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)
_,_,v,v2 = band.createGLVectors()
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)
p=p,
diff_stencil_arm=diff_stencil_arm)
cp2, distance2, _, _ = s.closest_point(grid)
assert np.allclose(cp, cp2)
assert np.allclose(distance, distance2)
# Corners of the virtual grid, superset of `grid`
ll = np.array(dim * [grid.min()]) - 3 * dx
ur = np.array(dim * [grid.max()]) + 3 * dx
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)
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
p=p,
diff_stencil_arm=diff_stencil_arm)
cp2, distance2, _, _ = s.closest_point(grid)
assert np.allclose(cp, cp2)
assert np.allclose(distance, distance2)
# Corners of the virtual grid, superset of `grid`
ll = np.array(dim * [grid.min()]) - 3 * dx
ur = np.array(dim * [grid.max()]) + 3 * dx
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:
def initialu(cp):
th, phi, r = cart2sph(cp[:, 0], cp[:, 1], cp[:, 2])
return np.cos(phi + np.pi / 2)
def initialu(cp):
th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2])
return np.cos(phi + np.pi / 2)
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}
band = Band(surface,comm,opt)
