def gradient_interface_monitor(mesh, alpha=alpha, beta=beta, gamma=gamma):
"""
Monitor function focused around the steep_gradient (budd acta numerica)
NOTE: Defined on the *computational* mesh.
"""
P1 = FunctionSpace(mesh, "CG", 1)
b = swp.fwd_solutions_bathymetry[0]
bath_gradient = recovery.recover_gradient(b)
bath_hess = recovery.recover_hessian(b, op=op)
frob_bath_hess = Function(b.function_space()).project(
local_frobenius_norm(bath_hess))
frob_bath_norm = Function(b.function_space()).project(
frob_bath_hess / max(frob_bath_hess.dat.data[:]))
l2_bath_grad = Function(b.function_space()).project(
local_norm(bath_gradient))
bath_dx_l2_norm = Function(b.function_space()).interpolate(
l2_bath_grad / max(l2_bath_grad.dat.data[:]))
comp = interpolate(
conditional(
alpha * beta * bath_dx_l2_norm > alpha * gamma * frob_bath_norm,
alpha * beta * bath_dx_l2_norm, alpha * gamma * frob_bath_norm),
b.function_space())
comp_new = project(comp, P1)
comp_new2 = interpolate(
conditional(comp_new > Constant(0.0), comp_new, Constant(0.0)), P1)
mon_init = project(Constant(1.0) + comp_new2, P1)
return mon_init
def frobenius_monitor(mesh, x=None): # NOQA: Version above not smooth enough
"""
Frobenius norm taken element-wise.
"""
P1 = FunctionSpace(mesh, "CG", 1)
b = swp.fwd_solutions_bathymetry[0]
P0 = FunctionSpace(b.function_space().mesh(), "DG", 0)
H = recovery.recover_hessian(b, op=op)
frob = interpolate(local_frobenius_norm(H), P0)
return 1 + alpha_const*project(frob, P1)/frob.vector().gather().max()
def frobenius(mesh=None, x=None):
"""
Adapt to the Frobenius norm of an L1-normalised
Hessian metric for the sensor.
"""
P1 = FunctionSpace(mesh, "CG", 1)
M = steady_metric(sensor(mesh, xy=x),
mesh=mesh,
op=op,
**hessian_kwargs)
M_F = local_frobenius_norm(M, space=P1)
return 1.0 + alpha * M_F / interpolate(M_F, P1).vector().gather().max()
def gradient_interface_monitor(mesh,
mod=mod,
beta_mod=beta_mod,
alpha=alpha,
beta=beta,
gamma=gamma,
x=None):
"""
Monitor function focused around the steep_gradient (budd acta numerica)
NOTE: Defined on the *computational* mesh.
"""
P1 = FunctionSpace(mesh, "CG", 1)
eta = swp.fwd_solutions[0].split()[1]
b = swp.fwd_solutions_bathymetry[0]
bath_gradient = recovery.recover_gradient(b)
bath_hess = recovery.recover_hessian(b, op=op)
frob_bath_hess = Function(b.function_space()).project(
local_frobenius_norm(bath_hess))
if max(abs(frob_bath_hess.dat.data[:])) < 1e-10:
frob_bath_norm = Function(b.function_space()).project(frob_bath_hess)
else:
frob_bath_norm = Function(b.function_space()).project(
frob_bath_hess / max(frob_bath_hess.dat.data[:]))
current_mesh = b.function_space().mesh()
l2_bath_grad = Function(b.function_space()).project(
abs(local_norm(bath_gradient)))
bath_dx_l2_norm = Function(b.function_space()).interpolate(
l2_bath_grad / max(l2_bath_grad.dat.data[:]))
alpha_mod = alpha * mod
#beta_mod = 5
elev_abs_norm = Function(eta.function_space()).interpolate(
alpha_mod * pow(cosh(beta_mod * (eta + b)), -2))
comp_int = conditional(
alpha * beta * bath_dx_l2_norm > alpha * gamma * frob_bath_norm,
alpha * beta * bath_dx_l2_norm, alpha * gamma * frob_bath_norm)
comp = interpolate(comp_int + elev_abs_norm, b.function_space())
comp_new = project(comp, P1)
comp_new2 = interpolate(
conditional(comp_new > Constant(0.0), comp_new, Constant(0.0)), P1)
mon_init = project(Constant(1.0) + comp_new2, P1)
return mon_init
def gradient_interface_monitor(mesh,
alpha=alpha,
beta=beta,
gamma=gamma,
K=kappa):
"""
Monitor function focused around the steep_gradient (budd acta numerica)
NOTE: Defined on the *computational* mesh.
"""
P1 = FunctionSpace(mesh, "CG", 1)
b = swp.fwd_solutions_bathymetry[0]
bath_gradient = recovery.recover_gradient(b)
bath_hess = recovery.recover_hessian(b, op=op)
frob_bath_hess = Function(b.function_space()).project(
local_frobenius_norm(bath_hess))
if max(abs(frob_bath_hess.dat.data[:])) < 1e-10:
frob_bath_norm = Function(b.function_space()).project(frob_bath_hess)
else:
frob_bath_norm = Function(b.function_space()).project(
frob_bath_hess / max(frob_bath_hess.dat.data[:]))
l2_bath_grad = Function(b.function_space()).project(
abs(local_norm(bath_gradient)))
bath_dx_l2_norm = Function(b.function_space()).interpolate(
l2_bath_grad / max(l2_bath_grad.dat.data[:]))
comp = interpolate(
conditional(
alpha * beta * bath_dx_l2_norm > alpha * gamma * frob_bath_norm,
alpha * beta * bath_dx_l2_norm, alpha * gamma * frob_bath_norm),
b.function_space())
comp_new = project(comp, P1)
comp_new2 = interpolate(
conditional(comp_new > Constant(0.0), comp_new, Constant(0.0)), P1)
mon_init = project(Constant(1.0) + comp_new2, P1)
H = Function(P1)
tau = TestFunction(P1)
a = (inner(tau, H) * dx) + (K * inner(tau.dx(1), H.dx(1)) *
dx) - inner(tau, mon_init) * dx
solve(a == 0, H)
return H