def get_cartesian_coords(q1, q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian = False
):
q1_midpoint = 0.5*(af.max(q1) + af.min(q1))
q2_midpoint = 0.5*(af.max(q2) + af.min(q2))
x = q1
y = q2
jacobian = [[1. + 0.*q1, 0.*q1],
[ 0.*q1, 1. + 0.*q1]
]
print("coords.py : ", q1_midpoint, q2_midpoint)
if (q1_start_local_left != None and q2_start_local_bottom != None):
if (return_jacobian):
return(x, y, jacobian)
else:
return(x, y)
else:
print("Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided")
return(x, y)
def get_cartesian_coords(q1, q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian = False
):
q1_midpoint = 0.5*(af.max(q1) + af.min(q1))
q2_midpoint = 0.5*(af.max(q2) + af.min(q2))
# Default initializsation to rectangular grid
x = q1
y = q2
jacobian = None
if (q1_start_local_left != None and q2_start_local_bottom != None):
if (return_jacobian):
return (x, y, jacobian)
else:
return(x, y)
else:
print("Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided")
return(x, y)
def get_cartesian_coords(q1,
q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian=False):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
d_q1 = (q1[0, 0, 1, 0] - q1[0, 0, 0, 0]).scalar()
d_q2 = (q2[0, 0, 0, 1] - q2[0, 0, 0, 0]).scalar()
# Default initializsation to rectangular grid
x = q1
y = q2
#x = q1*(2+q2)
#y = q2
jacobian = None #[[1. + 0.*q1, 0.*q1],
#[ 0.*q1, 1. + 0.*q1]
#]
if (q1_start_local_left != None and q2_start_local_bottom != None):
if (return_jacobian):
return (x, y, jacobian)
else:
return (x, y)
else:
print(
"Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided"
)
def get_cartesian_coords(q1, q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian = False
):
q1_midpoint = 0.5*(af.max(q1) + af.min(q1))
q2_midpoint = 0.5*(af.max(q2) + af.min(q2))
d_q1 = (q1[0, 0, 1, 0] - q1[0, 0, 0, 0]).scalar()
d_q2 = (q2[0, 0, 0, 1] - q2[0, 0, 0, 0]).scalar()
N_g = domain.N_ghost
N_q1 = q1.dims()[2] - 2*N_g # Manually apply quadratic transformation for each zone along q1
N_q2 = q2.dims()[3] - 2*N_g # Manually apply quadratic transformation for each zone along q1
# Default initializsation to rectangular grid
x = q1
y = q2
jacobian = [[1. + 0.*q1, 0.*q1],
[ 0.*q1, 1. + 0.*q1]
]
if (q1_start_local_left != None and q2_start_local_bottom != None):
if (return_jacobian):
return (x, y, jacobian)
else:
return(x, y)
else:
print("Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided")
def get_cartesian_coords(q1, q2):
q1_midpoint = 0.5*(af.max(q1) + af.min(q1))
q2_midpoint = 0.5*(af.max(q2) + af.min(q2))
x = q1
y = q2
return(x, y)
def tau_defect(q1, q2, p1, p2, p3):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
if (q2_midpoint < 0.75):
tau_mr = np.inf
else:
tau_mr = 0.01
return (tau_mr * q1**0 * p1**0)
def get_cartesian_coords(q1, q2):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
x = q1
y = q2
# if (q1_midpoint > 1.) and (q1_midpoint < 4.):
# y = 0.5*q2+0.125
return (x, y)
def get_cartesian_coords(q1, q2):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
x = q1
y = q2
# if (q1_midpoint > 4.25):
# y = 3*q2-1
return (x, y)
def get_cartesian_coords(q1,
q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian=False):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
x = q1
y = q2
jacobian = None
if (q1_start_local_left != None and q2_start_local_bottom != None):
if (q1_midpoint < -4.62): # Domain 1 and 7
y = 0.816 * q2
elif ((q1_midpoint > -4.62) and (q1_midpoint < 0)): # Domain 2 and 8
y = (q2 * (1 + 0.04 * (q1)))
elif ((q1_midpoint > 29.46) and (q1_midpoint < 32.98)
and (q2_midpoint < 12)): # Domain 5
y = ((q2 - 12) * (1 - 0.1193 * (q1 - 29.46))) + 12
elif ((q1_midpoint > 32.98) and (q2_midpoint < 12)): # Domain 6
y = 0.58 * (q2 - 12) + 12
elif ((q1_midpoint > 26.3) and (q1_midpoint < 29.46)
and (q2_midpoint > 12)): # Domain 10
y = ((q2 - 12) * (1 - 2 * 0.0451 * (q1 - 26.3))) + 12
elif ((q1_midpoint > 29.46) and (q1_midpoint < 32.98)
and (q2_midpoint > 12)): # Domain 11
y = ((q2 - 12) * (1 - 2 * 0.0451 * (q1 - 26.3))) + 12
elif ((q1_midpoint > 32.98) and (q2_midpoint > 12)): # Domain 12
y = 0.40 * (q2 - 12) + 12
# Numerically calculate Jacobian
jacobian = None
if (return_jacobian):
return (x, y, jacobian)
else:
return (x, y)
else:
print(
"Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided"
)
def get_cartesian_coords(q1,
q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian=False):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
d_q1 = (q1[0, 0, 1, 0] - q1[0, 0, 0, 0]).scalar()
d_q2 = (q2[0, 0, 0, 1] - q2[0, 0, 0, 0]).scalar()
# Default initializsation to rectangular grid
x = q1
y = q2
#x = q1*(2+q2)
#y = q2
jacobian = None #[[1. + 0.*q1, 0.*q1],
#[ 0.*q1, 1. + 0.*q1]
#]
if (q1_start_local_left != None and q2_start_local_bottom != None):
# X_Y_top_right = [1, 1]
# X_Y_top_left = [-1, 1]
# X_Y_bottom_left = [-1, -1]
# X_Y_bottom_right = [1, -1]
#
# x_y_top_right = [1, 1]
# x_y_top_left = [-1, 1]
# x_y_bottom_left = [-1, -0.5]
# x_y_bottom_right = [1, -1]
#
# x, y = affine(q1, q2,
# x_y_bottom_left, x_y_bottom_right,
# x_y_top_right, x_y_top_left,
# X_Y_bottom_left, X_Y_bottom_right,
# X_Y_top_right, X_Y_top_left,
# )
# # Numerically calculate Jacobian
# jacobian = None
if (return_jacobian):
return (x, y, jacobian)
else:
return (x, y)
else:
print(
"Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided"
)
def _bps_idx_af(E, angles, symbols, N):
global NMAX
prec_dtype = E.dtype
Ntestangles = angles.shape[1]
Nmax = NMAX // Ntestangles // symbols.shape[0] // 16
L = E.shape[0]
EE = E[:, np.newaxis] * np.exp(1.j * angles)
syms = af.np_to_af_array(symbols.astype(prec_dtype).reshape(1, 1, -1))
idxnd = np.zeros(L, dtype=np.int32)
if L <= Nmax + N:
Eaf = af.np_to_af_array(EE.astype(prec_dtype))
tmp = af.min(af.abs(af.broadcast(lambda x, y: x - y, Eaf[0:L, :],
syms))**2,
dim=2)
cs = _movavg_af(tmp, 2 * N, axis=0)
val, idx = af.imin(cs, dim=1)
idxnd[N:-N] = np.array(idx)
else:
K = L // Nmax
R = L % Nmax
if R < N:
R = R + Nmax
K -= 1
Eaf = af.np_to_af_array(EE[0:Nmax + N].astype(prec_dtype))
tmp = af.min(af.abs(af.broadcast(lambda x, y: x - y, Eaf, syms))**2,
dim=2)
tt = np.array(tmp)
cs = _movavg_af(tmp, 2 * N, axis=0)
val, idx = af.imin(cs, dim=1)
idxnd[N:Nmax] = np.array(idx)
for i in range(1, K):
Eaf = af.np_to_af_array(EE[i * Nmax - N:(i + 1) * Nmax + N].astype(
np.complex128))
tmp = af.min(af.abs(af.broadcast(lambda x, y: x - y, Eaf,
syms))**2,
dim=2)
cs = _movavg_af(tmp, 2 * N, axis=0)
val, idx = af.imin(cs, dim=1)
idxnd[i * Nmax:(i + 1) * Nmax] = np.array(idx)
Eaf = af.np_to_af_array(EE[K * Nmax - N:K * Nmax + R].astype(
np.complex128))
tmp = af.min(af.abs(af.broadcast(lambda x, y: x - y, Eaf, syms))**2,
dim=2)
cs = _movavg_af(tmp, 2 * N, axis=0)
val, idx = af.imin(cs, dim=1)
idxnd[K * Nmax:-N] = np.array(idx)
return idxnd
def get_cartesian_coords(q1, q2):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
y = q2
if (q2_midpoint < 0):
x = q1
else:
x = q1 * (1 + q2)
#x = q1
#indices = q2>0
#x[indices] = (q1*(1 + q2))[indices]
return (x, y)
def min(self, axis: tp.Optional[int] = None):
"""
Returns the minimum along given axis.
"""
new_array = af.min(self._af_array, dim=axis)
if isinstance(new_array, af.Array):
return ndarray(new_array)
else:
return new_array
def lowpass_filter(f):
f_hat = af.fft(f)
dp1 = (domain.p1_end[0] - domain.p1_start[0]) / domain.N_p1
k_v = af.tile(af.to_array(np.fft.fftfreq(domain.N_p1, dp1)), 1, 1,
f.shape[2], f.shape[3])
# Applying the filter:
f_hat_filtered = 0.5 * (f_hat * (af.tanh(
(k_v + 0.9 * af.max(k_v)) / 0.5) - af.tanh(
(k_v + 0.9 * af.min(k_v)) / 0.5)))
f_hat = af.select(af.abs(k_v) < 0.8 * af.max(k_v), f_hat, f_hat_filtered)
f = af.real(af.ifft(f_hat))
return (f)
def time_evolution():
for time_index, t0 in enumerate(time_array):
print('For Time =', t0)
print('MIN(f) =', af.min(nls.f[3:-3, 3:-3]))
print('MAX(f) =', af.max(nls.f[3:-3, 3:-3]))
print('SUM(f) =', af.sum(nls.f[3:-3, 3:-3]))
print()
nls.strang_timestep(dt)
n_nls = nls.compute_moments('density')
h5f = h5py.File('dump/%04d' % (time_index + 1) + '.h5', 'w')
h5f.create_dataset('n', data=n_nls)
h5f.close()
def min(self, s, axis):
return arrayfire.min(s, axis)
def get_cartesian_coords(q1, q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian = False
):
q1_midpoint = 0.5*(af.max(q1) + af.min(q1))
q2_midpoint = 0.5*(af.max(q2) + af.min(q2))
N_g = domain.N_ghost
# Default initialisation to rectangular grid
x = q1
y = q2
jacobian = [[1. + 0.*q1, 0.*q1],
[ 0.*q1, 1. + 0.*q1]
]
[[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]] = jacobian
# Radius and center of circular region
radius = 0.5
center = [0, 0]
if (q1_start_local_left != None and q2_start_local_bottom != None):
N_q1 = q1.dims()[2] - 2*N_g # Manually apply quadratic transformation for each zone along q1
N_q2 = q2.dims()[3] - 2*N_g # Manually apply quadratic transformation for each zone along q1
N_i = N_q1
N_j = N_q2
# Bottom-left most point of the transformation
x_0 = -radius/np.sqrt(2)
y_0 = np.sqrt(radius**2 - x_0**2)
# Initialize to zero
x = 0*q1
y = 0*q2
# Loop over each zone in x
#for i in range(N_g, N_q1 + N_g):
for i in range(0, N_q1 + 2*N_g):
#for j in range(N_g, N_q2 + N_g):
for j in range(0, N_q2 + 2*N_g):
index_i = i - N_g # Index of the vertical slice, left-most being 0
index_j = j - N_g # Index of the horizontal slice, bottom-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, j]
q2_slice = q2[0, 0, i, j]
x_step = 0.66666666/N_i
y_step = 1./N_j
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
# y_n = y_0 + y_step*index_j # Bottom
# y_n_plus_half = y_0 + y_step*(index_j+0.5) # y-center
# y_n_plus_1 = y_0 + y_step*(index_j+1) # Top
x_n = x_0 + x_step*index_i #+ x_step*(np.abs(index_j - N_j/2.))# Left
x_n_plus_half = x_0 + x_step*(index_i+0.5) #+ x_step*(np.abs(index_j - N_j/2.))# x-center
x_n_plus_1 = x_0 + x_step*(index_i+1) #+ x_step*(np.abs(index_j - N_j/2.))# Right
x_y_bottom_left = [x_n, np.sqrt(np.abs(radius**2 - x_n**2)) + index_j*y_step]
x_y_bottom_center = [x_n_plus_half, np.sqrt(np.abs(radius**2 - x_n_plus_half**2)) + index_j*y_step]
x_y_bottom_right = [x_n_plus_1, np.sqrt(np.abs(radius**2 - x_n_plus_1**2)) + index_j*y_step]
x_y_left_center = [x_n, np.sqrt(np.abs(radius**2 - x_n**2)) + (index_j+0.5)*y_step]
x_y_right_center = [x_n_plus_1, np.sqrt(np.abs(radius**2 - x_n_plus_1**2)) + (index_j+0.5)*y_step]
x_y_top_left = [x_n, np.sqrt(np.abs(radius**2 - x_n**2)) + (index_j+1)*y_step]
x_y_top_center = [x_n_plus_half, np.sqrt(np.abs(radius**2 - x_n_plus_half**2)) + (index_j+1)*y_step]
x_y_top_right = [x_n_plus_1, np.sqrt(np.abs(radius**2 - x_n_plus_1**2)) + (index_j+1)*y_step]
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(q1_i, q2_i, q1_slice, q2_slice,
x_y_bottom_left, x_y_bottom_right,
x_y_top_right, x_y_top_left,
x_y_bottom_center, x_y_right_center,
x_y_top_center, x_y_left_center,
q1_start_local_left + index_i*domain.dq1,
q2_start_local_bottom + index_j*domain.dq2
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
pl.plot(af.moddims(dx_dq1[0, 0, i, :], q1.dims()[2]).to_ndarray(), '-o', color = 'C0', alpha = 0.1, label = "dx_dq1")
pl.plot(af.moddims(dy_dq1[0, 0, i, :], q1.dims()[2]).to_ndarray(), '-o', color = 'k', alpha = 0.1, label = "dy_dq1")
pl.plot(af.moddims(dx_dq2[0, 0, i, :], q1.dims()[2]).to_ndarray(), '-o', color = 'C2', alpha = 0.1, label = "dx_dq2")
pl.plot(af.moddims(dy_dq2[0, 0, i, :], q1.dims()[2]).to_ndarray(), '-o', color = 'C3', alpha = 0.1, label = "dy_dq2")
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# pl.plot(af.moddims(dx_dq1[0, 0, :, N_g], q1.dims()[2]).to_ndarray(), '-o', color = 'C0', alpha = 0.5, label = "dx_dq1")
# pl.plot(af.moddims(dy_dq1[0, 0, :, N_g], q1.dims()[2]).to_ndarray(), '-o', color = 'k', alpha = 0.5, label = "dy_dq1")
# pl.plot(af.moddims(dx_dq2[0, 0, :, N_g], q1.dims()[2]).to_ndarray(), '-o', color = 'C2', alpha = 0.5, label = "dx_dq2")
# pl.plot(af.moddims(dy_dq2[0, 0, :, N_g], q1.dims()[2]).to_ndarray(), '-o', color = 'C3', alpha = 0.5, label = "dy_dq2")
#pl.legend(loc='best')
pl.savefig("/home/quazartech/bolt/example_problems/electronic_boltzmann/test_quadratic_2/iv.png")
pl.clf()
if (return_jacobian):
return (x, y, jacobian)
else:
return(x, y)
else:
print("Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided")
def get_cartesian_coords(q1,
q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian=False):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
# Default initializsation to rectangular grid
x = q1
y = q2
jacobian = None # Numerically compute the Jacobian
if (q1_start_local_left != None and q2_start_local_bottom != None):
if ((q2_midpoint < 0.5) and (q1_midpoint > -1.)
and (q1_midpoint < 0.)):
x0 = -1.
y0 = -2.0 # Bottom-left
x1 = 0
y1 = -2.0 # Bottom-right
x2 = 0
y2 = -0.5 # Top-right
x3 = -1.
y3 = 0.5 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[-1., -2.0], [0, -2.0],
[0, 0.5], [-1., 0.5]
)
elif ((q2_midpoint < 0.5) and (q1_midpoint > 0)
and (q1_midpoint < 1.)):
x0 = 0.
y0 = -2.0 # Bottom-left
x1 = 1.0
y1 = -2.0 # Bottom-right
x2 = 1.0
y2 = 0.5 # Top-right
x3 = 0
y3 = -0.5 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[0., -2.0], [1., -2.],
[1., 0.5], [0., 0.5]
)
if (return_jacobian):
return (x, y, jacobian)
else:
return (x, y)
else:
print(
"Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided"
)
#!/usr/bin/python
#######################################################
# Copyright (c) 2015, ArrayFire
# All rights reserved.
#
# This file is distributed under 3-clause BSD license.
# The complete license agreement can be obtained at:
# http://arrayfire.com/licenses/BSD-3-Clause
########################################################
import arrayfire as af
# Display backend information
af.info()
# Generate a uniform random array with a size of 5 elements
a = af.randu(5, 1)
# Print a and its minimum value
print(a)
# Print min and max values of a
print("Minimum, Maximum: ", af.min(a), af.max(a))
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params, initialize,
advection_terms, collision_operator.BGK, moments)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost
# Time parameters:
dt = 0.001 * 32 / nls.N_q1
t_final = params.t_final
time_array = np.arange(dt, t_final + dt, dt)
print('Printing the minimum and maximum of the distribution functions :')
print('f_min:', af.min(nls.f))
print('f_max:', af.max(nls.f))
# Dumping the distribution function at t = 0:
nls.dump_distribution_function('dump_f/t=0.000')
# nls.dump_moments('dump_moments/t=0.000')
for time_index, t0 in enumerate(time_array):
nls.strang_timestep(dt)
PETSc.Sys.Print('Computing For Time =', t0)
delta_dt = (1 - math.modf(t0/params.dt_dump_moments)[0]) \
* params.dt_dump_moments
# nls.dump_moments('dump_moments/t=' + '%.3f'%t0)
A[1,:] = B[2,:]
af.display(A)
print("\n---- Bitwise operations\n")
af.display(A & B)
af.display(A | B)
af.display(A ^ B)
print("\n---- Transpose\n")
af.display(A)
af.display(af.transpose(A))
print("\n---- Flip Vertically / Horizontally\n")
af.display(A)
af.display(af.flip(A, 0))
af.display(af.flip(A, 1))
print("\n---- Sum, Min, Max along row / columns\n")
af.display(A)
af.display(af.sum(A, 0))
af.display(af.min(A, 0))
af.display(af.max(A, 0))
af.display(af.sum(A, 1))
af.display(af.min(A, 1))
af.display(af.max(A, 1))
print("\n---- Get minimum with index\n")
(min_val, min_idx) = af.imin(A, 0)
af.display(min_val)
af.display(min_idx)
#!/usr/bin/python import arrayfire as af a = af.randu(3, 3) print(af.sum(a), af.product(a), af.min(a), af.max(a), af.count(a), af.any_true(a), af.all_true(a)) af.print_array(af.sum(a, 0)) af.print_array(af.sum(a, 1)) af.print_array(af.product(a, 0)) af.print_array(af.product(a, 1)) af.print_array(af.min(a, 0)) af.print_array(af.min(a, 1)) af.print_array(af.max(a, 0)) af.print_array(af.max(a, 1)) af.print_array(af.count(a, 0)) af.print_array(af.count(a, 1)) af.print_array(af.any_true(a, 0)) af.print_array(af.any_true(a, 1)) af.print_array(af.all_true(a, 0)) af.print_array(af.all_true(a, 1)) af.print_array(af.accum(a, 0)) af.print_array(af.accum(a, 1))
def Umeda_b1_deposition( charge_electron, positions_x, positions_y, velocity_x, velocity_y,\
x_grid, y_grid, ghost_cells, length_domain_x, length_domain_y, dt ):
'''
A modified Umeda's scheme was implemented to handle a pure one dimensional case.
function Umeda_b1_deposition( charge, x, velocity_x,\
x_grid, ghost_cells, length_domain_x, dt\
)
-----------------------------------------------------------------------
Input variables: charge, x, velocity_required_x, x_grid, ghost_cells, length_domain_x, dt
charge: This is an array containing the charges deposited at the density grid nodes.
positions_x: An one dimensional array of size equal to number of particles taken in the PIC code.
It contains the positions of particles in x direction.
positions_y: An one dimensional array of size equal to number of particles taken in the PIC code.
It contains the positions of particles in y direction.
velocity_x: An one dimensional array of size equal to number of particles taken in the PIC code.
It contains the velocities of particles in y direction.
velocity_y: An one dimensional array of size equal to number of particles taken in the PIC code.
It contains the velocities of particles in x direction.
x_grid: This is an array denoting the position grid in x direction chosen in the PIC simulation
y_grid: This is an array denoting the position grid in y direction chosen in the PIC simulation
ghost_cells: This is the number of ghost cells used in the simulation domain.
length_domain_x: This is the length of the domain in x direction
dt: this is the dt/time step chosen in the simulation
-----------------------------------------------------------------------
returns: Jx_x_indices, Jx_y_indices, Jx_values_at_these_indices,\
Jy_x_indices, Jy_y_indices, Jy_values_at_these_indices
Jx_x_indices: This returns the x indices (columns) of the array where the respective currents stored in
Jx_values_at_these_indices have to be deposited
Jx_y_indices: This returns the y indices (rows) of the array where the respective currents stored in
Jx_values_at_these_indices have to be deposited
Jx_values_at_these_indices: This is an array containing the currents to be deposited.
Jy_x_indices, Jy_y_indices and Jy_values_at_these_indices are similar to Jx_x_indices,
Jx_y_indices and Jx_values_at_these_indices for Jy
For further details on the scheme refer to Umeda's paper provided in the sagemath folder as the
naming conventions used in the function use the papers naming convention.(x_1, x_2, x_r, F_x, )
'''
nx = (x_grid.elements() - 1 - 2 * ghost_cells) # number of zones
ny = (y_grid.elements() - 1 - 2 * ghost_cells) # number of zones
dx = length_domain_x / nx
dy = length_domain_y / ny
# Start location x_1, y_1 at t = n * dt
# Start location x_2, y_2 at t = (n+1) * dt
x_1 = (positions_x).as_type(af.Dtype.f64)
x_2 = (positions_x + (velocity_x * dt)).as_type(af.Dtype.f64)
y_1 = (positions_y).as_type(af.Dtype.f64)
y_2 = (positions_y + (velocity_y * dt)).as_type(af.Dtype.f64)
# Calculation i_1 and i_2, indices of left corners of cells containing the particles
# at x_1 and x_2 respectively and j_1 and j_2: indices of bottoms of cells containing the particles
# at y_1 and y_2 respectively
i_1 = af.arith.floor(((af.abs(x_1 - af.sum(x_grid[0]))) / dx) -
ghost_cells)
j_1 = af.arith.floor(((af.abs(y_1 - af.sum(y_grid[0]))) / dy) -
ghost_cells)
i_2 = af.arith.floor(((af.abs(x_2 - af.sum(x_grid[0]))) / dx) -
ghost_cells)
j_2 = af.arith.floor(((af.abs(y_2 - af.sum(y_grid[0]))) / dy) -
ghost_cells)
i_dx = dx * af.join(1, i_1, i_2)
j_dy = dy * af.join(1, j_1, j_2)
i_dx_x_avg = af.join(1, af.max(i_dx, 1), ((x_1 + x_2) / 2))
j_dy_y_avg = af.join(1, af.max(j_dy, 1), ((y_1 + y_2) / 2))
x_r_term_1 = dx + af.min(i_dx, 1)
x_r_term_2 = af.max(i_dx_x_avg, 1)
y_r_term_1 = dy + af.min(j_dy, 1)
y_r_term_2 = af.max(j_dy_y_avg, 1)
x_r_combined_term = af.join(1, x_r_term_1, x_r_term_2)
y_r_combined_term = af.join(1, y_r_term_1, y_r_term_2)
# Computing the relay point (x_r, y_r)
x_r = af.min(x_r_combined_term, 1)
y_r = af.min(y_r_combined_term, 1)
# Calculating the fluxes and the weights
F_x_1 = charge_electron * (x_r - x_1) / dt
F_x_2 = charge_electron * (x_2 - x_r) / dt
F_y_1 = charge_electron * (y_r - y_1) / dt
F_y_2 = charge_electron * (y_2 - y_r) / dt
W_x_1 = (x_1 + x_r) / (2 * dx) - i_1
W_x_2 = (x_2 + x_r) / (2 * dx) - i_2
W_y_1 = (y_1 + y_r) / (2 * dy) - j_1
W_y_2 = (y_2 + y_r) / (2 * dy) - j_2
# computing the charge densities at the grid nodes using the
# fluxes and the weights
J_x_1_1 = (1 / (dx * dy)) * (F_x_1 * (1 - W_y_1))
J_x_1_2 = (1 / (dx * dy)) * (F_x_1 * (W_y_1))
J_x_2_1 = (1 / (dx * dy)) * (F_x_2 * (1 - W_y_2))
J_x_2_2 = (1 / (dx * dy)) * (F_x_2 * (W_y_2))
J_y_1_1 = (1 / (dx * dy)) * (F_y_1 * (1 - W_x_1))
J_y_1_2 = (1 / (dx * dy)) * (F_y_1 * (W_x_1))
J_y_2_1 = (1 / (dx * dy)) * (F_y_2 * (1 - W_x_2))
J_y_2_2 = (1 / (dx * dy)) * (F_y_2 * (W_x_2))
# concatenating the x, y indices for Jx
Jx_x_indices = af.join(0,\
i_1 + ghost_cells,\
i_1 + ghost_cells,\
i_2 + ghost_cells,\
i_2 + ghost_cells\
)
Jx_y_indices = af.join(0,\
j_1 + ghost_cells,\
(j_1 + 1 + ghost_cells),\
j_2 + ghost_cells,\
(j_2 + 1 + ghost_cells)\
)
# concatenating the currents at x, y indices for Jx
Jx_values_at_these_indices = af.join(0,\
J_x_1_1,\
J_x_1_2,\
J_x_2_1,\
J_x_2_2\
)
# concatenating the x, y indices for Jy
Jy_x_indices = af.join(0,\
i_1 + ghost_cells,\
(i_1 + 1 + ghost_cells),\
i_2 + ghost_cells,\
(i_2 + 1 + ghost_cells)\
)
Jy_y_indices = af.join(0,\
j_1 + ghost_cells,\
j_1 + ghost_cells,\
j_2 + ghost_cells,\
j_2 + ghost_cells\
)
# concatenating the currents at x, y indices for Jx
Jy_values_at_these_indices = af.join(0,\
J_y_1_1,\
J_y_1_2,\
J_y_2_1,\
J_y_2_2\
)
af.eval(Jx_x_indices, Jx_y_indices, Jy_x_indices, Jy_y_indices)
af.eval(Jx_values_at_these_indices, Jy_values_at_these_indices)
return Jx_x_indices, Jx_y_indices, Jx_values_at_these_indices,\
Jy_x_indices, Jy_y_indices, Jy_values_at_these_indices
def min(self, s, axis):
return arrayfire.min(s, axis)
def simple_algorithm(verbose = False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(3, 3)
print_func(af.sum(a), af.product(a), af.min(a), af.max(a),
af.count(a), af.any_true(a), af.all_true(a))
display_func(af.sum(a, 0))
display_func(af.sum(a, 1))
display_func(af.product(a, 0))
display_func(af.product(a, 1))
display_func(af.min(a, 0))
display_func(af.min(a, 1))
display_func(af.max(a, 0))
display_func(af.max(a, 1))
display_func(af.count(a, 0))
display_func(af.count(a, 1))
display_func(af.any_true(a, 0))
display_func(af.any_true(a, 1))
display_func(af.all_true(a, 0))
display_func(af.all_true(a, 1))
display_func(af.accum(a, 0))
display_func(af.accum(a, 1))
display_func(af.sort(a, is_ascending=True))
display_func(af.sort(a, is_ascending=False))
b = (a > 0.1) * a
c = (a > 0.4) * a
d = b / c
print_func(af.sum(d));
print_func(af.sum(d, nan_val=0.0));
display_func(af.sum(d, dim=0, nan_val=0.0));
val,idx = af.sort_index(a, is_ascending=True)
display_func(val)
display_func(idx)
val,idx = af.sort_index(a, is_ascending=False)
display_func(val)
display_func(idx)
b = af.randu(3,3)
keys,vals = af.sort_by_key(a, b, is_ascending=True)
display_func(keys)
display_func(vals)
keys,vals = af.sort_by_key(a, b, is_ascending=False)
display_func(keys)
display_func(vals)
c = af.randu(5,1)
d = af.randu(5,1)
cc = af.set_unique(c, is_sorted=False)
dd = af.set_unique(af.sort(d), is_sorted=True)
display_func(cc)
display_func(dd)
display_func(af.set_union(cc, dd, is_unique=True))
display_func(af.set_union(cc, dd, is_unique=False))
display_func(af.set_intersect(cc, cc, is_unique=True))
display_func(af.set_intersect(cc, cc, is_unique=False))
dt_fdtd = params.N_cfl * dq1 \
/ params.c # lightspeed
dt = min(dt_fvm, dt_fdtd)
params.dt = dt
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params, initialize,
advection_terms, collision_operator.BGK, moments)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost
print('Minimum Value of f_e:', af.min(nls.f[:, 0]))
print('Minimum Value of f_i:', af.min(nls.f[:, 1]))
print('Error in density_e:',
af.mean(af.abs(nls.compute_moments('density')[:, 0] - 1)))
print('Error in density_i:',
af.mean(af.abs(nls.compute_moments('density')[:, 1] - 1)))
v2_bulk = nls.compute_moments('mom_v2_bulk') / nls.compute_moments('density')
v3_bulk = nls.compute_moments('mom_v3_bulk') / nls.compute_moments('density')
v2_bulk_i = params.amplitude * -4.801714581503802e-15 * af.cos(params.k_q1 * nls.q1_center) \
- params.amplitude * -0.3692429960259134 * af.sin(params.k_q1 * nls.q1_center)
v2_bulk_e = params.amplitude * -4.85722573273506e-15 * af.cos(params.k_q1 * nls.q1_center) \
- params.amplitude * - 0.333061857862197* af.sin(params.k_q1 * nls.q1_center)
dt = 0.001
t_final = 1.0
time_array = np.arange(dt, t_final + dt, dt)
n_nls = nls.compute_moments('density')
h5f = h5py.File('dump/0000.h5', 'w')
h5f.create_dataset('q1', data = nls.q1_center[:, :, N_g:-N_g, N_g:-N_g])
h5f.create_dataset('q2', data = nls.q2_center[:, :, N_g:-N_g, N_g:-N_g])
h5f.create_dataset('n', data = n_nls[:, :, N_g:-N_g, N_g:-N_g])
h5f.close()
init_sum = af.sum(nls.f[:, :, N_g:-N_g, N_g:-N_g])
for time_index, t0 in enumerate(time_array):
# Used to debug:
print('For Time =', t0)
print('MIN(f) =', af.min(nls.f[:, :, N_g:-N_g, N_g:-N_g]))
print('MAX(f) =', af.max(nls.f[:, :, N_g:-N_g, N_g:-N_g]))
print('d(SUM(f)) =', af.sum(nls.f[:, :, N_g:-N_g, N_g:-N_g]) - init_sum)
print()
nls.strang_timestep(dt)
n_nls = nls.compute_moments('density')
h5f = h5py.File('dump/%04d'%(time_index+1) + '.h5', 'w')
h5f.create_dataset('n', data = n_nls[:, :, N_g:-N_g, N_g:-N_g])
h5f.close()
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params, initialize,
advection_terms, collision_operator.BGK, moments)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost
# Time parameters:
dt = params.N_cfl * min(nls.dq1, nls.dq2) \
/ max(domain.p1_end + domain.p2_end + domain.p3_end)
print(
'Printing the minimum of the distribution functions for electrons and ions:'
)
print('f_min_electron:', af.min(nls.f[:, 0, :, :]))
print('f_min_ion:', af.min(nls.f[:, 1, :, :]))
if (params.t_restart == 0):
time_elapsed = 0
nls.dump_distribution_function('dump_f/t=0.000')
nls.dump_moments('dump_moments/t=0.000')
nls.dump_EM_fields('dump_fields/t=0.000')
else:
time_elapsed = params.t_restart
nls.load_distribution_function('dump_f/t=' + '%.3f' % time_elapsed)
nls.load_EM_fields('dump_fields/t=' + '%.3f' % time_elapsed)
# Checking that the file writing intervals are greater than dt:
assert (params.dt_dump_f > dt)
def get_cartesian_coords(q1, q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian = False
):
q1_midpoint = 0.5*(af.max(q1) + af.min(q1))
q2_midpoint = 0.5*(af.max(q2) + af.min(q2))
# Default initializsation to rectangular grid
x = q1
y = q2
jacobian = None # Numerically compute the Jacobian
if (q1_start_local_left != None and q2_start_local_bottom != None):
# Bottom center patch
if ((q2_midpoint < 0.3) and (q1_midpoint > 1.) and (q1_midpoint < 2.)):
x0 = 1.; y0 = 0 # Bottom-left
x1 = 2; y1 = 0 # Bottom-right
x2 = 2; y2 = 0.45 # Top-right
x3 = 1.; y3 = 0.1 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[1., 0], [2, 0],
[2, 0.3], [1., 0.3]
)
# Bottom left patch
elif ((q2_midpoint < 0.3) and (q1_midpoint > 0.) and (q1_midpoint < 1.)):
x0 = 0.; y0 = 0 # Bottom-left
x1 = 1; y1 = 0 # Bottom-right
x2 = 1; y2 = 0.1 # Top-right
x3 = 0.; y3 = 0.1 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[0., 0], [1, 0],
[1, 0.3], [0., 0.3]
)
# Bottom right patch
elif ((q2_midpoint < 0.3) and (q1_midpoint > 2.) and (q1_midpoint < 3.)):
x0 = 2.; y0 = 0 # Bottom-left
x1 = 3; y1 = 0 # Bottom-right
x2 = 3; y2 = 0.1 # Top-right
x3 = 2.; y3 = 0.45 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[2., 0], [3, 0],
[3, 0.3], [2., 0.3]
)
# Top right patch
elif ((q2_midpoint > 0.7) and (q1_midpoint > 2.) and (q1_midpoint < 3.)):
x0 = 2.; y0 = 0.55 # Bottom-left
x1 = 3; y1 = 0.9 # Bottom-right
x2 = 3; y2 = 1. # Top-right
x3 = 2.; y3 = 1. # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[2., 0.7], [3, 0.7],
[3, 1.], [2., 1.]
)
# Top left patch
elif ((q2_midpoint > 0.7) and (q1_midpoint > 0.) and (q1_midpoint < 1.)):
x0 = 0.; y0 = 0.9 # Bottom-left
x1 = 1; y1 = 0.9 # Bottom-right
x2 = 1; y2 = 1. # Top-right
x3 = 0.; y3 = 1. # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[0., 0.7], [1, 0.7],
[1, 1.], [0., 1.]
)
# Top center patch
elif ((q2_midpoint > 0.7) and (q1_midpoint > 1.) and (q1_midpoint < 2.)):
x0 = 1.; y0 = 0.9 # Bottom-left
x1 = 2; y1 = 0.55 # Bottom-right
x2 = 2; y2 = 1. # Top-right
x3 = 1.; y3 = 1. # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[1., 0.7], [2, 0.7],
[2, 1.], [1., 1.]
)
# Center center patch
elif ((q2_midpoint > 0.3) and (q2_midpoint < 0.7) and (q1_midpoint > 1.) and (q1_midpoint < 2.)):
x0 = 1.; y0 = 0.1 # Bottom-left
x1 = 2; y1 = 0.45 # Bottom-right
x2 = 2; y2 = 0.55 # Top-right
x3 = 1.; y3 = 0.9 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[1., 0.3], [2, 0.3],
[2, 0.7], [1., 0.7]
)
# Left center patch
elif ((q2_midpoint > 0.3) and (q2_midpoint < 0.7) and (q1_midpoint > 0.) and (q1_midpoint < 1.)):
x0 = 0.; y0 = 0.1 # Bottom-left
x1 = 1; y1 = 0.1 # Bottom-right
x2 = 1; y2 = 0.9 # Top-right
x3 = 0.; y3 = 0.9 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[0., 0.3], [1, 0.3],
[1, 0.7], [0., 0.7]
)
# Right center patch
elif ((q2_midpoint > 0.3) and (q2_midpoint < 0.7) and (q1_midpoint > 2.) and (q1_midpoint < 3.)):
x0 = 2.; y0 = 0.45 # Bottom-left
x1 = 3; y1 = 0.1 # Bottom-right
x2 = 3; y2 = 0.9 # Top-right
x3 = 2.; y3 = 0.55 # Top-left
x, y = \
affine(q1, q2,
[x0, y0], [x1, y1],
[x2, y2], [x3, y3],
[2., 0.3], [3, 0.3],
[3, 0.7], [2., 0.7]
)
if (return_jacobian):
return (x, y, jacobian)
else:
return(x, y)
else:
print("Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided")
def normalize(a):
max_ = float(af.max(a))
min_ = float(af.min(a))
return (a - min_) / (max_ - min_)
def normalize(a):
mx = af.max(a)
mn = af.min(a)
return (a - mn)/(mx - mn)
advection_terms, collision_operator.BGK, moments)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost
# Time parameters:
dt_fvm = params.N_cfl * min(nls.dq1, nls.dq2) \
/ max(domain.p1_end + domain.p2_end + domain.p3_end) # joining elements of the list
dt_fdtd = params.N_cfl * min(nls.dq1, nls.dq2) \
/ params.c # lightspeed
dt = dt_fvm # min(dt_fvm, dt_fdtd)
print('Minimum Value of f:', af.min(nls.f))
print('Error in density:', af.mean(af.abs(nls.compute_moments('density') - 1)))
v2_bulk = nls.compute_moments('mom_v2_bulk') / nls.compute_moments('density')
v3_bulk = nls.compute_moments('mom_v3_bulk') / nls.compute_moments('density')
v2_bulk_ana = params.amplitude * -1.7450858652952794e-15 * af.cos(params.k_q1 * nls.q1_center) \
- params.amplitude * 0.5123323181646575 * af.sin(params.k_q1 * nls.q1_center)
v3_bulk_ana = params.amplitude * 0.5123323181646597 * af.cos(params.k_q1 * nls.q1_center) \
- params.amplitude * 0 * af.sin(params.k_q1 * nls.q1_center)
print('Error in v2_bulk:',
af.mean(af.abs((v2_bulk - v2_bulk_ana) / v2_bulk_ana)))
print('Error in v3_bulk:',
af.mean(af.abs((v3_bulk - v3_bulk_ana) / v3_bulk_ana)))
elements_xi_LGL = af.constant(0, N_Elements, N_LGL)
elements = utils.linspace(af.sum(x_nodes[0]),
af.sum(x_nodes[1] - element_size), N_Elements)
np_element_array = np.concatenate((af.transpose(elements),
af.transpose(elements + element_size)))
element_mesh_nodes = utils.linspace(af.sum(x_nodes[0]),
af.sum(x_nodes[1]),
N_Elements + 1)
element_array = af.transpose(af.interop.np_to_af_array(np_element_array))
element_LGL = wave_equation.mapping_xi_to_x(af.transpose(element_array),
xi_LGL)
# The minimum distance between 2 mapped LGL points.
delta_x = af.min((element_LGL - af.shift(element_LGL, 1, 0))[1:, :])
# dx_dxi for elements of equal size.
dx_dxi = af.mean(wave_equation.dx_dxi_numerical((element_mesh_nodes[0 : 2]),\
xi_LGL))
# The value of time-step.
delta_t = delta_x / (4 * abs(c))
# Array of timesteps seperated by delta_t.
time = utils.linspace(0, int(total_time / delta_t) * delta_t,
int(total_time / delta_t))
# The wave to be advected is either a sin or a Gaussian wave.
def get_cartesian_coords(q1,
q2,
q1_start_local_left=None,
q2_start_local_bottom=None,
return_jacobian=False):
q1_midpoint = 0.5 * (af.max(q1) + af.min(q1))
q2_midpoint = 0.5 * (af.max(q2) + af.min(q2))
d_q1 = (q1[0, 0, 1, 0] - q1[0, 0, 0, 0]).scalar()
d_q2 = (q2[0, 0, 0, 1] - q2[0, 0, 0, 0]).scalar()
N_g = domain.N_ghost
N_q1 = q1.dims(
)[2] - 2 * N_g # Manually apply quadratic transformation for each zone along q1
N_q2 = q2.dims(
)[3] - 2 * N_g # Manually apply quadratic transformation for each zone along q1
# Default initializsation to rectangular grid
x = q1
y = q2
jacobian = [[1. + 0. * q1, 0. * q1], [0. * q1, 1. + 0. * q1]]
[[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]] = jacobian
# Radius and center of circular region
radius = 0.5
center = [0, 0]
shift_x = 0. * d_q1 / 2
shift_y = 0. * d_q2 / 2
x_y_circle_top_left = [
-radius / np.sqrt(2) + shift_x, radius / np.sqrt(2) - shift_y
]
x_y_circle_bottom_left = [
-radius / np.sqrt(2) + shift_x, -radius / np.sqrt(2) + shift_y
]
x_y_circle_top_right = [
radius / np.sqrt(2) - shift_x, radius / np.sqrt(2) - shift_y
]
x_y_circle_bottom_right = [
radius / np.sqrt(2) - shift_x, -radius / np.sqrt(2) + shift_y
]
if (q1_start_local_left != None and q2_start_local_bottom != None):
# Bottom-center domain
if ((q2_midpoint < -0.33) and (q1_midpoint > -0.33)
and (q1_midpoint < 0.33)):
# Note : Never specify the x, y coordinates below in terms of q1 and q2 coordinates. Specify only in
# physical x, y values.
N = N_q1
x_0 = -radius / np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in x
for i in range(0, N_q1 + 2 * N_g):
index = i - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, N_g:-N_g]
q2_slice = q2[0, 0, i, N_g:-N_g]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
x_n = x_0 + np.sqrt(2) * radius * index / N # Top-left
y_n = -np.sqrt(radius**2 - x_n**2)
x_n_plus_1 = x_0 + np.sqrt(2) * radius * (index +
1) / N # Top-right
y_n_plus_1 = -np.sqrt(radius**2 - x_n_plus_1**2)
x_n_plus_half = x_0 + np.sqrt(2) * radius * (
index + 0.5) / N # Top-center
y_n_plus_half = -np.sqrt(radius**2 - x_n_plus_half**2)
x_y_bottom_left = [x_n, -1]
x_y_bottom_center = [x_n_plus_half, -1]
x_y_bottom_right = [x_n_plus_1, -1]
x_y_left_center = [x_n, (-1 + y_n) / 2]
x_y_right_center = [x_n_plus_1, (-1 + y_n_plus_1) / 2]
x_y_top_left = [x_n, y_n]
x_y_top_center = [x_n_plus_half, y_n_plus_half]
x_y_top_right = [x_n_plus_1, y_n_plus_1]
for j in range(0, N_q2 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left + index * domain.dq1,
q2_start_local_bottom,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Bottom-left domain
elif ((q2_midpoint < -0.33) and (q1_midpoint > -1)
and (q1_midpoint < -0.33)):
N = N_q1
x_0 = -1
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in x
for i in range(0, N_q1 + 2 * N_g):
index = i - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, N_g:-N_g]
q2_slice = q2[0, 0, i, N_g:-N_g]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
x_n = x_0 + (1 - radius / np.sqrt(2)) * index / N # Top-left
y_n = -radius / np.sqrt(2)
x_n_plus_1 = x_0 + (1 - radius / np.sqrt(2)) * (
index + 1) / N # Top-right
y_n_plus_1 = -radius / np.sqrt(2)
x_n_plus_half = x_0 + (1 - radius / np.sqrt(2)) * (
index + 0.5) / N # Top-center
y_n_plus_half = -radius / np.sqrt(2)
x_y_bottom_left = [x_n, -1]
x_y_bottom_center = [x_n_plus_half, -1]
x_y_bottom_right = [x_n_plus_1, -1]
x_y_left_center = [x_n, (-1 + y_n) / 2]
x_y_right_center = [x_n_plus_1, (-1 + y_n_plus_1) / 2]
x_y_top_left = [x_n, y_n]
x_y_top_center = [x_n_plus_half, y_n_plus_half]
x_y_top_right = [x_n_plus_1, y_n_plus_1]
for j in range(0, N_q2 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left + index * domain.dq1,
q2_start_local_bottom,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Bottom-right domain
elif ((q2_midpoint < -0.33) and (q1_midpoint > 0.33)
and (q1_midpoint < 1.)):
N = N_q1
x_0 = radius / np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in x
for i in range(0, N_q1 + 2 * N_g):
index = i - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, N_g:-N_g]
q2_slice = q2[0, 0, i, N_g:-N_g]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
x_n = x_0 + (1 - x_0) * index / N # Top-left
y_n = -radius / np.sqrt(2)
x_n_plus_1 = x_0 + (1 - x_0) * (index + 1) / N # Top-right
y_n_plus_1 = -radius / np.sqrt(2)
x_n_plus_half = x_0 + (1 - x_0) * (index +
0.5) / N # Top-center
y_n_plus_half = -radius / np.sqrt(2)
x_y_bottom_left = [x_n, -1]
x_y_bottom_center = [x_n_plus_half, -1]
x_y_bottom_right = [x_n_plus_1, -1]
x_y_left_center = [x_n, (-1 + y_n) / 2]
x_y_right_center = [x_n_plus_1, (-1 + y_n_plus_1) / 2]
x_y_top_left = [x_n, y_n]
x_y_top_center = [x_n_plus_half, y_n_plus_half]
x_y_top_right = [x_n_plus_1, y_n_plus_1]
for j in range(0, N_q2 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left + index * domain.dq1,
q2_start_local_bottom,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Top-center domain
if ((q2_midpoint > 0.33) and (q1_midpoint > -0.33)
and (q1_midpoint < 0.33)):
N = N_q1
x_0 = -radius / np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in x
for i in range(0, N_q1 + 2 * N_g):
index = i - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, N_g:-N_g]
q2_slice = q2[0, 0, i, N_g:-N_g]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
x_n = x_0 + np.sqrt(2) * radius * index / N # Bottom-left
y_n = np.sqrt(radius**2 - x_n**2)
x_n_plus_1 = x_0 + np.sqrt(2) * radius * (
index + 1) / N # Bottom-right
y_n_plus_1 = np.sqrt(radius**2 - x_n_plus_1**2)
x_n_plus_half = x_0 + np.sqrt(2) * radius * (
index + 0.5) / N # Bottom-center
y_n_plus_half = np.sqrt(radius**2 - x_n_plus_half**2)
x_y_bottom_left = [x_n, y_n]
x_y_bottom_center = [x_n_plus_half, y_n_plus_half]
x_y_bottom_right = [x_n_plus_1, y_n_plus_1]
x_y_left_center = [x_n, (1 + y_n) / 2]
x_y_right_center = [x_n_plus_1, (1 + y_n_plus_1) / 2]
x_y_top_left = [x_n, 1]
x_y_top_center = [x_n_plus_half, 1]
x_y_top_right = [x_n_plus_1, 1]
for j in range(0, N_q2 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left + index * domain.dq1,
q2_start_local_bottom,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Top-left domain
elif ((q2_midpoint > 0.33) and (q1_midpoint > -1)
and (q1_midpoint < -0.33)):
N = N_q1
x_0 = -1 #-radius/np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in x
for i in range(0, N_q1 + 2 * N_g):
index = i - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, N_g:-N_g]
q2_slice = q2[0, 0, i, N_g:-N_g]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
x_n = x_0 + (1 -
radius / np.sqrt(2)) * index / N # Bottom-left
y_n = radius / np.sqrt(2)
x_n_plus_1 = x_0 + (1 - radius / np.sqrt(2)) * (
index + 1) / N # Bottom-right
y_n_plus_1 = radius / np.sqrt(2)
x_n_plus_half = x_0 + (1 - radius / np.sqrt(2)) * (
index + 0.5) / N # Bottom-center
y_n_plus_half = radius / np.sqrt(2)
x_y_bottom_left = [x_n, y_n]
x_y_bottom_center = [x_n_plus_half, y_n_plus_half]
x_y_bottom_right = [x_n_plus_1, y_n_plus_1]
x_y_left_center = [x_n, (1 + y_n) / 2]
x_y_right_center = [x_n_plus_1, (1 + y_n_plus_1) / 2]
x_y_top_left = [x_n, 1]
x_y_top_center = [x_n_plus_half, 1]
x_y_top_right = [x_n_plus_1, 1]
for j in range(0, N_q2 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left + index * domain.dq1,
q2_start_local_bottom,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Top-right domain
elif ((q2_midpoint > 0.33) and (q1_midpoint > 0.33)
and (q1_midpoint < 1)):
N = N_q1
x_0 = radius / np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in x
for i in range(0, N_q1 + 2 * N_g):
index = i - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, i, N_g:-N_g]
q2_slice = q2[0, 0, i, N_g:-N_g]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
x_n = x_0 + (1 - x_0) * index / N # Bottom-left
y_n = radius / np.sqrt(2)
x_n_plus_1 = x_0 + (1 - x_0) * (index + 1) / N # Bottom-right
y_n_plus_1 = radius / np.sqrt(2)
x_n_plus_half = x_0 + (1 - x_0) * (index +
0.5) / N # Bottom-center
y_n_plus_half = radius / np.sqrt(2)
x_y_bottom_left = [x_n, y_n]
x_y_bottom_center = [x_n_plus_half, y_n_plus_half]
x_y_bottom_right = [x_n_plus_1, y_n_plus_1]
x_y_left_center = [x_n, (1 + y_n) / 2]
x_y_right_center = [x_n_plus_1, (1 + y_n_plus_1) / 2]
x_y_top_left = [x_n, 1]
x_y_top_center = [x_n_plus_half, 1]
x_y_top_right = [x_n_plus_1, 1]
for j in range(0, N_q2 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left + index * domain.dq1,
q2_start_local_bottom,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Center-Right domain
elif ((q2_midpoint > -0.33) and (q2_midpoint < 0.33)
and (q1_midpoint > 0.33)):
N = N_q1
y_0 = -radius / np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in y
for j in range(0, N_q2 + 2 * N_g):
print(j)
index = j - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, N_g:-N_g, j]
q2_slice = q2[0, 0, N_g:-N_g, j]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
y_n = y_0 + np.sqrt(2) * radius * index / N
x_n = np.sqrt(radius**2 - y_n**2) # Bottom-left
y_n_plus_1 = y_0 + np.sqrt(2) * radius * (index +
1) / N # top-left
x_n_plus_1 = np.sqrt(radius**2 - y_n_plus_1**2)
y_n_plus_half = y_0 + np.sqrt(2) * radius * (
index + 0.5) / N # Center-left
x_n_plus_half = np.sqrt(radius**2 - y_n_plus_half**2)
x_y_bottom_left = [x_n, y_n]
x_y_bottom_center = [(1 + x_n) / 2, y_n]
x_y_bottom_right = [1, y_n]
x_y_left_center = [x_n_plus_half, y_n_plus_half]
x_y_right_center = [1, y_n_plus_half]
x_y_top_left = [x_n_plus_1, y_n_plus_1]
x_y_top_center = [(1 + x_n_plus_1) / 2, y_n_plus_1]
x_y_top_right = [1, y_n_plus_1]
for i in range(0, N_q1 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left,
q2_start_local_bottom + index * domain.dq2,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Center-Left domain
elif ((q2_midpoint > -0.33) and (q2_midpoint < 0.33)
and (q1_midpoint < -0.33)):
N = N_q1
#x_0 = -radius/np.sqrt(2)
y_0 = -radius / np.sqrt(2)
# Initialize to zero
x = 0 * q1
y = 0 * q2
# Loop over each zone in y
for j in range(0, N_q2 + 2 * N_g):
print(j)
index = j - N_g # Index of the vertical slice, left-most being 0
# q1, q2 grid slices to be passed into quadratic for transformation
q1_slice = q1[0, 0, N_g:-N_g, j]
q2_slice = q2[0, 0, N_g:-N_g, j]
# Compute the x, y points using which the transformation will be defined
# x, y nodes remain the same for each point on a vertical slice
y_n = y_0 + np.sqrt(2) * radius * index / N
x_n = -np.sqrt(radius**2 - y_n**2) # Bottom-right
y_n_plus_1 = y_0 + np.sqrt(2) * radius * (index +
1) / N # top-right
x_n_plus_1 = -np.sqrt(radius**2 - y_n_plus_1**2)
y_n_plus_half = y_0 + np.sqrt(2) * radius * (
index + 0.5) / N # Center-right
x_n_plus_half = -np.sqrt(radius**2 - y_n_plus_half**2)
x_y_bottom_left = [-1, y_n]
x_y_bottom_center = [(-1 + x_n) / 2, y_n]
x_y_bottom_right = [x_n, y_n]
x_y_left_center = [-1, y_n_plus_half]
x_y_right_center = [x_n_plus_half, y_n_plus_half]
x_y_top_left = [-1, y_n_plus_1]
x_y_top_center = [(-1 + x_n_plus_1) / 2, y_n_plus_1]
x_y_top_right = [x_n_plus_1, y_n_plus_1]
for i in range(0, N_q1 + 2 * N_g):
# Get the transformation (x_i, y_i) for each point (q1_i, q2_i)
q1_i = q1[0, 0, i, j]
q2_i = q2[0, 0, i, j]
x_i, y_i, jacobian_i = quadratic_test(
q1_i,
q2_i,
q1_slice,
q2_slice,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left,
q2_start_local_bottom + index * domain.dq2,
)
# Reconstruct the x,y grid from the loop
x[0, 0, i, j] = x_i
y[0, 0, i, j] = y_i
# TODO : Reconstruct jacobian
[[dx_dq1_i, dx_dq2_i], [dy_dq1_i, dy_dq2_i]] = jacobian_i
dx_dq1[0, 0, i, j] = dx_dq1_i.scalar()
dx_dq2[0, 0, i, j] = dx_dq2_i.scalar()
dy_dq1[0, 0, i, j] = dy_dq1_i.scalar()
dy_dq2[0, 0, i, j] = dy_dq2_i.scalar()
jacobian = [[dx_dq1, dx_dq2], [dy_dq1, dy_dq2]]
# Center domain
elif ((q2_midpoint > -0.33) and (q2_midpoint < 0.33)
and (q1_midpoint > -0.33) and (q1_midpoint < 0.33)):
x_y_bottom_left = x_y_circle_bottom_left
x_y_bottom_center = [0., -radius]
x_y_bottom_right = x_y_circle_bottom_right
x_y_left_center = [-radius, 0]
x_y_right_center = [radius, 0]
x_y_top_left = x_y_circle_top_left
x_y_top_center = [0., radius]
x_y_top_right = x_y_circle_top_right
x, y, jacobian = quadratic(
q1,
q2,
x_y_bottom_left,
x_y_bottom_right,
x_y_top_right,
x_y_top_left,
x_y_bottom_center,
x_y_right_center,
x_y_top_center,
x_y_left_center,
q1_start_local_left,
q2_start_local_bottom,
)
if (return_jacobian):
return (x, y, jacobian)
else:
return (x, y)
else:
print(
"Error in get_cartesian_coords(): q1_start_local_left or q2_start_local_bottom not provided"
)
