# Let's keep a copy of the initial conditions
initial_u = u.copy()
# Let's build the matrices. TODO: I think it would be nicer to use
# `grid` instead of `int_grid`. It is a simple change.
E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape)
# TODO: being able to select different laplacian operators. Currently
# it uses the second order laplacian for 2D and 3D. We could probably
# use stencils.py, and give the stencil as a parameter
L = build_diff_matrix(int_grid, dx, virtual_grid_shape)
# Points in the surface of the sphere, used por plotting
xp, yp, zp = Sphere().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()
Tf = 2
dt = 0.1 * np.min(dx)**2
numtimesteps = int(Tf // dt + 1)
