def fundamental3D( cot ):
'''
plots fundamental solution in 3D
'''
x = dic[cot.mesh_name].source
V = cot.V
mesh_obj = cot.mesh_obj
kappa = cot.kappa
y = cot.mesh_obj.coordinates()
x_y = x-y
ra = x_y * x_y
ra = np.sum( ra, axis = 1 )
ra = np.sqrt( ra ) + 1e-13
kappara = kappa * ra
phi_arr = cot.factor * np.power( kappara, 0.5 ) * sp.kv( 0.5, kappara )
phi = Function( V )
phi.vector().set_local( phi_arr[dof_to_vertex_map(V)] )
helper.save_plots( phi,
["Free Space", "Greens Function"],
cot )
def green( cot, BC ):
'''
plots the domain Green's function with boundary
condition BC on the mesh for a source.
'''
u = cot.u
v = cot.v
normal = cot.normal
kappa = cot.kappa
f = Constant( 0.0 )
tmp = Function( cot.V )
loc_solver = cot.solvers( BC )
L = f*v*dx
b = assemble(L)
# Make the RHS have delta funcitons at the sources
helper.apply_sources( cot, b )
sol = Function( cot.V )
loc_solver( tmp.vector(), b )
loc_solver( sol.vector(), assemble(tmp*v*dx) )
# Create the descrition list so we keep track of files
desc = [ BC, "Greens Function" ]
if "ours" in BC:
desc.append( cot.quad )
helper.save_plots( sol,
desc,
cot )
def variance( cot, BC ):
'''
plots domain pointwise variance with boundary condition BC.
'''
u = cot.u
v = cot.v
kappa = cot.kappa
f = Constant( 0.0 )
tmp = Function( cot.V )
loc_solver = cot.solvers( BC )
L = f*v*dx
b = assemble(L)
if "dirichlet" in BC:
pass
else:
g = cot.gs( BC )
helper.apply_sources( cot, b, scaling = g )
sol_constant_var = Function( cot.V )
loc_solver( tmp.vector(), b )
loc_solver( sol_constant_var.vector(), assemble(tmp*v*dx) )
sol_constant_var.vector().set_local(
sol_constant_var.vector().array() * g.vector().array()
)
# Create the descrition list so we keep track of files
greens_desc = [ BC, "Constant Variance", "Greens Function"]
std_desc = [ BC, "Standard Deviation" ]
if "ours" in BC:
greens_desc.append( cot.quad )
std_desc.append( cot.quad )
helper.save_plots( cot.stds( BC ),
std_desc,
cot )
if not "dirichlet" in BC:
helper.save_plots( sol_constant_var,
greens_desc,
cot )