - tri_ctr[:, 1]
dz = transpose(ones((Ns, Nt)) * tar.zi) - tri_ctr[:, 2]
r_tri = sqrt(dx * dx + dy * dy + dz * dz)
L_d = logical_and(
greater_equal(sqrt(2 * src.Area) / (r_tri + eps), threshold),
same == 0)
# L_d = logical_and(greater_equal(sqrt(2*src.Area)/average(r,axis=2),threshold), same==0)
N_analytical = 0
for i in range(Ns):
panel = src.vertex[src.triangle[i]]
an_integrals = nonzero(L_d[:, i])[0]
local_center = zeros((len(an_integrals), 3))
local_center[:, 0] = tar.xi[an_integrals]
local_center[:, 1] = tar.yi[an_integrals]
local_center[:, 2] = tar.zi[an_integrals]
normal_tar = tar.normal[an_integrals]
K_aux, V_aux, Kp_aux = gaussIntegration_fine(local_center, panel,
src.normal[i],
src.Area[i], normal_tar,
K_fine, kappa, LorY, eps)
K_lyr[an_integrals, i] = K_aux[:, 0]
V_lyr[an_integrals, i] = V_aux[:, 0]
Kp_lyr[an_integrals, i] = Kp_aux[:, 0]
N_analytical += len(an_integrals)
if abs(src.xi[0] - tar.xi[0]) < 1e-10:
if same[i, i] == 1:
local_center = array([tar.xi[i], tar.yi[i], tar.zi[i]])
G_Y = zeros(1)
dG_Y = zeros(1)
G_L = zeros(1)
dG_L = zeros(1)
SA_wrap_arr(ravel(panel), local_center, G_Y, dG_Y, G_L, dG_L,
kappa, array([1], dtype=int32), xk, wk)
if LorY == 1: # if Laplace
K_lyr[i, i] = dG_L
V_lyr[i, i] = G_L
Kp_lyr[i, i] = dG_L
else: # if Yukawa
K_lyr[i, i] = dG_Y
V_lyr[i, i] = G_Y
Kp_lyr[i, i] = dG_Y
N_analytical += 1
print '\t%i analytical integrals' % (N_analytical / Ns)
return K_lyr, V_lyr, Kp_lyr
def blockMatrix(tar, src, WK, kappa, threshold, LorY, xk, wk, K_fine, eps):
Ns = len(src.xi)
Nt = len(tar.xi)
K = len(WK)
dx = transpose(ones((Ns*K,Nt))*tar.xi) - src.xj
dy = transpose(ones((Ns*K,Nt))*tar.yi) - src.yj
dz = transpose(ones((Ns*K,Nt))*tar.zi) - src.zj
r = sqrt(dx*dx+dy*dy+dz*dz+eps*eps)
dx = reshape(dx,(Nt,Ns,K))
dy = reshape(dy,(Nt,Ns,K))
dz = reshape(dz,(Nt,Ns,K))
r = reshape(r,(Nt,Ns,K))
if LorY==1: # if Laplace
# Double layer
K_lyr = src.Area * (sum(WK/r**3*dx, axis=2)*src.normal[:,0]
+ sum(WK/r**3*dy, axis=2)*src.normal[:,1]
+ sum(WK/r**3*dz, axis=2)*src.normal[:,2])
# Single layer
V_lyr = src.Area * sum(WK/r, axis=2)
# Adjoint double layer
Kp_lyr = -src.Area * ( transpose(transpose(sum(WK/r**3*dx, axis=2))*tar.normal[:,0])
+ transpose(transpose(sum(WK/r**3*dy, axis=2))*tar.normal[:,1])
+ transpose(transpose(sum(WK/r**3*dz, axis=2))*tar.normal[:,2]) )
else: # if Yukawa
# Double layer
K_lyr = src.Area * (sum(WK/r**2*exp(-kappa*r)*(kappa+1/r)*dx, axis=2)*src.normal[:,0]
+ sum(WK/r**2*exp(-kappa*r)*(kappa+1/r)*dy, axis=2)*src.normal[:,1]
+ sum(WK/r**2*exp(-kappa*r)*(kappa+1/r)*dz, axis=2)*src.normal[:,2])
# Single layer
V_lyr = src.Area * sum(WK * exp(-kappa*r)/r, axis=2)
# Adjoint double layer
Kp_lyr = zeros(shape(K_lyr)) #TO BE IMPLEMENTED
same = zeros((Nt,Ns),dtype=int32)
if abs(src.xi[0]-tar.xi[0])<1e-10:
for i in range(Nt):
same[i,i] = 1
tri_ctr = average(src.vertex[src.triangle[:]], axis=1)
dx = transpose(ones((Nt,Nt))*tar.xi) - tri_ctr[:,0]
dy = transpose(ones((Nt,Nt))*tar.yi) - tri_ctr[:,1]
dz = transpose(ones((Nt,Nt))*tar.zi) - tri_ctr[:,2]
r_tri = sqrt(dx*dx+dy*dy+dz*dz)
L_d = logical_and(greater_equal(sqrt(2*src.Area)/(r_tri+eps),threshold), same==0)
# L_d = logical_and(greater_equal(sqrt(2*src.Area)/average(r,axis=2),threshold), same==0)
N_analytical = 0
for i in range(Ns):
panel = src.vertex[src.triangle[i]]
an_integrals = nonzero(L_d[:,i])[0]
local_center = zeros((len(an_integrals),3))
local_center[:,0] = tar.xi[an_integrals]
local_center[:,1] = tar.yi[an_integrals]
local_center[:,2] = tar.zi[an_integrals]
normal_tar = tar.normal[an_integrals]
K_aux, V_aux, Kp_aux = gaussIntegration_fine(local_center, panel, src.normal[i], src.Area[i], normal_tar, K_fine, kappa, LorY, eps)
K_lyr[an_integrals,i] = K_aux[:,0]
V_lyr[an_integrals,i] = V_aux[:,0]
Kp_lyr[an_integrals,i] = Kp_aux[:,0]
N_analytical += len(an_integrals)
if same[i,i] == 1:
local_center = array([tar.xi[i], tar.yi[i], tar.zi[i]])
G_Y = zeros(1)
dG_Y = zeros(1)
G_L = zeros(1)
dG_L = zeros(1)
SA_wrap_arr(ravel(panel), local_center, G_Y, dG_Y, G_L, dG_L, kappa, array([1], dtype=int32), xk, wk)
if LorY==1: # if Laplace
K_lyr[i,i] = dG_L
V_lyr[i,i] = G_L
Kp_lyr[i,i] = dG_L
else: # if Yukawa
K_lyr[i,i] = dG_Y
V_lyr[i,i] = G_Y
Kp_lyr[i,i] = dG_Y
N_analytical += 1
print '\t%i analytical integrals'%(N_analytical/Ns)
return K_lyr, V_lyr, Kp_lyr
