def test_mesh1():
m = Mesh(-1, 1, 5, 2)
pts, p = m.get_mesh_data()
assert (abs(pts - array([-1, -0.6, -0.2, 0.2, 0.6, 1])) < eps).all()
assert (abs(p - array([2, 2, 2, 2, 2])) < eps).all()
m = Mesh(-1, 1, 4, 1)
pts, p = m.get_mesh_data()
assert (abs(pts - array([-1, -0.5, 0, 0.5, 1])) < eps).all()
assert (abs(p - array([1, 1, 1, 1])) < eps).all()
def test_mesh1():
m = Mesh(-1, 1, 5, 2)
pts, p = m.get_mesh_data()
assert (abs(pts - array([-1, -0.6, -0.2, 0.2, 0.6, 1])) < eps).all()
assert (abs(p - array([2, 2, 2, 2, 2])) < eps).all()
m = Mesh(-1, 1, 4, 1)
pts, p = m.get_mesh_data()
assert (abs(pts - array([-1, -0.5, 0, 0.5, 1])) < eps).all()
assert (abs(p - array([1, 1, 1, 1])) < eps).all()
def test_mesh3():
m = Mesh([0, 1, 3, 4], [2, 2, 2])
pts, p = m.get_mesh_data()
assert (abs(pts - array([0, 1, 3, 4])) < eps).all()
assert (abs(p - array([2, 2, 2])) < eps).all()
m = Mesh([-1, -0.5, 0, 0.5, 1], [2, 2, 2, 2])
pts, p = m.get_mesh_data()
assert (abs(pts - array([-1, -0.5, 0, 0.5, 1])) < eps).all()
assert (abs(p - array([2, 2, 2, 2])) < eps).all()
def radial_dirac_equation_adapt(params, error_tol=1e-8):
if params["mesh_uniform"]:
pts = create_uniform_mesh(params["a"],
params["b"],
n_elem=params["el_num"])
else:
pts = create_log_mesh(params["a"],
params["b"],
par=params["mesh_par1"],
n_elem=params["el_num"])
orders = [params["el_order"]] * (len(pts) - 1)
mesh = Mesh(pts, orders)
conv_graph = []
l = params["l"]
Z = params["Z"]
N_eig = params["eig_num"]
#exact_energies=[-1.*Z**2/(2*n**2) for n in range(1+l,N_eig+1+l)]
#old_energies = None
try:
for i in range(10000):
print "-" * 80
print "adaptivity iteration:", i
mesh.set_bc_right_dirichlet(0, 0)
pts, orders = mesh.get_mesh_data()
print "Current mesh:"
print pts
print orders
#stop
N_dof, energies, eigs = solve_dirac(mesh,
l=l,
Z=Z,
eqn_type=eqn_type,
eig_num=N_eig)
for n in range(1, 51):
print "%d %10.5f" % (n, energies[n - 1])
break
conv_graph.append((N_dof, energies))
# This doesn't work well:
if old_energies is not None:
err = max(abs(old_energies - energies))
print "Maximum error in energies:", err
if err < error_tol:
break
#err = max(abs(energies - exact_energies))
#print "Maximum error in energies:", err
#if err < error_tol:
# break
old_energies = energies
# exact_energies = array(exact_energies)
# print energies - exact_energies
mesh = adapt_mesh(mesh,
eigs,
l=l,
Z=Z,
adapt_type=params["adapt_type"])
finally:
plot_conv(conv_graph, exact=exact_energies, l=l)
def radial_schroedinger_equation_adapt(params, error_tol=1e-8):
if params["mesh_uniform"]:
pts = create_uniform_mesh(params["a"], params["b"],
n_elem=params["el_num"])
else:
pts = create_log_mesh(params["a"], params["b"],
par=params["mesh_par1"],
n_elem=params["el_num"])
orders = [params["el_order"]]*(len(pts)-1)
mesh = Mesh(pts, orders)
conv_graph = []
l = params["l"]
Z = params["Z"]
N_eig = params["eig_num"]
exact_energies=[-1.*Z**2/(2*n**2) for n in range(1+l,N_eig+1+l)]
old_energies = None
eqn_type = params["eqn_type"]
try:
for i in range(10000):
print "-"*80
print "adaptivity iteration:", i
if eqn_type == "rR":
mesh.set_bc_left_dirichlet(0, 0)
mesh.set_bc_right_dirichlet(0, 0)
# Use zero dirichlet for eqn_type="R" as well, just to make sure
# that we agree with sle1d
mesh.set_bc_right_dirichlet(0, 0)
pts, orders = mesh.get_mesh_data()
print "Current mesh:"
print pts
print orders
#stop
N_dof, energies, eigs = solve_schroedinger(mesh, l=l, Z=Z,
eqn_type=eqn_type, eig_num=N_eig)
for n in range(1, N_eig+1):
print "%d %10.5f" % (n, energies[n-1])
conv_graph.append((N_dof, energies))
# This doesn't work well:
if old_energies is not None:
err = max(abs(old_energies - energies))
print "Maximum error in energies:", err
if err < error_tol:
break
#err = max(abs(energies - exact_energies))
#print "Maximum error in energies:", err
#if err < error_tol:
# break
old_energies = energies
# exact_energies = array(exact_energies)
# print energies - exact_energies
mesh = adapt_mesh(mesh, eigs, l=l, Z=Z,
adapt_type=params["adapt_type"])
finally:
pass
#plot_conv(conv_graph, exact=exact_energies, l=l)
return [e for e in energies if e < 0]
def radial_dirac_equation_adapt(params, error_tol=1e-8):
if params["mesh_uniform"]:
pts = create_uniform_mesh(params["a"], params["b"],
n_elem=params["el_num"])
else:
pts = create_log_mesh(params["a"], params["b"],
par=params["mesh_par1"],
n_elem=params["el_num"])
orders = [params["el_order"]]*(len(pts)-1)
mesh = Mesh(pts, orders)
conv_graph = []
l = params["l"]
Z = params["Z"]
N_eig = params["eig_num"]
#exact_energies=[-1.*Z**2/(2*n**2) for n in range(1+l,N_eig+1+l)]
#old_energies = None
try:
for i in range(10000):
print "-"*80
print "adaptivity iteration:", i
mesh.set_bc_right_dirichlet(0, 0)
pts, orders = mesh.get_mesh_data()
print "Current mesh:"
print pts
print orders
#stop
N_dof, energies, eigs = solve_dirac(mesh, l=l, Z=Z,
eqn_type=eqn_type, eig_num=N_eig)
for n in range(1, 51):
print "%d %10.5f" % (n, energies[n-1])
break
conv_graph.append((N_dof, energies))
# This doesn't work well:
if old_energies is not None:
err = max(abs(old_energies - energies))
print "Maximum error in energies:", err
if err < error_tol:
break
#err = max(abs(energies - exact_energies))
#print "Maximum error in energies:", err
#if err < error_tol:
# break
old_energies = energies
# exact_energies = array(exact_energies)
# print energies - exact_energies
mesh = adapt_mesh(mesh, eigs, l=l, Z=Z,
adapt_type=params["adapt_type"])
finally:
plot_conv(conv_graph, exact=exact_energies, l=l)
def radial_schroedinger_equation_adapt(params, error_tol=1e-8):
if params["mesh_uniform"]:
pts = create_uniform_mesh(params["a"],
params["b"],
n_elem=params["el_num"])
else:
pts = create_log_mesh(params["a"],
params["b"],
par=params["mesh_par1"],
n_elem=params["el_num"])
orders = [params["el_order"]] * (len(pts) - 1)
mesh = Mesh(pts, orders)
conv_graph = []
l = params["l"]
Z = params["Z"]
N_eig = params["eig_num"]
exact_energies = [
-1. * Z**2 / (2 * n**2) for n in range(1 + l, N_eig + 1 + l)
]
old_energies = None
eqn_type = params["eqn_type"]
try:
for i in range(10000):
print "-" * 80
print "adaptivity iteration:", i
if eqn_type == "rR":
mesh.set_bc_left_dirichlet(0, 0)
mesh.set_bc_right_dirichlet(0, 0)
# Use zero dirichlet for eqn_type="R" as well, just to make sure
# that we agree with sle1d
mesh.set_bc_right_dirichlet(0, 0)
pts, orders = mesh.get_mesh_data()
print "Current mesh:"
print pts
print orders
#stop
N_dof, energies, eigs = solve_schroedinger(mesh,
l=l,
Z=Z,
eqn_type=eqn_type,
eig_num=N_eig)
for n in range(1, N_eig + 1):
print "%d %10.5f" % (n, energies[n - 1])
conv_graph.append((N_dof, energies))
# This doesn't work well:
if old_energies is not None:
err = max(abs(old_energies - energies))
print "Maximum error in energies:", err
if err < error_tol:
break
#err = max(abs(energies - exact_energies))
#print "Maximum error in energies:", err
#if err < error_tol:
# break
old_energies = energies
# exact_energies = array(exact_energies)
# print energies - exact_energies
mesh = adapt_mesh(mesh,
eigs,
l=l,
Z=Z,
adapt_type=params["adapt_type"])
finally:
pass
#plot_conv(conv_graph, exact=exact_energies, l=l)
return [e for e in energies if e < 0]
