def FastForce(X, Y, Xss, Yss, LinkIndices, LinkData, LinkCurL, TetherIndex,
TetherData):
Nb = len(X)
tx = X[LinkIndices[:, 1]] - X[LinkIndices[:, 0]]
ty = Y[LinkIndices[:, 1]] - Y[LinkIndices[:, 0]]
LinkCurL[:] = (tx**2 + ty**2)**.5
txl = tx / LinkCurL
tyl = ty / LinkCurL
for i in range(Nb):
if LinkCurL[i] == 0:
txl[i] = tyl[i] = 0.
Xss[:], Yss[:] = 0. * Xss, 0. * Yss
calc = LinkData[:, 0] * (tx - LinkData[:, 1] * txl)
IB_c.CollapseSum(Xss, LinkIndices[:, 0], calc)
IB_c.CollapseSum(Xss, LinkIndices[:, 1], -calc)
calc = LinkData[:, 0] * (ty - LinkData[:, 1] * tyl)
IB_c.CollapseSum(Yss, LinkIndices[:, 0], calc)
IB_c.CollapseSum(Yss, LinkIndices[:, 1], -calc)
Xss[TetherIndex] += TetherData[:, 0] * (TetherData[:, 1] - X[TetherIndex])
Yss[TetherIndex] += TetherData[:, 0] * (TetherData[:, 2] - Y[TetherIndex])
def CalculateLookupTable_3D(fluid, spread=True, Range=10000):
U = zeros((fluid.N[0], fluid.N[1], fluid.N[2], 3, 3), float64)
X = zeros((1, 3), float64)
F = X.copy()
# Calculate the lookup table for a unit force in the x direction
F[0] = [1, 0, 0]
FiberToGrid(fluid.N, fluid.h, 1, 1., X, F, fluid.f, fluid.DeltaType)
fluid.FluidSolve(fluid.f)
if (spread):
IB_c.WholeGridSpread(fluid.Output_u, fluid.N, fluid.h, U[..., 0, :],
Range, fluid.DeltaType)
else:
U[..., 0, :] = fluid.Output_u.copy()
# If the domain is perfectly cubic make use of symmetries
if fluid.N[0] == fluid.N[1] == fluid.N[2]:
U[..., 1, :] = U[..., 0, :].swapaxes(0, 1)
U[..., 1, 0], U[..., 1, 1] = U[..., 1, 1].copy(), U[..., 1, 0].copy()
U[..., 2, :] = U[..., 0, :].swapaxes(0, 2)
U[..., 2, 0], U[..., 2, 2] = U[..., 2, 2].copy(), U[..., 2, 0].copy()
# otherwise calculate y and z components from scratch
else:
# Calculate the lookup table for a unit force in the y direction
F[0] = [0, 1, 0]
FiberToGrid(fluid.N, fluid.h, 1, 1., X, F, fluid.f, fluid.DeltaType)
fluid.FluidSolve(fluid.f)
if (spread):
IB_c.WholeGridSpread(fluid.Output_u, fluid.N, fluid.h,
U[..., 1, :], Range, fluid.DeltaType)
else:
U[..., 1, :] = fluid.Output_u.copy()
# Calculate the lookup table for a unit force in the z direction
F[0] = [0, 0, 1]
FiberToGrid(fluid.N, fluid.h, 1, 1., X, F, fluid.f, fluid.DeltaType)
fluid.FluidSolve(fluid.f)
if (spread):
IB_c.WholeGridSpread(fluid.Output_u, fluid.N, fluid.h,
U[..., 2, :], Range, fluid.DeltaType)
else:
U[..., 2:] = fluid.Output_u.copy()
return U
def GridToFiber_3D(N, h, Nb, hb, X, u, U, DeltaType=0, UseNativePython=False):
"""Interpolate a vector-field u to the points in X.
The result is stored in U."""
U *= 0
if UseNativePython:
# Loop through fiber points
for i in range(Nb):
# Modify velocity for nearby points
jMin = int(X[i][0] / h[0] - 2.)
jMax = jMin + 5
kMin = int(X[i][1] / h[1] - 2.)
kMax = kMin + 5
lMin = int(X[i][2] / h[2] - 2.)
lMax = lMin + 5
for j in range(jMin, jMax + 1):
__delt = Delta(h[0], j * h[0] - X[i][0],
DeltaType) * h[0] * h[1] * h[2]
for k in range(kMin, kMax + 1):
_delt = __delt * Delta(h[1], k * h[1] - X[i][1], DeltaType)
for l in range(lMin, lMax + 1):
delt = _delt * Delta(h[2], l * h[2] - X[i][2],
DeltaType)
U[i] += u[j % N[0], k % N[1], l % N[2]] * delt
else:
IB_c.GridToFiber(N, h, Nb, hb, X, u, U, DeltaType)
return U
def FiberToGrid_3D(N, h, Nb, hb, X, F, f, DeltaType=0, UseNativePython=False):
"""Spread a distribution F on X to the Eulerian grid f."""
f *= 0
if UseNativePython:
# Loop through fiber points
for i in range(Nb):
# Modify force for nearby points
jMin = int(X[i][0] / h[0] - 2.)
jMax = jMin + 5
kMin = int(X[i][1] / h[1] - 2.)
kMax = kMin + 5
lMin = int(X[i][2] / h[2] - 2.)
lMax = lMin + 5
for j in range(jMin, jMax + 1):
__delt = Delta(h[0], j * h[0] - X[i][0], DeltaType) * hb
for k in range(kMin, kMax + 1):
_delt = __delt * Delta(h[1], k * h[1] - X[i][1], DeltaType)
for l in range(lMin, lMax + 1):
delt = _delt * Delta(h[2], l * h[2] - X[i][2],
DeltaType)
f[j % N[0], k % N[1], l % N[2]] += F[i] * delt
else:
IB_c.FiberToGrid(N, h, Nb, hb, X, F, f, DeltaType)
return f
def FastJacobian2(z, D, args, LinkIndices, LinkData, LinkCurL, TetherIndex,
TetherData):
tx = z[LinkIndices[:, 1]] - z[LinkIndices[:, 0]]
ty = z[LinkIndices[:, 1] + Nb] - z[LinkIndices[:, 0] + Nb]
l3 = LinkCurL**3
l1 = 1. / LinkCurL
dxdx = (-1. + LinkData[:, 1] * (l1 - tx**2 / l3))
dydy = (-1. + LinkData[:, 1] * (l1 - ty**2 / l3))
dxdy = -LinkData[:, 1] * tx * ty / l3
for i in range(Nb):
if LinkCurL[i] == 0:
dxdx[i] = -1.
dydy[i] = -1.
dxdy[i] = 0.
print i, LinkCurL[i], dxdx[i], dxdy[i], dydy[i]
data = 0. * D.data
n = len(dxdx)
data[:n] -= dxdx
data[n:2 * n] -= dxdx
data[2 * n:3 * n] -= dydy
data[3 * n:4 * n] -= dydy
data[4 * n:5 * n] -= dxdy
data[5 * n:6 * n] -= dxdy
data[6 * n:7 * n] -= dxdy
data[7 * n:8 * n] -= dxdy
Diag = zeros(Nb, float64)
IB_c.CollapseSum(Diag, LinkIndices[:, 0], dxdx)
IB_c.CollapseSum(Diag, LinkIndices[:, 1], dxdx)
Diag[TetherIndex] -= 1. #TetherData[:,0]
data[8 * n:8 * n + Nb] = 1. * Diag
Diag = zeros(Nb, float64)
IB_c.CollapseSum(Diag, LinkIndices[:, 0], dydy)
IB_c.CollapseSum(Diag, LinkIndices[:, 1], dydy)
Diag[TetherIndex] -= 1. #TetherData[:,0]
data[8 * n + Nb:8 * n + 2 * Nb] = 1. * Diag
Diag = zeros(Nb, float64)
IB_c.CollapseSum(Diag, LinkIndices[:, 0], dxdy)
IB_c.CollapseSum(Diag, LinkIndices[:, 1], dxdy)
data[8 * n + 2 * Nb:8 * n + 3 * Nb] = 1. * Diag
Diag = zeros(Nb, float64)
IB_c.CollapseSum(Diag, LinkIndices[:, 1], dxdy)
IB_c.CollapseSum(Diag, LinkIndices[:, 0], dxdy)
data[8 * n + 3 * Nb:8 * n + 4 * Nb] = 1. * Diag
D.data[args] = data
def EzSparse(N, M, A):
IShell = zeros((N, 3), float64)
IShelli = zeros((N, 3), int32)
IShelld = zeros(N, int32)
IB_c.EzSparse(N, M, A, IShell, IShelli, IShelld)
return (N, M, max(list(IShelld)), IShell, IShelli, IShelld)
def ModVCycle(A, P, L, b, I, x, damp=.3):
if len(I) <= 1:
return
# GaussSeidel(len(x), A[0], b, x)
IB_c.GaussSeidel(len(x), A[0], b, x, damp)
# Jacobi(A[0], b, x)
r = b - dot(A[0], x)
x[L] += linalg.solve(P, r[L])
r = I[0].T * (b - dot(A[0], x))
_x = zeros(len(r), float64)
FastVCycle(A[1:], r, I[1:], _x)
x += I[0] * _x
# GaussSeidel(len(x), A[0], b, x)
IB_c.GaussSeidel(len(x), A[0], b, x, damp)
def ConstructFluidMatrix(self, fluid, M=None): if M == None: # Allocate memory to store the matrix Dim = fluid.Dim M = zeros((Dim * self.Nb, Dim * self.Nb), float64) else: M *= 0 # Construct the matrix IB_c.ComputeMatrix(self.X, fluid.N, self.Nb, fluid.h, self.hb, fluid.GetLookup(), M, 100000) return M
def FastVCycle(A, b, I, x, damp=.3):
if len(I) <= 1:
return
#Jacobi(A[0], b, x)
#GaussSeidel(len(x), A[0], b, x)
IB_c.GaussSeidel(len(x), A[0], b, x, damp)
r = I[0].T * (b - dot(A[0], x))
_x = zeros(len(r), float64)
FastVCycle(A[1:], r, I[1:], _x)
x += I[0] * _x
def FluidSolve(u, v, ux, vx, uy, vy, X, Y, Fx, Fy):
IB_c.CentralDerivative_x(N, M, h, u, ux)
IB_c.CentralDerivative_x(N, M, h, v, vx)
IB_c.CentralDerivative_y(N, M, h, u, uy)
IB_c.CentralDerivative_y(N, M, h, v, vy)
fx, fy = ForceToGrid(N, M, h, Nb, hb, Old_X, Old_Y, Fx, Fy)
fx, fy = ExplicitTerms(dt, u, v, ux, uy, vx, vy, fx, fy)
fx = fft2(fx)
fy = fft2(fy)
P = Solve_P_Hat(dt, WideLambda, DxSymbol, DySymbol, fx, fy)
P[0, 0] = 0.
u, v = Solve_uv_Hat(dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy)
u = ifft2(u).real
v = ifft2(v).real
return VelToFiber(N, M, h, Nb, hb, 1., X, Y, u, v)
def EzSparseMM(A1, A2, newB=True, B=-1):
N, M, s, IShell, IShelli, IShelld = A1
_N, _M = A2.shape
if M != _N:
raise ("Incompatible dimensions")
if newB:
B = zeros((N, _M), float64)
IB_c.SparseMM(N, M, _M, s, IShell, IShelli, IShelld, A2, B)
return B
def CalculateLookupTable2(fluid, M=4, spread=True, Range=10000, offset=0):
"""Calculates a lookup table for the interpolated velocity generated by a point force
The table has dimensions 3xN[0]xN[1]xN[2]x3, where the first dimension specifies the direction of the force"""
if Range > fluid.N[0]:
Range = fluid.N[0] / 2 + 1
U = zeros((M + 1, M + 1, M + 1, 3, Range, Range, Range, 3), float64)
X = zeros((1, 3), float64)
F = X.copy()
for j in range(M + 1):
for k in range(M + 1):
for l in range(M + 1):
X[0] = 1. / M * array([j, k, l]) * fluid.h
X[0] += array([1, 1, 1]) * fluid.h * offset
print j, k, l, X[0] / fluid.h, array([1, 1, 1]) * fluid.h
F[0] = [1, 0, 0]
FiberToGrid(fluid.N, fluid.h, 1, 1., X, F, fluid.f,
fluid.DeltaType)
fluid.FluidSolve(fluid.f)
if (spread):
IB_c.WholeGridSpread2(fluid.Output_u, fluid.N, fluid.h,
U[j, k, l,
0], Range, fluid.DeltaType)
raise ValueError("WholeGridSpread2 not yet implemented")
else:
U[j, k, l,
0] = fluid.Output_u[:Range, :Range, :Range].copy()
if fluid.N[0] == fluid.N[1] == fluid.N[2]:
U[j, k, l, 1] = U[j, k, l, 0].swapaxes(0, 1)
U[j, k, l, 1, :, :, :,
0], U[j, k, l, 1, :, :, :,
1] = U[j, k, l, 1, :, :, :,
1].copy(), U[j, k, l, 1, :, :, :, 0].copy()
U[j, k, l, 2] = U[j, k, l, 0].swapaxes(0, 2)
U[j, k, l, 2, :, :, :,
0], U[j, k, l, 2, :, :, :,
2] = U[j, k, l, 2, :, :, :,
2].copy(), U[j, k, l, 2, :, :, :, 0].copy()
else:
raise ValueError(
"CalculateLookupTable2 not implemented for non-cube domains."
)
return U
def ForceToGrid(N, M, h, Nb, hb, X, Y, Boundary_fx, Boundary_fy, DeltaType=0):
fx = zeros((N, M), float64)
fy = zeros((N, M), float64)
## # Loop through fiber points
## for i in range(Nb):
## # Modify force for nearby points
## jMin = int(X[i] / h - 2.)
## jMax = jMin + 5
## kMin = int(Y[i] / h - 2.)
## kMax = kMin + 5
##
## for j in range(jMin, jMax + 1):
## deltx = Delta (h, j * h - X[i])
## for k in range(kMin, kMax + 1):
## delt = deltx * Delta (h, k * h - Y[i]) * hb
## fx[j%N][k%M] = fx[j%N][k%M] + Boundary_fx[i] * delt
## fy[j%N][k%M] = fy[j%N][k%M] + Boundary_fy[i] * delt
IB_c.ForceToGrid(N, M, h, Nb, hb, X, Y, Boundary_fx, Boundary_fy, fx, fy,
DeltaType)
return fx, fy
def VelToFiber(N, M, h, Nb, hb, dt, X, Y, u, v, DeltaType=0):
## Xvel = zeros(Nb, float64)
## Yvel = zeros(Nb, float64)
##
## # Loop through fiber points
## for i in range(Nb):
## # Modify velocity for nearby points
## jMin = int(X[i] / h - 2.)
## jMax = jMin + 5
## kMin = int(Y[i] / h - 2.)
## kMax = kMin + 5
##
## for j in range(jMin, jMax + 1):
## deltx = Delta (h, j * h - X[i])
## for k in range(kMin, kMax + 1):
## delt = deltx * Delta (h, k * h - Y[i]) * h**2
## Xvel[i] += u[j%N][k%M] * delt
## Yvel[i] += v[j%N][k%M] * delt
Xvel = zeros(Nb, float64)
Yvel = zeros(Nb, float64)
IB_c.VelToFiber(N, M, h, Nb, hb, dt, X, Y, u, v, Xvel, Yvel, DeltaType)
return dt * Xvel, dt * Yvel
Domain_x, Domain_y = 2., 1.
#h = .003
h = Domain_x / 100.
N, M = int(Domain_x / h), int(Domain_y / h)
Domain_x, Domain_y = N * h, M * h
print "N, M =", N, M
dt = .003
T = 5.
CurT = 0
_s = 5000000000.
Current = 100.
WideLambda = zeros((N, M), float64)
ShortLambda = zeros((N, M), float64)
IB_c.InitWideLaplacian(N, M, h, WideLambda)
IB_c.InitShortLaplacian(N, M, h, ShortLambda)
DxSymbol = InitDxSymbol(N, M, h)
DySymbol = InitDySymbol(N, M, h)
_h = h
_N, _M = int(Domain_x / _h), int(Domain_y / _h)
UField, VField, UField2, VField2 = InitVelField(_N, _M, _h, h, dt)
print UField[0, 0], VField2[0, 0]
clf()
clf()
imshow(UField)
colorbar()
#show(); #&&raw_input("")
clf()
def ExplicitHeartValveSim(N, dx, dt, T):
Domain_x, Domain_y = 2., 1.
#h = .003#.007
h = Domain_x / N
dx = h / 2.
N, M = int(Domain_x / h), int(Domain_y / h)
#dt = .0000065
CurT = 0
_s = 1000000000. / dx**2
#_s = 500000000000. / dx**2
dt = 30. * h / _s**.5
Current = 100.
WideLambda = zeros((N, M), float64)
ShortLambda = zeros((N, M), float64)
IB_c.InitWideLaplacian(N, M, h, WideLambda)
IB_c.InitShortLaplacian(N, M, h, ShortLambda)
DxSymbol = InitDxSymbol(N, M, h)
DySymbol = InitDySymbol(N, M, h)
#UField, VField = InitVelField(N, M, h, h, dt)
X, Y, Links, Tethers, Parts = ConstructValve(_s, 0., Domain_x, 0.,
Domain_y, dx, False, 1.3,
1.1) #.01)
#X, Y, Links, Tethers, Parts = ConstructValve (_s, 0., Domain_x, 0., Domain_y, .012, True,1.5,1.)#.01)
#X, Y, Links, Tethers, Valve = ConstructValve (_s, 0., 2., 0., 1., .03)#.01)
Links = []
Nb = len(X)
hb = 1. / Nb
##for j in range(Nb):
## X[j] += .002*cos(j)
## Y[j] += .002*sin(j**2)
Xs = zeros(Nb, float64)
Ys = zeros(Nb, float64)
Xss = zeros(Nb, float64)
Yss = zeros(Nb, float64)
u = zeros((N, M), float64)
v = zeros((N, M), float64)
ux = zeros((N, M), float64)
vx = zeros((N, M), float64)
uy = zeros((N, M), float64)
vy = zeros((N, M), float64)
fx = zeros((N, M), float64)
fy = zeros((N, M), float64)
# Unpack link and tether data into arrays
LinkIndices = zeros((len(Links), 2), int64)
LinkData = zeros((len(Links), 2), float64)
LinkCurL = zeros(len(Links), float64)
TetherData = zeros((len(Tethers), 3), float64)
TetherIndex = zeros(len(Tethers), int64)
for l in range(len(Links)):
a, b, s, L = Links[l]
LinkIndices[l, :] = [a, b]
LinkData[l, :] = [s, L]
for l in range(len(Tethers)):
a, x, s = Tethers[l]
x, y = x
TetherData[l, :] = [s, x, y]
TetherIndex[l] = a
PlotValve(X, Y, Links)
Times = []
A = zeros((2 * Nb, 2 * Nb), float64)
print N, dx, Nb, dt
b = zeros(2 * Nb, float64)
count = 0
TotalTime = 0
print
print "Time:",
while CurT < T:
Old_X, Old_Y = 1. * X, 1. * Y
# print "Time:", CurT, count
# print CurT,
# CurT += dt
Time = time.time()
IB_c.CentralDerivative_x(N, M, h, u, ux)
IB_c.CentralDerivative_x(N, M, h, v, vx)
IB_c.CentralDerivative_y(N, M, h, u, uy)
IB_c.CentralDerivative_y(N, M, h, v, vy)
FastForce(X, Y, Xss, Yss, LinkIndices, LinkData, LinkCurL, TetherIndex,
TetherData)
# Xss, Yss = FiberForce (Nb, X, Y, Xss, Yss, Links, Tethers)
fx, fy = ForceToGrid(N, M, h, Nb, hb, X, Y, Xss, Yss)
fx, fy = ExplicitTerms(dt, u, v, ux, uy, vx, vy, fx, fy)
fx += dt * Current * ones((N, M), float64)
fx = fft2(fx)
fy = fft2(fy)
P = Solve_P_Hat(dt, WideLambda, DxSymbol, DySymbol, fx, fy)
P[0, 0] = 0.
u, v = Solve_uv_Hat(dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy)
u = ifft2(u).real
v = ifft2(v).real
Xvel, Yvel = VelToFiber(N, M, h, Nb, hb, 1., X, Y, u, v)
X, Y = X + dt * Xvel, Y + dt * Yvel
# print "Explicit time:", time.time() - Time
# Times.append(time.time() - Time)
# print "avg:", sum(Times)/len(Times)
## if time.time()-Time > 1:
## P = ifft2(P).real
## clf()
## imshow(P)
## scatter(M*Y,N*X/2)
## quiver(M*Y,N*X/2,Yvel,-Xvel)
## print "Halt!"
## raw_input("")
Time = time.time() - Time
TotalTime += Time
count += 1
Ts = [.0001, .0002, .0005, .001, .005]
for _T in Ts:
if CurT < _T and CurT + dt >= _T:
print "Time", _T, ":", count, TotalTime, TotalTime / count
#print "Time:", CurT
CurT += dt
if count % 500 == 0:
print CurT, count
P = ifft2(P).real
clf()
#imshow(P)
imshow(u)
colorbar()
scatter(M * Y, N * X / 2)
quiver(M * Y, N * X / 2, Yvel, -Xvel)
# #_!_print gaussx[0:Nb]
# raw_input("")
print
print
print "End:", count, TotalTime, TotalTime / count
return Times
def Call(N):
# N = 128
Domain_x, Domain_y = 2., 1.
#h = .003#.007
h = Domain_x / N
dx = h / 2.
N, M = int(Domain_x / h), int(Domain_y / h)
#dt = .0000065
CurT = 0
T = .5
#_s = 500000000000. / dx**2
_s = 1000000000. / dx**2
dt = .0025
Current = 100.
WideLambda = zeros((N, M), float64)
ShortLambda = zeros((N, M), float64)
IB_c.InitWideLaplacian(N, M, h, WideLambda)
IB_c.InitShortLaplacian(N, M, h, ShortLambda)
DxSymbol = InitDxSymbol(N, M, h)
DySymbol = InitDySymbol(N, M, h)
_h = h
_N, _M = int(Domain_x / _h), int(Domain_y / _h)
UField, VField, UField2, VField2 = InitVelField(_N, _M, _h, h, dt)
print UField[0, 0], VField2[0, 0]
clf()
clf()
imshow(UField)
colorbar()
#show(); #&&raw_input("")
clf()
imshow(VField2)
colorbar()
#show(); #&&raw_input("")
X, Y, Links, Tethers, Parts = ConstructValve(
_s, 0., Domain_x, 0., Domain_y, dx,
False) #, 1., 1.15)#, True, 1.3,1.7)#.01)
Nb = len(X)
Xs = zeros(Nb, float64)
Ys = zeros(Nb, float64)
Xss = zeros(Nb, float64)
Yss = zeros(Nb, float64)
u = zeros((N, M), float64)
v = zeros((N, M), float64)
ux = zeros((N, M), float64)
vx = zeros((N, M), float64)
uy = zeros((N, M), float64)
vy = zeros((N, M), float64)
fx = zeros((N, M), float64)
fy = zeros((N, M), float64)
# Unpack link and tether data into arrays
LinkIndices = zeros((len(Links), 2), int64)
LinkData = zeros((len(Links), 2), float64)
LinkCurL = zeros(len(Links), float64)
TetherData = zeros((len(Tethers), 3), float64)
TetherIndex = zeros(len(Tethers), int64)
for l in range(len(Links)):
a, b, s, L = Links[l]
LinkIndices[l, :] = [a, b]
LinkData[l, :] = [s, L]
for l in range(len(Tethers)):
a, x, s = Tethers[l]
x, y = x
TetherData[l, :] = [s, x, y]
TetherIndex[l] = a
DSeed = SeedJacobian(Nb, LinkIndices)
SeedArgs = argsort(DSeed.data)
__I, _x2, _y2, Parts2 = ReduceValve3(X, Y, Parts)
#s2, __I, _x2, _y2, Links2, Tethers2, Parts2 = ReduceValve(_s, X, Y, Links, Tethers, Parts)
Nb2 = len(_x2)
_II = 1. * __I
_n, _m = _II.shape
__II = zeros((2 * _n, 2 * _m), float64)
__II[:_n, :_m] = 1. * _II
__II[_n:, _m:] = 1. * _II
II = [sparse.csr_matrix(__II)]
IIspT = [EzSparse(2 * _m, 2 * _n, __II.T)]
_x3, _y3, Parts3 = _x2, _y2, Parts2
#s3, _x3, _y3, Links3, Tethers3, Parts3 = s2, _x2, _y2, Links2, Tethers2, Parts2
while len(_II) > 10 and len(II) < 7:
holdlen = len(_II)
print holdlen
_II, _x3, _y3, Parts3 = ReduceValve3(_x3, _y3, Parts3)
#s3, _II, _x3, _y3, Links3, Tethers3, Parts3 = ReduceValve(s3, _x3, _y3, Links3, Tethers3, Parts3)
if len(_II) == holdlen:
II = II[:len(II) - 2]
break
_n, _m = _II.shape
__II = zeros((2 * _n, 2 * _m), float64)
__II[:_n, :_m] = 1. * _II
__II[_n:, _m:] = 1. * _II
II.append(sparse.csr_matrix(__II))
IIspT.append(EzSparse(2 * _m, 2 * _n, __II.T))
print N, dt, _s
print "Nb =", Nb
hb = 1. / Nb
hb = 1.
PlotValve(X, Y, Links)
i1, i2, i3 = Parts[3][0], Parts[3][0] + Nb, Parts[3][len(Parts[3]) - 1]
Reduce = zeros((2 * Nb - 3, 2 * Nb), float64)
j = 0
for i in range(2 * Nb):
if i != i1 and i != i2 and i != i3:
Reduce[j, i] = 1.
j += 1
Reduce = sparse.csr_matrix(Reduce)
l = []
for i in range(Nb):
if X[i] > .25 and X[i] < .4 and Y[i] < .49 and Y[i] > .31:
l.extend([i, i + Nb])
A = zeros((2 * Nb, 2 * Nb), float64)
x = zeros(2 * Nb, float64)
f = zeros(2 * Nb, float64)
_f = zeros(2 * Nb, float64)
_e1, _e2, _e3, F = 0 * x, 0 * x, 0 * x, 0 * x
e1, e2, e3 = 0. * x, 0. * x, 0. * x
for p in range(2, 7):
for i in Parts[p]:
e1[i] = 1.
e2[i + Nb] = 1.
Old_X, Old_Y = 1. * X, 1. * Y
b = zeros(2 * Nb, float64)
count = 0
ShowStats = False
TotalTime = 0
TotalCount = 0
MaxCurrent = 150.
while CurT < T:
## if CurT < .1:
## Current = MaxCurrent * (CurT - 0.) * (.1 - CurT) / (.1 - .05)**2
## else:
## Current = -MaxCurrent * (CurT - .1) * (.2 - CurT) / (.1 - .05)**2
## print "Current:", Current
Time = time.time()
Predict_X, Predict_Y = X + .5 * (X - Old_X), Y + .25 * (Y - Old_Y)
Old_u, Old_v = 1. * u, 1. * v
Old_X, Old_Y = 1. * X, 1. * Y
IB_c.CentralDerivative_x(N, M, h, u, ux)
IB_c.CentralDerivative_x(N, M, h, v, vx)
IB_c.CentralDerivative_y(N, M, h, u, uy)
IB_c.CentralDerivative_y(N, M, h, v, vy)
fx, fy = ExplicitTerms(dt, u, v, ux, uy, vx, vy, 0., 0.)
fx += dt * Current * ones((N, M), float64)
fx = fft2(fx)
fy = fft2(fy)
P = Solve_P_Hat(dt, WideLambda, DxSymbol, DySymbol, fx, fy)
P[0, 0] = 0.
u, v = Solve_uv_Hat(dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy)
u = ifft2(u).real
v = ifft2(v).real
Xvel, Yvel = VelToFiber(N, M, h, Nb, hb, 1., X, Y, u, v)
if ShowStats:
print "Explicit:", time.time() - Time
A = zeros((2 * Nb, 2 * Nb), float64)
IB_c.ComputeMatrix(X, Y, _N, _M, Nb, _h, hb, UField, VField, UField2,
VField2, A, -1) #N/6)
if ShowStats:
print "Compute A:", time.time() - Time
__A = [dt * A]
for i in range(len(II)):
__A.append(EzSparseMM(IIspT[i], EzSparseMM(IIspT[i], __A[i].T).T))
if ShowStats:
print "Init Multi:", time.time() - Time
P = dt * A[l, :][:, l]
b[:Nb], b[Nb:] = X + dt * Xvel, Y + dt * Yvel
x[0:Nb], x[Nb:2 * Nb] = 1. * X, 1. * Y
## FastForce(x[:Nb], x[Nb:], f[:Nb], f[Nb:], LinkIndices, LinkData, LinkCurL, TetherIndex, TetherData)
## xp = x + dt*dot(A,f)
##
## for i in range(4):
## x = x + e1 * dot(xp-x,e1)/dot(e1,e1) + e2 * dot(xp-x,e2)/dot(e2,e2)
##
## center = e1*dot(x,e1)/dot(e1,e1) + e2*dot(x,e2)/dot(e2,e2)
##
## z = x - center
## e3 = 0. * x
## for p in range(9,10):#range(2,7):
## for i in Parts[p]:
## e3[i] = z[i+Nb]
## e3[i+Nb] = -z[i]
## theta = dot(xp-x,e3)/dot(e3,e3)
##
## Rot = zeros((2,2),float64)
## Rot[0,0] = cos(theta)
## Rot[1,0] = -sin(theta)
## Rot[0,1] = -Rot[1,0]
## Rot[1,1] = Rot[0,0]
##
## for p in range(2,7):
## for i in Parts[p]:
## [z[i],z[i+Nb]] = dot(Rot, [z[i],z[i+Nb]])
##
## x = z + center
# Solve for rotational eigenvalue
e3 = 0. * x
z = x - e1 * dot(x, e1) / dot(e1, e1) - e2 * dot(x, e2) / dot(e2, e2)
for p in range(2, 7):
for i in Parts[p]:
e3[i] = z[i + Nb]
e3[i + Nb] = -z[i]
_e1 = ModMultigridStep(__A, P, l, e1, II, _e1, 1.)
_e2 = ModMultigridStep(__A, P, l, e2, II, _e2, 1.)
_e3 = ModMultigridStep(__A, P, l, e3, II, _e3, 1.)
ChangeX = 1.
MaxRes = 1.
count = 0
F = 0. * F
while MaxRes > .5 * dt and count < 4:
holdx = 1. * x
count += 1
F = ModMultigridStep(__A, P, l, x - b, II, F, 1.)
FastForce(x[:Nb], x[Nb:], _f[:Nb], _f[Nb:], LinkIndices, LinkData,
LinkCurL, TetherIndex, TetherData)
f = F - _f
# Solve for rotational eigenvalue
e3 = 0. * x
z = x - e1 * dot(x, e1) / dot(e1, e1) - e2 * dot(x, e2) / dot(
e2, e2)
for p in range(2, 7):
for i in Parts[p]:
e3[i] = z[i + Nb]
e3[i + Nb] = -z[i]
K = zeros((3, 3))
K[0, 0] = dot(_e1, e1)
K[0, 1] = dot(_e2, e1)
K[0, 2] = dot(_e3, e1)
K[1, 0] = dot(_e1, e2)
K[1, 1] = dot(_e2, e2)
K[1, 2] = dot(_e3, e2)
K[2, 0] = dot(_e1, e3)
K[2, 1] = dot(_e2, e3)
K[2, 2] = dot(_e3, e3)
_K = linalg.solve(K, array([dot(F, e1), dot(F, e2), dot(F, e3)]))
x -= e1 * _K[0] + e2 * _K[1]
center = e1 * dot(x, e1) / dot(e1, e1) + e2 * dot(x, e2) / dot(
e2, e2)
z = x - center
e3 = 0. * x
theta = -_K[2]
Rot = zeros((2, 2), float64)
Rot[0, 0] = cos(theta)
Rot[1, 0] = -sin(theta)
Rot[0, 1] = -Rot[1, 0]
Rot[1, 1] = Rot[0, 0]
for p in range(2, 7):
for i in Parts[p]:
[z[i], z[i + Nb]] = dot(Rot, [z[i], z[i + Nb]])
x = z + center
subMax = 1000.
SubCount = 0
while SubCount < 2: #subMax > .000000000000001*_s:
SubCount += 1
FastForce(x[:Nb], x[Nb:], _f[:Nb], _f[Nb:], LinkIndices,
LinkData, LinkCurL, TetherIndex, TetherData)
D = 0. * DSeed
FastJacobian2(x, D, SeedArgs, LinkIndices, LinkData, LinkCurL,
TetherIndex, TetherData)
f = F - _f
e3 = 0. * x
z = x - e1 * dot(x, e1) / dot(e1, e1) - e2 * dot(x, e2) / dot(
e2, e2)
for p in range(2, 7):
for i in Parts[p]:
e3[i] = z[i + Nb]
e3[i + Nb] = -z[i]
f -= e1 * dot(f, e1) / dot(e1, e1)
f -= e2 * dot(f, e2) / dot(e2, e2)
f -= e3 * dot(f, e3) / dot(e3, e3)
subMax = max(list(abs(f)))
if ShowStats:
print " subRes:", subMax, .000000000000001 * _s
ReduceD = Reduce * D * Reduce.T
Dlu = scipy.linsolve.splu(ReduceD)
y = Dlu.solve(Reduce * f) / _s
#y = linsolve.spsolve(ReduceD, Reduce*f)
y = Reduce.T * y
y -= e1 * dot(y, e1) / dot(e1, e1)
y -= e2 * dot(y, e2) / dot(e2, e2)
y -= e3 * dot(y, e3) / dot(e3, e3)
x += y
FastForce(x[:Nb], x[Nb:], f[:Nb], f[Nb:], LinkIndices, LinkData,
LinkCurL, TetherIndex, TetherData)
r = b + dot(dt * A, f) - x
MaxRes = max(list(abs(r)))
if ShowStats:
print " Residual:", MaxRes, "at time:", time.time() - Time
FastForce(x[:Nb], x[Nb:], f[:Nb], f[Nb:], LinkIndices, LinkData,
LinkCurL, TetherIndex, TetherData)
r = b + dot(dt * A, f) - x
if ShowStats:
print "Residual:", max(list(abs(r)))
## print
## print
X, Y = 1. * x[0:Nb], 1. * x[Nb:2 * Nb]
u, v = 1. * Old_u, 1. * Old_v
## IB_c.CentralDerivative_x (N, M, h, u, ux)
## IB_c.CentralDerivative_x (N, M, h, v, vx)
## IB_c.CentralDerivative_y (N, M, h, u, uy)
## IB_c.CentralDerivative_y (N, M, h, v, vy)
Xss, Yss = FiberForce(Nb, X, Y, Xss, Yss, Links, Tethers)
fx, fy = ForceToGrid(N, M, h, Nb, hb, Old_X, Old_Y, Xss, Yss)
fx, fy = ExplicitTerms(dt, u, v, ux, uy, vx, vy, fx, fy)
fx += dt * Current * ones((N, M), float64)
fx = fft2(fx)
fy = fft2(fy)
P = Solve_P_Hat(dt, WideLambda, DxSymbol, DySymbol, fx, fy)
P[0, 0] = 0.
u, v = Solve_uv_Hat(dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy)
u = ifft2(u).real
v = ifft2(v).real
Xvel, Yvel = VelToFiber(N, M, h, Nb, hb, 1., Old_X, Old_Y, u, v)
Time = time.time() - Time
TotalTime += Time
TotalCount += 1
Ts = [.01, .02, .05, .1, .5]
for _T in Ts:
if CurT < _T and CurT + dt >= _T:
print "Time", _T, ":", count, TotalTime, TotalTime / TotalCount
#print "Time:", CurT
CurT += dt
print CurT, "Implicit:", Time
count += 1
x = zeros(2 * Nb, float64) UField, VField, UField2, VField2 = InitVelField(N, N, h, h, dt) print abs(UField).max(), abs(VField).max() ##print UField[0,0], UField[4,0], UField[0,0] - UField[4,0] ##raise A = zeros((2 * Nb, 2 * Nb), float64) u = zeros((N, N), float64) v = zeros((N, N), float64) fx = zeros((N, N), float64) fy = zeros((N, N), float64) WideLambda = zeros((N, N), float64) ShortLambda = zeros((N, N), float64) IB_c.InitWideLaplacian(N, N, h, WideLambda) IB_c.InitShortLaplacian(N, N, h, ShortLambda) DxSymbol = InitDxSymbol(N, N, h) DySymbol = InitDySymbol(N, N, h) ########fx, fy = ForceToGrid (N, N, h, 1, 1, array([0],float64), array([0],float64), array([1],float64), array([0],float64)) ########print fx[:,0] ########print sum(fx) ######## ########fx = fft2(fx) ########fy = fft2(fy) ######## ########P = Solve_P_Hat (dt, WideLambda, DxSymbol, DySymbol, fx, fy) ########P[0,0] = 0. ######## ########u, v = Solve_uv_Hat (dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy)
def InitDySymbol(N, M, h):
_DySymbol = zeros((N, M), float64)
IB_c.InitDySymbol(N, M, h, _DySymbol)
return 1j * _DySymbol
def InitVelField(_N, _M, _h, h, dt, rho=1., mu=1., DeltaType=0):
WideLambda = zeros((_N, _M), float64)
ShortLambda = zeros((_N, _M), float64)
IB_c.InitWideLaplacian(_N, _M, _h, WideLambda)
IB_c.InitShortLaplacian(_N, _M, _h, ShortLambda)
DxSymbol = InitDxSymbol(_N, _M, _h)
DySymbol = InitDySymbol(_N, _M, _h)
r = int(ceil(3. * h / _h))
fx = zeros((_N, _M), float64)
for j in range(-r, r + 1):
deltx = Delta(h, j * _h, DeltaType)
for k in range(-r, r + 1):
delt = deltx * Delta(h, k * _h, DeltaType) * 1.
fx[j % _N][k % _M] = fx[j % _N][k % _M] + delt
# print j%_N, k%_M, fx[j%_N][k%_M]
fx, fy = fft2(dt * fx), zeros((_N, _M), float64)
P = Solve_P_Hat(dt, WideLambda, DxSymbol, DySymbol, fx, fy)
P[0, 0] = 0.
u, v = Solve_uv_Hat(dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy, rho,
mu)
u = 1. * ifft2(u).real
v = 1. * ifft2(v).real
# P = ifft2(P).real
Fx1 = array(zeros((_N, _M), float64))
Fy1 = array(zeros((_N, _M), float64))
IB_c.WholeGridSpread(u, float(h), float(_h), int(r), Fx1, DeltaType)
IB_c.WholeGridSpread(v, float(h), float(_h), int(r), Fy1, DeltaType)
fy = zeros((_N, _M), float64)
for j in range(-r, r + 1):
deltx = Delta(h, j * _h, DeltaType)
for k in range(-r, r + 1):
delt = deltx * Delta(h, k * _h, DeltaType) * 1.
fy[j % _N][k % _M] = fy[j % _N][k % _M] + delt
# print j%_N, k%_M, fx[j%_N][k%_M]
fx, fy = zeros((_N, _M), float64), fft2(dt * fy)
P = Solve_P_Hat(dt, WideLambda, DxSymbol, DySymbol, fx, fy)
P[0, 0] = 0.
u, v = Solve_uv_Hat(dt, ShortLambda, DxSymbol, DySymbol, P, fx, fy, rho,
mu)
u = 1. * ifft2(u).real
v = 1. * ifft2(v).real
Fx2 = array(zeros((_N, _M), float64))
Fy2 = array(zeros((_N, _M), float64))
IB_c.WholeGridSpread(u, float(h), float(_h), int(r), Fx2, DeltaType)
IB_c.WholeGridSpread(v, float(h), float(_h), int(r), Fy2, DeltaType)
return Fx1, Fy1, Fx2, Fy2
return f Domain_x, Domain_y = 1., 1. N, M = 15, 15 h = 1. / N print "N, M =", N, M dt = .01 T = 5. CurT = 0 _s = 5000000000. WideLambda = zeros((N, M), float64) ShortLambda = zeros((N, M), float64) IB_c.InitWideLaplacian(N, M, h, WideLambda) IB_c.InitShortLaplacian(N, M, h, ShortLambda) DxSymbol = InitDxSymbol(N, M, h) DySymbol = InitDySymbol(N, M, h) _h = h _N, _M = int(Domain_x / _h), int(Domain_y / _h) UField, VField, UField2, VField2 = InitVelField(_N, _M, _h, h, dt) Nb = 2 * N Xs = zeros(Nb, float64) Ys = zeros(Nb, float64) Xss = zeros(Nb, float64) Yss = zeros(Nb, float64) u = zeros((N, M), float64) v = zeros((N, M), float64)
Nb = 2*N #2*128 h = 1. / N hb = 1. / Nb dt = .001#.25 * .0015 / 2. T = 1. CurT = 0 mu = .05 rho = 1. s = 1. print "h:",h, ", dt:", dt WideLambda = zeros((N,N),float64) ShortLambda = zeros((N,N),float64) IB_c.InitWideLaplacian(N, N, h, WideLambda) IB_c.InitShortLaplacian(N, N, h, ShortLambda) DxSymbol = InitDxSymbol(N, N, h) DySymbol = InitDySymbol(N, N, h) _h = h _N, _M = int(1. / _h), int(1. / _h) UField, VField, UField2, VField2 = InitVelField(_N, _M, _h, h, dt, rho, mu) print UField[0,0],VField2[0,0] X = zeros(Nb, float64) Y = zeros(Nb, float64) Xs = zeros(Nb, float64) Ys = zeros(Nb, float64) Xss = zeros(Nb, float64)
_h = 1. / _N
hb = 1. / Nb
dt = .0005
#dt = .02 * h
#dt = .00003 * h
T = .05
CurT = 0
s = 100000.
#s = 10000000.
print "h:",h, ", dt:", dt
WideLambda = zeros((N,N),float64)
ShortLambda = zeros((N,N),float64)
IB_c.InitWideLaplacian(N, N, h, WideLambda)
IB_c.InitShortLaplacian(N, N, h, ShortLambda)
DxSymbol = InitDxSymbol(N, N, h)
DySymbol = InitDySymbol(N, N, h)
_h = h
_N, _M = int(1. / _h), int(1. / _h)
UField, VField, UField2, VField2 = InitVelField(_N, _M, _h, h, dt)
print UField[0,0],VField2[0,0]
clf()
clf(); imshow(UField); colorbar(); #show(); #&&raw_input("")
clf(); imshow(VField2); colorbar(); #show(); #&&raw_input("")
X = zeros(Nb, float64)
return VelToFiber(N, M, h, Nb, hb, 1., X, Y, u, v) N = 256 All = AllDecompositions(root, N, Terms) MaxDepth = len(All.UField) Domain_x, Domain_y = 1., 1. h = Domain_x / N N, M = int(Domain_x / h), int(Domain_y / h) dt = .002 WideLambda = zeros((N, M), float64) ShortLambda = zeros((N, M), float64) IB_c.InitWideLaplacian(N, M, h, WideLambda) IB_c.InitShortLaplacian(N, M, h, ShortLambda) DxSymbol = InitDxSymbol(N, M, h) DySymbol = InitDySymbol(N, M, h) _h = h _N, _M = int(Domain_x / _h), int(Domain_y / _h) UField, VField, UField2, VField2 = InitVelField(_N, _M, _h, h, dt) ##UField = ones((N,N),float64) ##UField = zeros((N,N), float64) ##for j in range(N): ## for k in range(N): ## UField[j,k] = cos(2*j*pi*h)