def __init__(self, radius, L_max, N_max, R_max, L_dealias, N_dealias, m_max=None, mesh=None, comm=None):
if m_max is None:
m_max = L_max
self.radius = radius
self.L_max = L_max
self.N_max = N_max
self.R_max = R_max
self.L_dealias = L_dealias
self.N_dealias = N_dealias
# Domain
phi_basis = de.Fourier('phi', 2*(L_max+1), interval=(0, 2*np.pi), dealias=L_dealias)
theta_basis = de.Chebyshev('theta', L_max+1, interval=(0, np.pi), dealias=L_dealias)
r_basis = de.Chebyshev('r', N_max+1, interval=(0, 1), dealias=N_dealias)
self.domain = domain = de.Domain([phi_basis, theta_basis, r_basis], grid_dtype=np.float64, mesh=mesh, comm=comm)
# Local m
mesh = self.domain.distributor.mesh
if len(mesh) == 0:
phi_layout = domain.distributor.layouts[3]
th_m_layout = domain.distributor.layouts[2]
ell_r_layout = domain.distributor.layouts[1]
r_ell_layout = domain.distributor.layouts[1]
elif len(mesh) == 1:
phi_layout = domain.distributor.layouts[4]
th_m_layout = domain.distributor.layouts[2]
ell_r_layout = domain.distributor.layouts[1]
r_ell_layout = domain.distributor.layouts[1]
elif len(mesh) == 2:
phi_layout = domain.distributor.layouts[5]
th_m_layout = domain.distributor.layouts[3]
ell_r_layout = domain.distributor.layouts[2]
r_ell_layout = domain.distributor.layouts[1]
self.m_start = th_m_layout.slices(scales=1)[0].start
self.m_end = th_m_layout.slices(scales=1)[0].stop-1
self.m_size = self.m_end - self.m_start + 1
self.ell_start = r_ell_layout.slices(scales=1)[1].start
self.ell_end = r_ell_layout.slices(scales=1)[1].stop-1
# Ball wrapper
N_theta = int((L_max+1)*L_dealias)
N_r = int((N_max+1)*N_dealias)
self.B = B = ball_wrapper.Ball(N_max, L_max, N_theta=N_theta, N_r=N_r, R_max=R_max,
ell_min=self.ell_start, ell_max=self.ell_end, m_min=self.m_start, m_max=self.m_end, a=0.)
# Grids
grid_slices = phi_layout.slices(domain.dealias)
self.phi = domain.grid(0, scales=domain.dealias)[grid_slices[0], :, :]
self.theta = B.grid(1, dimensions=3)[:, grid_slices[1], :] # local
self.r = radius * B.grid(2, dimensions=3)[:, :, grid_slices[2]] # local
self.weight_theta = B.weight(1, dimensions=3)[:, grid_slices[1], :]
self.weight_r = radius**3 * B.weight(2, dimensions=3)[:, :, grid_slices[2]]
elif len(mesh) == 2:
phi_layout = domain.distributor.layouts[5]
th_m_layout = domain.distributor.layouts[3]
ell_r_layout = domain.distributor.layouts[2]
r_ell_layout = domain.distributor.layouts[1]
m_start = th_m_layout.slices(scales=1)[0].start
m_end = th_m_layout.slices(scales=1)[0].stop-1
m_size = m_end - m_start + 1
ell_start = r_ell_layout.slices(scales=1)[1].start
ell_end = r_ell_layout.slices(scales=1)[1].stop-1
# set up ball
N_theta = int((L_max+1)*L_dealias)
N_r = int((N_r+1)*N_dealias)
B = ball.Ball(N_max,L_max,N_theta=N_theta,N_r=N_r,R_max=R_max,ell_min=ell_start,ell_max=ell_end,m_min=m_start,m_max=m_end,a=0)
theta_global = B.grid(0)
r_global = B.grid(1)
z, R = r_global*np.cos(theta_global), r_global*np.sin(theta_global) # global
grid_slices = phi_layout.slices(domain.dealias)
phi = domain.grid(0,scales=domain.dealias)[grid_slices[0],:,:]
theta = B.grid(1,dimensions=3)[:,grid_slices[1],:] # local
r = B.grid(2,dimensions=3)[:,:,grid_slices[2]] # local
weight_theta = B.weight(1,dimensions=3)[:,grid_slices[1],:]
weight_r = B.weight(2,dimensions=3)[:,:,grid_slices[2]]
om = ball.TensorField_3D(1,B,domain)
u = ball.TensorField_3D(1,B,domain)
p = ball.TensorField_3D(0,B,domain)
plt.setp(plot_axis.get_yticklabels(), visible=False)
eigs = []
text_label = [
r'${\rm no-slip}$', r'${\rm stress-free}$', r'${\rm potential}$',
r'${\rm perfectly-conducting}$', r'${\rm pseudo-vacuum}$'
]
text_x = 0.025
text_y = 0.875
ell = 50
L_max, R_max = 63, 3
B = ball.Ball(N_max, L_max, R_max=R_max, ell_min=48, ell_max=52)
calculate = True
if not os.path.isdir('data'):
os.mkdir('data')
if not os.path.isdir('data/eigenvalues_256'):
os.mkdir('data/eigenvalues_256')
boundary_conditions = 'no-slip'
if calculate:
vals, vecs = bd.eigensystem(N_max,
ell,
B,
alpha_BC=2,
boundary_conditions=boundary_conditions)
from dedalus_sphere import ball_wrapper as ball
import numpy as np
from scipy.sparse import linalg as spla
import scipy.sparse as sparse
import dedalus.public as de
from dedalus.core.distributor import Distributor
def err(a, b):
print(np.max(np.abs(a - b)) / np.max(np.abs(b)))
L_max, N_max, R_max = 31, 31, 2
B_3D = ball.Ball(N_max, L_max, R_max=R_max)
L_dealias = 1
N_dealias = 1
N_r = N_max
comm = None
mesh = None
phi_basis_3D = de.Fourier('phi',
2 * (L_max + 1),
interval=(0, 2 * np.pi),
dealias=L_dealias)
theta_basis_3D = de.Fourier('theta',
L_max + 1,
interval=(0, np.pi),
dealias=L_dealias)
r_basis_3D = de.Fourier('r', N_max + 1, interval=(0, 1), dealias=N_dealias)
domain_3D = de.Domain([phi_basis_3D, theta_basis_3D, r_basis_3D],
theta_basis = de.Fourier('theta', 2 * L_max + 1, interval=(0, np.pi))
r_basis = de.Fourier('r', N_max + 1, interval=(0, 1))
domain = de.Domain([theta_basis, r_basis], grid_dtype=np.float64)
mesh = domain.distributor.mesh
if len(mesh) == 0: #serial
ell_r_layout = domain.distributor.layouts[1]
r_ell_layout = domain.distributor.layouts[1]
else:
ell_r_layout = domain.distributor.layouts[2]
r_ell_layout = domain.distributor.layouts[1]
ell_min = r_ell_layout.slices(scales=1)[0].start
ell_max = r_ell_layout.slices(scales=1)[0].stop - 1
B = ball.Ball(N_max, L_max, R_max=R_max, ell_min=ell_min, ell_max=ell_max)
r = B.grid(1)[0]
m = 0
eig_num = 100
f = ball.TensorField_2D(0, m, B, domain)
f['c'][ell][:512] = vec[eig_num]
f['g'][0, 10, :] = f['g'][0, 10, :].real
f['g'][0, 10, :] /= np.max(np.abs(f['g'][0, 10, :]))
print(np.max(np.abs(f['g'][0, 10, :])))
k = np.sqrt(vals[eig_num])
sol = spec.jv(ell + 1 / 2, k * r) / np.sqrt(k * r)
sol /= np.max(np.abs(sol))
eig_axes.plot(r,