def test_temporal_convergence():
"""Take a very small mesh, reduce timestep, expect 2nd order
convergence."""
v_errors = []
u_errors = []
dts = []
hs = []
T = 1.0
dt = 1.0
theta = 0.5
N = 50
for level in (0, 1, 2, 3):
a = dt / (2**level)
(v_error, u_error, h, a, T) = main(N, a, T, theta)
v_errors.append(v_error)
u_errors.append(u_error)
dts.append(a)
hs.append(h)
v_rates = convergence_rate(dts, v_errors)
u_rates = convergence_rate(dts, u_errors)
print("v_errors = ", v_errors)
print("u_errors = ", u_errors)
print("v_rates = ", v_rates)
print("u_rates = ", u_rates)
assert v_rates[-1] > 1.95, "Failed convergence for v"
def test_spatial_and_temporal_convergence():
v_errors = []
u_errors = []
dts = []
hs = []
T = 0.5
dt = 0.05
theta = 0.5
N = 5
for level in (0, 1, 2, 3):
a = dt / (2**level)
(v_error, u_error, h, a, T) = main(N * (2**level), a, T, theta)
v_errors.append(v_error)
u_errors.append(u_error)
dts.append(a)
hs.append(h)
v_rates = convergence_rate(hs, v_errors)
u_rates = convergence_rate(hs, u_errors)
print("v_errors = ", v_errors)
print("u_errors = ", u_errors)
print("v_rates = ", v_rates)
print("u_rates = ", u_rates)
assert v_rates[-1] > 1.95, "Failed convergence for v"
assert u_rates[-1] > 1.9, "Failed convergence for u"
def test_spatial_and_temporal_convergence():
"Test convergence rates for bidomain solver."
v_errors = []
u_errors = []
dts = []
hs = []
T = 0.1
dt = 0.01
theta = 0.5
N = 10
for level in (0, 1, 2):
a = dt/(2**level)
(v_error, u_error, h, a, T) = main(N*(2**level), a, T, theta)
v_errors.append(v_error)
u_errors.append(u_error)
dts.append(a)
hs.append(h)
v_rates = convergence_rate(hs, v_errors)
u_rates = convergence_rate(hs, u_errors)
print(("v_errors = ", v_errors))
print(("u_errors = ", u_errors))
print(("v_rates = ", v_rates))
print(("u_rates = ", u_rates))
assert all(v > 1.9 for v in v_rates), "Failed convergence for v"
assert all(u > 1.9 for u in u_rates), "Failed convergence for u"
def test_temporal_convergence():
"""Take a small mesh, reduce timestep size, expect 2nd order convergence."""
v_errors = []
u_errors = []
dts = []
dt = 1.0
T = 1.0
N = 150
for level in (0, 1, 2, 3):
a = dt / (2**level)
v_error, u_error, h, a, T = main(N, a, T)
v_errors.append(v_error)
u_errors.append(u_error)
dts.append(a)
v_rates = convergence_rate(dts, v_errors)
u_rates = convergence_rate(dts, u_errors)
print("v_errors = ", v_errors)
print("u_errors = ", u_errors)
print("v_rates = ", v_rates)
print("u_rates = ", u_rates)
assert v_rates[-1] > 1.95, "Failed convergence for v"
# Increase spatial resolution to get better temporal convergence for u
assert u_rates[-1] > 1.78, "Failed convergence for u"
def test_spatial_convergence():
"""Take a very small timestep, reduce mesh size, expect 2nd order convergence."""
v_errors = []
u_errors = []
hs = []
dt = 0.01
T = 1.0
for N in (5, 10, 20, 40):
v_error, u_error, h, dt_, T = main(N, dt, T)
v_errors.append(v_error)
u_errors.append(u_error)
hs.append(h)
v_rates = convergence_rate(hs, v_errors)
u_rates = convergence_rate(hs, u_errors)
print("dt, T = ", dt, T)
print("v_errors = ", v_errors)
print("u_errors = ", u_errors)
print("v_rates = ", v_rates)
print("u_rates = ", u_rates)
assert all(v > 1.9 for v in v_rates), "Failed convergence for v"
assert all(u > 1.85 for u in u_rates), "Failed convergence for u"