def lap_div(pdof, grids, point):
s = grids[0].shape
ndim = len(grids)
# Center div equation
center_eq = div_eq( grids, point )
# Initialize the equations
div_lap_eqs = []
for x in range( ndim ):
div_lap_eqs.append( Equation() )
for pp in ndimed.perturb(point):
# PBC correction
pp = ndimed.roller(pp, s)
# If there is a single -3 dof, it must be a solid square
if pdof[pp] < 0:
continue
pert_eq = div_eq(grids, pp)
for dim in range(ndim):
div_lap_eqs[dim] = div_lap_eqs[dim] + ( pert_eq[dim] - center_eq[dim] )
return div_lap_eqs
def momentum_eq(dof_grid, point):
# Correct for pbc's
shape = dof_grid.shape
ndim = len(shape)
point = ndimed.roller(point, shape)
# If solid . . . there is no momentum equation
if dof_grid[ point ] < 0:
return Equation()
# DOF at the center point
center_dof_num = dof_grid[ point ]
m_eq = Equation()
m_eq[ center_dof_num ] = -2 * ndim
# Move one step in each direction
for p in ndimed.perturb( point ):
# Wrap where necessary
p = ndimed.roller(p, shape)
# Get the current dof number
current_dof = dof_grid[p]
# If moving in one direction is a dof
if current_dof >= 0:
# This could glitch if the domain is small enough
# For the laplacian est. to touch itself (3x3 or smaller . . .)
m_eq[ current_dof ] = 1
# If it is solid
elif current_dof == -2:
continue
# If it is completely enclosed solid
elif current_dof == -3:
m_eq[ center_dof_num ] -= 1
return m_eq
