def fvm_timestep_RK2(self, dt):
f_initial = self.f
self.f = self.f + df_dt_fvm(self.f, self, True) * (dt / 2)
self._communicate_f()
self._apply_bcs_f()
if (self.physical_system.params.charge_electron != 0
and self.physical_system.params.fields_solver == 'fdtd'):
# Will return a flattened array containing the values of
# J1,2,3 in 2D space:
self.J1 = self.physical_system.params.charge_electron \
* self.compute_moments('mom_p1_bulk') # (i + 1/2, j + 1/2)
self.J2 = self.physical_system.params.charge_electron \
* self.compute_moments('mom_p2_bulk') # (i + 1/2, j + 1/2)
self.J3 = self.physical_system.params.charge_electron \
* self.compute_moments('mom_p3_bulk') # (i + 1/2, j + 1/2)
# Obtaining the values for current density on the Yee-Grid:
self.J1 = 0.5 * (self.J1 + af.shift(self.J1, 0, 0, 1)) # (i + 1/2, j)
self.J2 = 0.5 * (self.J2 + af.shift(self.J2, 0, 1, 0)) # (i, j + 1/2)
self.J3 = 0.25 * (
self.J3 + af.shift(self.J3, 0, 1, 0) +
+af.shift(self.J3, 0, 0, 1) + af.shift(self.J3, 0, 1, 1)) # (i, j)
# Here:
# cell_centered_EM_fields[:3] is at n
# cell_centered_EM_fields[3:] is at n+1/2
# cell_centered_EM_fields_at_n_plus_half[3:] is at n-1/2
self.cell_centered_EM_fields_at_n[:3] = self.cell_centered_EM_fields[:
3]
self.cell_centered_EM_fields_at_n[3:] = \
0.5 * ( self.cell_centered_EM_fields_at_n_plus_half[3:]
+ self.cell_centered_EM_fields[3:]
)
self.cell_centered_EM_fields_at_n_plus_half[
3:] = self.cell_centered_EM_fields[3:]
fdtd(self, dt)
fdtd_grid_to_ck_grid(self)
# Here
# cell_centered_EM_fields[:3] is at n+1
# cell_centered_EM_fields[3:] is at n+3/2
self.cell_centered_EM_fields_at_n_plus_half[:3] = \
0.5 * ( self.cell_centered_EM_fields_at_n_plus_half[:3]
+ self.cell_centered_EM_fields[:3]
)
self.f = f_initial + df_dt_fvm(self.f, self, False) * dt
af.eval(self.f)
return
def test_fdtd_mode1():
error_B1 = np.zeros(3)
error_B2 = np.zeros(3)
error_E3 = np.zeros(3)
N = 2**np.arange(5, 8)
for i in range(N.size):
obj = test(N[i])
N_g = obj.N_ghost
B1_fdtd = gauss1D(obj.q2[:, N_g:-N_g, N_g:-N_g], 0.1)
B2_fdtd = gauss1D(obj.q1[:, N_g:-N_g, N_g:-N_g], 0.1)
obj.yee_grid_EM_fields[3, N_g:-N_g, N_g:-N_g] = B1_fdtd
obj.yee_grid_EM_fields[4, N_g:-N_g, N_g:-N_g] = B2_fdtd
dt = obj.dq1 / 2
time = np.arange(dt, 1 + dt, dt)
E3_initial = obj.yee_grid_EM_fields[2].copy()
B1_initial = obj.yee_grid_EM_fields[3].copy()
B2_initial = obj.yee_grid_EM_fields[4].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
fdtd(obj, dt)
error_B1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[3, N_g:-N_g, N_g:-N_g] -
B1_initial[0, N_g:-N_g, N_g:-N_g])) / (
B1_initial.elements())
error_B2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[4, N_g:-N_g, N_g:-N_g] -
B2_initial[0, N_g:-N_g, N_g:-N_g])) / (
B2_initial.elements())
error_E3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[2, N_g:-N_g, N_g:-N_g] -
E3_initial[0, N_g:-N_g, N_g:-N_g])) / (
E3_initial.elements())
poly_B1 = np.polyfit(np.log10(N), np.log10(error_B1), 1)
poly_B2 = np.polyfit(np.log10(N), np.log10(error_B2), 1)
poly_E3 = np.polyfit(np.log10(N), np.log10(error_E3), 1)
assert (abs(poly_B1[0] + 3) < 0.6)
assert (abs(poly_B2[0] + 3) < 0.6)
assert (abs(poly_E3[0] + 2) < 0.6)
def test_fdtd_mode2():
error_E1 = np.zeros(3)
error_E2 = np.zeros(3)
error_B3 = np.zeros(3)
N = 2**np.arange(5, 8)
for i in range(N.size):
obj = test(N[i])
N_g = obj.N_ghost
obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] = gauss1D(
obj.q2[:, N_g:-N_g, N_g:-N_g], 0.1)
obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] = gauss1D(
obj.q1[:, N_g:-N_g, N_g:-N_g], 0.1)
dt = obj.dq1 / 2
time = np.arange(dt, 1 + dt, dt)
B3_initial = obj.yee_grid_EM_fields[5].copy()
E1_initial = obj.yee_grid_EM_fields[0].copy()
E2_initial = obj.yee_grid_EM_fields[1].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
fdtd(obj, dt)
error_E1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] -
E1_initial[:, N_g:-N_g, N_g:-N_g])) / (
E1_initial.elements())
error_E2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] -
E2_initial[:, N_g:-N_g, N_g:-N_g])) / (
E2_initial.elements())
error_B3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[5, N_g:-N_g, N_g:-N_g] -
B3_initial[:, N_g:-N_g, N_g:-N_g])) / (
B3_initial.elements())
poly_E1 = np.polyfit(np.log10(N), np.log10(error_E1), 1)
poly_E2 = np.polyfit(np.log10(N), np.log10(error_E2), 1)
poly_B3 = np.polyfit(np.log10(N), np.log10(error_B3), 1)
assert (abs(poly_E1[0] + 3) < 0.4)
assert (abs(poly_E2[0] + 3) < 0.4)
assert (abs(poly_B3[0] + 2) < 0.4)
def test_fdtd_modeTE():
error_E1 = np.zeros(3)
error_E2 = np.zeros(3)
error_B3 = np.zeros(3)
N = 2**np.arange(5, 8)
for i in range(N.size):
obj = test(N[i])
dt = obj.dq1 / 2
time = np.arange(dt, 1 + dt, dt)
N_g = obj.N_ghost
E1_fdtd = 8 * np.pi * af.cos(4 * np.pi * obj.q2_center_bot)
E2_fdtd = 4 * np.pi * af.cos(2 * np.pi * obj.q1_left_center)
B3_fdtd = 2 * np.pi * af.cos(2 * np.pi * (obj.q1_left_center - dt)) \
- 4 * np.pi * af.cos(4 * np.pi * (obj.q2_center_bot - dt))
obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] = E1_fdtd[:, N_g:-N_g,
N_g:-N_g]
obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] = E2_fdtd[:, N_g:-N_g,
N_g:-N_g]
obj.yee_grid_EM_fields[5, N_g:-N_g, N_g:-N_g] = B3_fdtd[:, N_g:-N_g,
N_g:-N_g]
B3_initial = obj.yee_grid_EM_fields[5].copy()
E1_initial = obj.yee_grid_EM_fields[0].copy()
E2_initial = obj.yee_grid_EM_fields[1].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
obj.J1 = 48 * np.pi**2 * af.sin(4 * np.pi *
(obj.q2_center_bot - 2 * t0))
obj.J2 = 12 * np.pi**2 * af.sin(2 * np.pi *
(obj.q1_left_center - 2 * t0))
fdtd(obj, dt)
error_E1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] -
E1_initial[:, N_g:-N_g, N_g:-N_g])) / (
E1_initial.elements())
error_E2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] -
E2_initial[:, N_g:-N_g, N_g:-N_g])) / (
E2_initial.elements())
error_B3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[5, N_g:-N_g, N_g:-N_g] -
B3_initial[:, N_g:-N_g, N_g:-N_g])) / (
B3_initial.elements())
poly_E1 = np.polyfit(np.log10(N), np.log10(error_E1), 1)
poly_E2 = np.polyfit(np.log10(N), np.log10(error_E2), 1)
poly_B3 = np.polyfit(np.log10(N), np.log10(error_B3), 1)
assert (abs(poly_E1[0] + 2) < 0.25)
assert (abs(poly_E2[0] + 2) < 0.25)
assert (abs(poly_B3[0] + 2) < 0.25)
def test_fdtd_modeTM():
error_B1 = np.zeros(3)
error_B2 = np.zeros(3)
error_E3 = np.zeros(3)
N = 2**np.arange(5, 8)
for i in range(N.size):
obj = test(N[i])
dt = obj.dq1 / 2
time = np.arange(dt, 1 + dt, dt)
N_g = obj.N_ghost
A3 = af.sin(2 * np.pi * (obj.q1_left_bot - 0.5 * dt) + 4 * np.pi *
(obj.q2_left_bot - 0.5 * dt))
B1_fdtd = (af.shift(A3, 0, 0, -1) - A3) / obj.dq2
B2_fdtd = -(af.shift(A3, 0, -1) - A3) / obj.dq1
E3_fdtd = 6 * np.pi * af.cos(2 * np.pi * obj.q1_left_bot +
4 * np.pi * obj.q2_left_bot)
obj.yee_grid_EM_fields[2] = E3_fdtd
obj.yee_grid_EM_fields[3] = B1_fdtd
obj.yee_grid_EM_fields[4] = B2_fdtd
E3_initial = obj.yee_grid_EM_fields[2].copy()
B1_initial = obj.yee_grid_EM_fields[3].copy()
B2_initial = obj.yee_grid_EM_fields[4].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
obj.J3 = -16 * np.pi**2 * af.sin(
2 * np.pi * (obj.q1_left_bot - t0 + 0.5 * dt) + 4 * np.pi *
(obj.q2_left_bot - t0 + 0.5 * dt))
fdtd(obj, dt)
error_B1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[3, N_g:-N_g, N_g:-N_g] -
B1_initial[0, N_g:-N_g, N_g:-N_g])) / (
B1_initial.elements())
error_B2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[4, N_g:-N_g, N_g:-N_g] -
B2_initial[0, N_g:-N_g, N_g:-N_g])) / (
B2_initial.elements())
error_E3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[2, N_g:-N_g, N_g:-N_g] -
E3_initial[0, N_g:-N_g, N_g:-N_g])) / (
E3_initial.elements())
poly_B1 = np.polyfit(np.log10(N), np.log10(error_B1), 1)
poly_B2 = np.polyfit(np.log10(N), np.log10(error_B2), 1)
poly_E3 = np.polyfit(np.log10(N), np.log10(error_E3), 1)
assert (abs(poly_B1[0] + 2) < 0.25)
assert (abs(poly_B2[0] + 2) < 0.25)
assert (abs(poly_E3[0] + 2) < 0.25)
def test_fdtd_mode2():
error_E1 = np.zeros(5)
error_E2 = np.zeros(5)
error_B3 = np.zeros(5)
N = 2**np.arange(5, 10)
for i in range(N.size):
obj = test(N[i])
dt = obj.dq1 * np.sqrt(9 / 5) / 2
time = np.arange(dt, np.sqrt(9 / 5) + dt, dt)
N_g = obj.N_ghost
E1_fdtd = 6 * np.pi * np.sqrt(
5 / 9) * af.cos(2 * np.pi * obj.q1_left_bot +
4 * np.pi * obj.q2_left_bot)
E2_fdtd = -3 * np.pi * np.sqrt(
5 / 9) * af.cos(2 * np.pi * obj.q1_left_bot +
4 * np.pi * obj.q2_left_bot)
B3_fdtd = -5 * np.pi * af.cos(
2 * np.pi *
(obj.q1_left_bot - 0.5 * np.sqrt(5 / 9) * dt) + 4 * np.pi *
(obj.q2_left_bot - 0.5 * np.sqrt(5 / 9) * dt))
obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] = E1_fdtd[:, N_g:-N_g,
N_g:-N_g]
obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] = E2_fdtd[:, N_g:-N_g,
N_g:-N_g]
obj.yee_grid_EM_fields[5, N_g:-N_g, N_g:-N_g] = B3_fdtd[:, N_g:-N_g,
N_g:-N_g]
B3_initial = obj.yee_grid_EM_fields[5].copy()
E1_initial = obj.yee_grid_EM_fields[0].copy()
E2_initial = obj.yee_grid_EM_fields[1].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
fdtd(obj, dt)
error_E1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] -
E1_initial[:, N_g:-N_g, N_g:-N_g])) / (
E1_initial.elements())
error_E2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] -
E2_initial[:, N_g:-N_g, N_g:-N_g])) / (
E2_initial.elements())
error_B3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[5, N_g:-N_g, N_g:-N_g] -
B3_initial[:, N_g:-N_g, N_g:-N_g])) / (
B3_initial.elements())
poly_E1 = np.polyfit(np.log10(N), np.log10(error_E1), 1)
poly_E2 = np.polyfit(np.log10(N), np.log10(error_E2), 1)
poly_B3 = np.polyfit(np.log10(N), np.log10(error_B3), 1)
assert (abs(poly_E1[0] + 2) < 0.2)
assert (abs(poly_E2[0] + 2) < 0.2)
assert (abs(poly_B3[0] + 2) < 0.2)