def uexactfn(t,cp):
th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2])
return np.exp(-2*t)*np.cos(phi + np.pi / 2)
if __name__ == '__main__':
MBlocklist = [10,20,40,80]
error = []
dx = []
comm = MPI.COMM_WORLD
surface = Sphere(center=np.array([0.0, 0.0, 0.0]))
# exact solution
rez = 30
xx, yy, zz = surface.parametric_grid(rez)
th, phi, r = cart2sph(xx,yy,zz)
exactu = np.cos(phi + np.pi / 2).ravel()
points = np.array([xx.ravel(),yy.ravel(),zz.ravel()]).T
vsize = xx.ravel().shape[0]
vAssigned = vsize // comm.size + int(comm.rank < (vsize % comm.size))
vstart = comm.exscan(vAssigned)
if comm.rank == 0:
vstart = 0
for MBlock in MBlocklist:
opt = {'M':MBlock,'m':5,'d':3}
band = Band(surface,comm,opt)
u = np.cos(phi + np.pi / 2)
# Let's keep a copy of the initial conditions
initial_u = u.copy()
# Build interpolation and differential matrix.
E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape)
L = build_diff_matrix(int_grid, dx, virtual_grid_shape)
M = build_linear_diagonal_splitting(L, E)
# Compute eigenvalues
t = time()
print "Computing eigenvalues..."
Evals, Evecs = splinalg.eigs(-M, k=32, which="SM")
sorted_indices = np.argsort(Evals)
print "...took", time() -t
xp, yp, zp = s.parametric_grid(65)
_, phi_plot, _ = cart2sph(xp, yp, zp)
Eplot = build_interp_matrix(int_grid,
np.column_stack((xp.ravel(),
yp.ravel(),
zp.ravel())),
dx, p, ll, virtual_grid_shape)
if PLOT:
# Plotting code. Build a pipeline to be able to change the data later.
src = mlab.pipeline.grid_source(xp, yp, zp,
scalars=zp)
normals = mlab.pipeline.poly_data_normals(src)
surf = mlab.pipeline.surface(normals)
mlab.colorbar()
virtual_grid_shape = np.abs(ur - ll) / dx + 1
# The (i,j,...) indices of the grid points, taking `ll` as origin.
int_grid = np.round((grid - ll) / dx).astype(np.int)
# Initial conditions
th, phi, r = cart2sph(grid[:, 0], grid[:, 1], grid[:, 2])
u = np.cos(phi + np.pi / 2)
# Let's keep a copy of the initial conditions
initial_u = u.copy()
# Build interpolation and differential matrix.
E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape)
L = build_diff_matrix(int_grid, dx, virtual_grid_shape)
xp, yp, zp = s.parametric_grid(65)
_, phi_plot, _ = cart2sph(xp, yp, zp)
Eplot = build_interp_matrix(
int_grid, np.column_stack((xp.ravel(), yp.ravel(), zp.ravel())), dx, p, ll,
virtual_grid_shape)
if PLOT:
# Plotting code. Build a pipeline to be able to change the data later.
src = mlab.pipeline.grid_source(xp,
yp,
zp,
scalars=(Eplot * u).reshape(xp.shape))
normals = mlab.pipeline.poly_data_normals(src)
surf = mlab.pipeline.surface(normals)
mlab.colorbar()
ymin, ymax = -1.5, 1.5
xi = np.round(horizontal_res * (grid[:, 0] - xmin) / (xmax - xmin)).astype(
np.int)
yi = (vertical_res - np.round(vertical_res * (grid[:, 1] - ymin) /
(ymax - ymin))).astype(np.int)
# Forcing functions
chi = np.zeros(grid.shape[0])
# Create forcing function
ix = grid[:, 2] >= surf_plane
chi[ix] = image[xi[ix], yi[ix]]
# Make sure forcing is a cp extension
chi = E * chi
# Re-threshold
chi = (chi > 0.9).astype(np.int)
xp, yp, zp = s.parametric_grid(256)
Eplot = build_interp_matrix(
int_grid, np.column_stack((xp.ravel(), yp.ravel(), zp.ravel())), dx, p, ll,
virtual_grid_shape)
# Plot forcing function
mlab.figure(1, fgcolor=(1.0, 1.0, 1.0))
mlab.mesh(xp, yp, zp, scalars=(Eplot * (1 - chi)).reshape(xp.shape))
mlab.view(azimuth=158, elevation=25, distance=7)
mlab.title('forcing function')
# Parameters and functions for Gray--Scott
F = 0.054
kk = 0.063
nuu = 1 / (3 / dx.min())**2
nuv = nuu / 2.
ymin, ymax = -1.5, 1.5
xi = np.round(horizontal_res * (grid[:, 0] - xmin) /
(xmax - xmin)).astype(np.int)
yi = (vertical_res - np.round(vertical_res * (grid[:, 1] - ymin) /
(ymax - ymin))).astype(np.int)
# Forcing functions
chi = np.zeros(grid.shape[0])
# Create forcing function
ix = grid[:, 2] >= surf_plane
chi[ix] = image[xi[ix], yi[ix]]
# Make sure forcing is a cp extension
chi = E * chi
# Re-threshold
chi = (chi > 0.9).astype(np.int)
xp, yp, zp = s.parametric_grid(256)
Eplot = build_interp_matrix(int_grid,
np.column_stack((xp.ravel(),
yp.ravel(),
zp.ravel())),
dx, p, ll, virtual_grid_shape)
# Plot forcing function
mlab.figure(1,fgcolor=(1.0,1.0,1.0))
mlab.mesh(xp, yp, zp, scalars=(Eplot*(1-chi)).reshape(xp.shape))
mlab.view(azimuth=158, elevation=25, distance=7)
mlab.title('forcing function')
# Parameters and functions for Gray--Scott
F = 0.054
def initialu(cp):
th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2])
return np.cos(phi + np.pi / 2)
if __name__ == '__main__':
MBlocklist = [10,20,40,80]
Tf = 0.5
error = []
dx = []
comm = MPI.COMM_WORLD
surface = Sphere(center=np.array([0.0, 0.0, 0.0]))
# exact solution
rez = 30
xx, yy, zz = surface.parametric_grid(rez)
th, phi, r = cart2sph(xx,yy,zz)
exactu = np.cos(phi + np.pi / 2).ravel()
points = np.array([xx.ravel(),yy.ravel(),zz.ravel()]).T
vsize = xx.ravel().shape[0]
vAssigned = vsize // comm.size + int(comm.rank < (vsize % comm.size))
vstart = comm.exscan(vAssigned)
if comm.rank == 0:
vstart = 0
for MBlock in MBlocklist:
opt = {'M':MBlock,'m':5,'d':3}
