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#!/usr/bin/env python3
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1.axes_divider import make_axes_locatable
import numpy as np
from pywarpx import picmi
# Number of time steps
max_steps = 100
# Grid
nx = 128
nz = 128
# Domain
xmin = 0.e-6
zmin = 0.e-6
xmax = 50.e-6
zmax = 50.e-6
# Cell size
dx = (xmax - xmin) / nx
dz = (zmax - zmin) / nz
# Domain decomposition
max_grid_size_x = 64
max_grid_size_z = 64
# PML
nxpml = 10
nzpml = 10
field_boundary = ['open', 'open']
# Spectral order
nox = 8
noz = 8
# Guard cells
nxg = 8
nzg = 8
# Initialize grid
grid = picmi.Cartesian2DGrid(number_of_cells = [nx,nz],
lower_bound = [xmin,zmin],
upper_bound = [xmax,zmax],
lower_boundary_conditions = field_boundary,
upper_boundary_conditions = field_boundary,
guard_cells = [nxg,nzg],
moving_window_velocity = [0.,0.,0],
warpx_max_grid_size_x = max_grid_size_x,
warpx_max_grid_size_y = max_grid_size_z)
# Initialize field solver
solver = picmi.ElectromagneticSolver(grid=grid, cfl=0.95, method='PSATD',
stencil_order = [nox,noz],
divE_cleaning = 1,
divB_cleaning = 1,
pml_divE_cleaning = 1,
pml_divB_cleaning = 1,
warpx_psatd_update_with_rho = True)
# Initialize diagnostics
diag_field_list = ["E", "B"]
field_diag = picmi.FieldDiagnostic(name = 'diag1',
grid = grid,
period = 10,
write_dir = '.',
warpx_file_prefix = 'Python_wrappers_plt',
data_list = diag_field_list)
# Initialize simulation
sim = picmi.Simulation(solver = solver,
max_steps = max_steps,
verbose = 1,
particle_shape = 'cubic',
warpx_current_deposition_algo = 'direct',
warpx_particle_pusher_algo = 'boris',
warpx_field_gathering_algo = 'energy-conserving',
warpx_use_filter = 1)
# Add diagnostics to simulation
sim.add_diagnostic(field_diag)
# Write input file to run with compiled version
sim.write_input_file(file_name = 'inputs_2d')
# Whether to include guard cells in data returned by Python wrappers
include_ghosts = 1
# Compute min and max of fields data
def compute_minmax(data):
vmax = np.abs(data).max()
vmin = -vmax
return vmin, vmax
# Plot fields data either in valid domain or in PML
def plot_data(data, pml, title, name):
fig, ax = plt.subplots(nrows = 1, ncols = 1, gridspec_kw = dict(wspace = 0.5), figsize = [6,5])
cax = make_axes_locatable(ax).append_axes('right', size='5%', pad='5%')
lw = 0.8
ls = '--'
if pml:
# Draw PMLs and ghost regions
ax.axvline(x = 0 , linewidth = lw, linestyle = ls)
ax.axvline(x = 0+nxg , linewidth = lw, linestyle = ls)
ax.axvline(x = -nxpml , linewidth = lw, linestyle = ls)
ax.axvline(x = nx , linewidth = lw, linestyle = ls)
ax.axvline(x = nx-nxg , linewidth = lw, linestyle = ls)
ax.axvline(x = nx+nxpml, linewidth = lw, linestyle = ls)
ax.axhline(y = 0 , linewidth = lw, linestyle = ls)
ax.axhline(y = 0+nzg , linewidth = lw, linestyle = ls)
ax.axhline(y = -nzpml , linewidth = lw, linestyle = ls)
ax.axhline(y = nz , linewidth = lw, linestyle = ls)
ax.axhline(y = nz-nzg , linewidth = lw, linestyle = ls)
ax.axhline(y = nz+nzpml, linewidth = lw, linestyle = ls)
# Annotations
ax.annotate('PML', xy = (-nxpml//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('PML', xy = (nx+nxpml//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('PML', xy = (nx//2,-nzpml//2), rotation = 'horizontal', ha = 'center', va = 'center')
ax.annotate('PML', xy = (nx//2,nz+nzpml//2), rotation = 'horizontal', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nxg//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (-nxpml-nxg//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nx-nxg//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nx+nxpml+nxg//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nx//2,nzg//2), rotation = 'horizontal', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nx//2,-nzpml-nzg//2), rotation = 'horizontal', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nx//2,nz-nzg//2), rotation = 'horizontal', ha = 'center', va = 'center')
ax.annotate('PML ghost', xy = (nx//2,nz+nzpml+nzg//2), rotation = 'horizontal', ha = 'center', va = 'center')
# Set extent and sliced data
extent = np.array([-nxg-nxpml, nx+nxpml+nxg, -nzg-nzpml, nz+nzpml+nzg])
else:
# Draw ghost regions
ax.axvline(x = 0 , linewidth = lw, linestyle = ls)
ax.axvline(x = nx, linewidth = lw, linestyle = ls)
ax.axhline(y = 0 , linewidth = lw, linestyle = ls)
ax.axhline(y = nz, linewidth = lw, linestyle = ls)
# Annotations
ax.annotate('ghost', xy = (-nxg//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('ghost', xy = (nx+nxg//2,nz//2), rotation = 'vertical', ha = 'center', va = 'center')
ax.annotate('ghost', xy = (nx//2,-nzg//2), rotation = 'horizontal', ha = 'center', va = 'center')
ax.annotate('ghost', xy = (nx//2,nz+nzg//2), rotation = 'horizontal', ha = 'center', va = 'center')
# Set extent and sliced data
extent = np.array([-nxg, nx+nxg, -nzg, nz+nzg])
X = data[:,:].transpose()
# Min and max for colorbar
vmin, vmax = compute_minmax(X)
# Display data as image
im = ax.imshow(X = X, origin = 'lower', extent = extent, vmin = vmin, vmax = vmax, cmap = 'seismic')
# Add colorbar to plot
fig.colorbar(im, cax = cax)
# Set label for x- and y-axis, set title
ax.set_xlabel('x')
ax.set_ylabel('z')
ax.set_title(title)
# Set plot title
suptitle = 'PML in (x,z), 4 grids 64 x 64'
plt.suptitle(suptitle)
# Save figure
figname = 'figure_' + name + '.png'
fig.savefig(figname, dpi = 100)
# Initialize fields data (unit pulse) and apply smoothing
def init_data(data):
impulse_1d = np.array([1./4., 1./2., 1./4.])
impulse = np.outer(impulse_1d, impulse_1d)
data[nx//2-1:nx//2+2,nz//2-1:nz//2+2] = impulse
# Initialize inputs and WarpX instance
sim.initialize_inputs()
sim.initialize_warpx()
# Get fields data using Python wrappers
import pywarpx.fields as pwxf
Ex = pwxf.ExFPWrapper(include_ghosts = include_ghosts)
Ey = pwxf.EyFPWrapper(include_ghosts = include_ghosts)
Ez = pwxf.EzFPWrapper(include_ghosts = include_ghosts)
Bx = pwxf.BxFPWrapper(include_ghosts = include_ghosts)
By = pwxf.ByFPWrapper(include_ghosts = include_ghosts)
Bz = pwxf.BzFPWrapper(include_ghosts = include_ghosts)
F = pwxf.FFPWrapper(include_ghosts = include_ghosts)
G = pwxf.GFPWrapper(include_ghosts = include_ghosts)
Expml = pwxf.ExFPPMLWrapper(include_ghosts = include_ghosts)
Eypml = pwxf.EyFPPMLWrapper(include_ghosts = include_ghosts)
Ezpml = pwxf.EzFPPMLWrapper(include_ghosts = include_ghosts)
Bxpml = pwxf.BxFPPMLWrapper(include_ghosts = include_ghosts)
Bypml = pwxf.ByFPPMLWrapper(include_ghosts = include_ghosts)
Bzpml = pwxf.BzFPPMLWrapper(include_ghosts = include_ghosts)
Fpml = pwxf.FFPPMLWrapper(include_ghosts = include_ghosts)
Gpml = pwxf.GFPPMLWrapper(include_ghosts = include_ghosts)
# Initialize fields data in valid domain
init_data(Ex)
init_data(Ey)
init_data(Ez)
init_data(Bx)
init_data(By)
init_data(Bz)
init_data(F)
init_data(G)
# Advance simulation until last time step
sim.step(max_steps)
# Plot E
plot_data(Ex, pml = False, title = 'Ex', name = 'Ex')
plot_data(Ey, pml = False, title = 'Ey', name = 'Ey')
plot_data(Ez, pml = False, title = 'Ez', name = 'Ez')
# Plot B
plot_data(Bx, pml = False, title = 'Bx', name = 'Bx')
plot_data(By, pml = False, title = 'By', name = 'By')
plot_data(Bz, pml = False, title = 'Bz', name = 'Bz')
# F and G
plot_data(F, pml = False, title = 'F', name = 'F')
plot_data(G, pml = False, title = 'G', name = 'G')
# Plot E in PML
plot_data(Expml[:,:,0], pml = True, title = 'Exy in PML', name = 'Exy')
plot_data(Expml[:,:,1], pml = True, title = 'Exz in PML', name = 'Exz')
plot_data(Expml[:,:,2], pml = True, title = 'Exx in PML', name = 'Exx')
plot_data(Eypml[:,:,0], pml = True, title = 'Eyz in PML', name = 'Eyz')
plot_data(Eypml[:,:,1], pml = True, title = 'Eyx in PML', name = 'Eyx')
plot_data(Eypml[:,:,2], pml = True, title = 'Eyy in PML', name = 'Eyy') # zero
plot_data(Ezpml[:,:,0], pml = True, title = 'Ezx in PML', name = 'Ezx')
plot_data(Ezpml[:,:,1], pml = True, title = 'Ezy in PML', name = 'Ezy') # zero
plot_data(Ezpml[:,:,2], pml = True, title = 'Ezz in PML', name = 'Ezz')
# Plot B in PML
plot_data(Bxpml[:,:,0], pml = True, title = 'Bxy in PML', name = 'Bxy')
plot_data(Bxpml[:,:,1], pml = True, title = 'Bxz in PML', name = 'Bxz')
plot_data(Bxpml[:,:,2], pml = True, title = 'Bxx in PML', name = 'Bxx')
plot_data(Bypml[:,:,0], pml = True, title = 'Byz in PML', name = 'Byz')
plot_data(Bypml[:,:,1], pml = True, title = 'Byx in PML', name = 'Byx')
plot_data(Bypml[:,:,2], pml = True, title = 'Byy in PML', name = 'Byy') # zero
plot_data(Bzpml[:,:,0], pml = True, title = 'Bzx in PML', name = 'Bzx')
plot_data(Bzpml[:,:,1], pml = True, title = 'Bzy in PML', name = 'Bzy') # zero
plot_data(Bzpml[:,:,2], pml = True, title = 'Bzz in PML', name = 'Bzz')
# Plot F and G in PML
plot_data(Fpml[:,:,0], pml = True, title = 'Fx in PML', name = 'Fx')
plot_data(Fpml[:,:,1], pml = True, title = 'Fy in PML', name = 'Fy')
plot_data(Fpml[:,:,2], pml = True, title = 'Fz in PML', name = 'Fz')
plot_data(Gpml[:,:,0], pml = True, title = 'Gx in PML', name = 'Gx')
plot_data(Gpml[:,:,1], pml = True, title = 'Gy in PML', name = 'Gy')
plot_data(Gpml[:,:,2], pml = True, title = 'Gz in PML', name = 'Gz')
# Check values with benchmarks (precomputed from the same Python arrays)
def check_values(benchmark, data, rtol, atol):
passed = np.allclose(benchmark, np.sum(np.abs(data[:,:])), rtol = rtol, atol = atol)
assert(passed)
rtol = 5e-08
atol = 1e-12
# E
check_values(1013263608.6369569, Ex[:,:], rtol, atol)
check_values(717278256.7957529 , Ey[:,:], rtol, atol)
check_values(717866566.5718911 , Ez[:,:], rtol, atol)
# B
check_values(3.0214509313437636, Bx[:,:], rtol, atol)
check_values(3.0242765102729985, By[:,:], rtol, atol)
check_values(3.0214509326970465, Bz[:,:], rtol, atol)
# F and G
check_values(3.0188584528062377, F[:,:], rtol, atol)
check_values(1013672631.8764204, G[:,:], rtol, atol)
# E in PML
check_values(364287936.1526477 , Expml[:,:,0], rtol, atol)
check_values(183582352.20753333, Expml[:,:,1], rtol, atol)
check_values(190065766.41491824, Expml[:,:,2], rtol, atol)
check_values(440581907.0828975 , Eypml[:,:,0], rtol, atol)
check_values(178117294.05871135, Eypml[:,:,1], rtol, atol)
check_values(0.0 , Eypml[:,:,2], rtol, atol)
check_values(430277101.26568377, Ezpml[:,:,0], rtol, atol)
check_values(0.0 , Ezpml[:,:,1], rtol, atol)
check_values(190919663.2167449 , Ezpml[:,:,2], rtol, atol)
# B in PML
check_values(1.0565189315366146 , Bxpml[:,:,0], rtol, atol)
check_values(0.46181913800643065, Bxpml[:,:,1], rtol, atol)
check_values(0.6849858305343736 , Bxpml[:,:,2], rtol, atol)
check_values(1.7228584190213505 , Bypml[:,:,0], rtol, atol)
check_values(0.47697332248020935, Bypml[:,:,1], rtol, atol)
check_values(0.0 , Bypml[:,:,2], rtol, atol)
check_values(1.518338068658267 , Bzpml[:,:,0], rtol, atol)
check_values(0.0 , Bzpml[:,:,1], rtol, atol)
check_values(0.6849858291863835 , Bzpml[:,:,2], rtol, atol)
# F and G in PML
check_values(1.7808748509425263, Fpml[:,:,0], rtol, atol)
check_values(0.0 , Fpml[:,:,1], rtol, atol)
check_values(0.4307845604625681, Fpml[:,:,2], rtol, atol)
check_values(536552745.42701197, Gpml[:,:,0], rtol, atol)
check_values(0.0 , Gpml[:,:,1], rtol, atol)
check_values(196016270.97767758, Gpml[:,:,2], rtol, atol)
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