Overhaul of PMLs and introduction of new, optional MRIPML formulation.

2025-08-06 12:36:51 +08:00 · 2019-04-12 16:23:55 +01:00
--- a/tests/models_pmls/plot_pml_comparison.py
+++ b/tests/models_pmls/plot_pml_comparison.py
@@ -0,0 +1,108 @@
+import itertools
+from operator import add
+import os
+import sys
+
+from colorama import init, Fore, Style
+init()
+import h5py
+import matplotlib.pyplot as plt
+import numpy as np
+
+# Create/setup plot figure
+#colors = ['#E60D30', '#5CB7C6', '#A21797', '#A3B347'] # Plot colours from http://tools.medialab.sciences-po.fr/iwanthue/index.php
+#colorIDs = ["#62a85b", "#9967c7", "#b3943f", "#6095cd", "#cb5c42", "#c95889"]
+colorIDs = ["#79c72e", "#5774ff", "#ff7c2c", "#4b4e80", "#d7004e", "#007545", "#ff83ec"]
+#colorIDs = ["#ba0044", "#b2d334", "#470055", "#185300", "#ff96b1", "#3e2700", "#0162a9", "#fdb786"]
+colors = itertools.cycle(colorIDs)
+# for i in range(2):
+#     next(colors)
+lines = itertools.cycle(('--', ':', '-.', '-'))
+markers = ['o', 'd', '^', 's', '*']
+
+basepath = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'pml_3D_pec_plate')
+path = 'rxs/rx1/'
+refmodel = 'pml_3D_pec_plate_ref'
+PMLIDs = ['CFS-PML', 'HORIPML-1', 'HORIPML-2', 'MRIPML-1', 'MRIPML-2']
+maxerrors = []
+testmodels = ['pml_3D_pec_plate_' + s for s in PMLIDs]
+
+fig, ax = plt.subplots(subplot_kw=dict(xlabel='Iterations', ylabel='Error [dB]'), figsize=(20, 10), facecolor='w', edgecolor='w')
+
+for x, model in enumerate(testmodels):
+    # Get output for model and reference files
+    fileref = h5py.File(os.path.join(basepath, refmodel + '.out'), 'r')
+    filetest = h5py.File(os.path.join(basepath, model + '.out'), 'r')
+
+    # Get available field output component names
+    outputsref = list(fileref[path].keys())
+    outputstest = list(filetest[path].keys())
+    if outputsref != outputstest:
+        raise GeneralError('Field output components do not match reference solution')
+
+    # Check that type of float used to store fields matches
+    if filetest[path + outputstest[0]].dtype != fileref[path + outputsref[0]].dtype:
+        print(Fore.RED + 'WARNING: Type of floating point number in test model ({}) does not match type in reference solution ({})\n'.format(filetest[path + outputstest[0]].dtype, fileref[path + outputsref[0]].dtype) + Style.RESET_ALL)
+    floattyperef = fileref[path + outputsref[0]].dtype
+    floattypetest = filetest[path + outputstest[0]].dtype
+    # print('Data type: {}'.format(floattypetest))
+
+    # Arrays for storing time
+    # timeref = np.zeros((fileref.attrs['Iterations']), dtype=floattyperef)
+    # timeref = np.linspace(0, (fileref.attrs['Iterations'] - 1) * fileref.attrs['dt'], num=fileref.attrs['Iterations']) / 1e-9
+    # timetest = np.zeros((filetest.attrs['Iterations']), dtype=floattypetest)
+    # timetest = np.linspace(0, (filetest.attrs['Iterations'] - 1) * filetest.attrs['dt'], num=filetest.attrs['Iterations']) / 1e-9
+    timeref = np.zeros((fileref.attrs['Iterations']), dtype=floattyperef)
+    timeref = np.linspace(0, (fileref.attrs['Iterations'] - 1), num=fileref.attrs['Iterations'])
+    timetest = np.zeros((filetest.attrs['Iterations']), dtype=floattypetest)
+    timetest = np.linspace(0, (filetest.attrs['Iterations'] - 1), num=filetest.attrs['Iterations'])
+
+    # Arrays for storing field data
+    dataref = np.zeros((fileref.attrs['Iterations'], len(outputsref)), dtype=floattyperef)
+    datatest = np.zeros((filetest.attrs['Iterations'], len(outputstest)), dtype=floattypetest)
+    for ID, name in enumerate(outputsref):
+        dataref[:, ID] = fileref[path + str(name)][:]
+        datatest[:, ID] = filetest[path + str(name)][:]
+        if np.any(np.isnan(datatest[:, ID])):
+            raise ValueError('Test data contains NaNs')
+
+    fileref.close()
+    filetest.close()
+
+    # Diffs
+    datadiffs = np.zeros(datatest.shape, dtype=np.float64)
+    for i in range(len(outputstest)):
+        max = np.amax(np.abs(dataref[:, i]))
+        datadiffs[:, i] = np.divide(np.abs(datatest[:, i] - dataref[:, i]), max, out=np.zeros_like(dataref[:, i]), where=max != 0)  # Replace any division by zero with zero
+
+        # Calculate power (ignore warning from taking a log of any zero values)
+        with np.errstate(divide='ignore'):
+            datadiffs[:, i] = 20 * np.log10(datadiffs[:, i])
+        # Replace any NaNs or Infs from zero division
+        datadiffs[:, i][np.invert(np.isfinite(datadiffs[:, i]))] = 0
+
+    # Print maximum error value
+    start = 210
+    maxerrors.append(': {:.1f} [dB]'.format(np.amax(datadiffs[start::, 1])))
+    print('{}: Max. error {}'.format(model, maxerrors[x]))
+
+    # Plot diffs (select column to choose field component, 0-Ex, 1-Ey etc..)
+    ax.plot(timeref[start::], datadiffs[start::, 1], color=next(colors), lw=2, ls=next(lines), label=model)
+    ax.set_xticks(np.arange(0, 2200, step=100))
+    ax.set_xlim([0, 2100])
+    ax.set_yticks(np.arange(-160, 0, step=20))
+    ax.set_ylim([-160, -20])
+    ax.set_axisbelow(True)
+    ax.grid(color=(0.75,0.75,0.75), linestyle='dashed')
+
+mylegend = list(map(add, PMLIDs, maxerrors))
+legend = ax.legend(mylegend, loc=1, fontsize=14)
+frame = legend.get_frame()
+frame.set_edgecolor('white')
+frame.set_alpha(0)
+
+plt.show()
+
+# Save a PDF/PNG of the figure
+fig.savefig(basepath + '.pdf', dpi=None, format='pdf', bbox_inches='tight', pad_inches=0.1)
+#fig.savefig(savename + '.png', dpi=150, format='png', bbox_inches='tight', pad_inches=0.1)
--- a/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_CFS-PML.in
+++ b/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_CFS-PML.in
@@ -0,0 +1,34 @@
+#title: Response from an elongated thin PEC plate
+#domain: 0.051 0.126 0.026
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 2100
+#time_step_stability_factor: 0.99
+
+################################################
+## PML parameters
+## CFS (alpha, kappa, sigma)
+## sigma_max = (0.8 * (m + 1)) / (z0 * d * np.sqrt(er * mr))
+## z0 = 376.73, d = 0.001
+################################################
+
+#pml_cells: 10
+
+#############
+## CFS PML ##
+#############
+#python:
+import numpy as np
+
+# Parameters from http://dx.doi.org/10.1109/TAP.2018.2823864
+smax = 1.1 * ((4 + 1) / (150 * np.pi * 0.001))
+print('#pml_cfs: constant forward 0.05 0.05 quartic forward 1 8 quartic forward 0 {}'.format(smax))
+#end_python:
+
+#waveform: gaussiandotnorm 1 9.42e9 mypulse
+#hertzian_dipole: z 0.013 0.013 0.014 mypulse
+#rx: 0.038 0.114 0.013
+
+#plate: 0.013 0.013 0.013 0.038 0.113 0.013 pec
+
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_f f
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_n n
--- a/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_HORIPML-1.in
+++ b/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_HORIPML-1.in
@@ -0,0 +1,34 @@
+#title: Response from an elongated thin PEC plate
+#domain: 0.051 0.126 0.026
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 2100
+#time_step_stability_factor: 0.99
+
+################################################
+## PML parameters
+## CFS (alpha, kappa, sigma)
+## sigma_max = (0.8 * (m + 1)) / (z0 * d * np.sqrt(er * mr))
+## z0 = 376.73, d = 0.001
+################################################
+
+#pml_cells: 10
+
+################################################
+## 1st order (default) HORIPML - Standard PML ##
+################################################
+#python:
+import numpy as np
+
+# Parameters from http://dx.doi.org/10.1109/TAP.2011.2180344
+smax = 0.7 * ((4 + 1) / (150 * np.pi * 0.001))
+print('#pml_cfs: constant forward 0 0 quartic forward 1 12 quartic forward 0 {}'.format(smax))
+#end_python:
+
+#waveform: gaussiandotnorm 1 9.42e9 mypulse
+#hertzian_dipole: z 0.013 0.013 0.014 mypulse
+#rx: 0.038 0.114 0.013
+
+#plate: 0.013 0.013 0.013 0.038 0.113 0.013 pec
+
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_f f
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_n n
--- a/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_HORIPML-2.in
+++ b/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_HORIPML-2.in
@@ -0,0 +1,37 @@
+#title: Response from an elongated thin PEC plate
+#domain: 0.051 0.126 0.026
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 2100
+#time_step_stability_factor: 0.99
+
+################################################
+## PML parameters
+## CFS (alpha, kappa, sigma)
+## sigma_max = (0.8 * (m + 1)) / (z0 * d * np.sqrt(er * mr))
+## z0 = 376.73, d = 0.001
+################################################
+
+#pml_cells: 10
+
+#######################
+## 2nd order HORIPML ##
+#######################
+#python:
+import numpy as np
+
+# Parameters from http://dx.doi.org/10.1109/TAP.2018.2823864
+smax1 = 0.275 / (150 * np.pi * 0.001)
+smax2 = 2.75 / (150 * np.pi * 0.001)
+a0 = 0.07
+print('#pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 {}'.format(smax1))
+print('#pml_cfs: sextic forward {} {} cubic forward 1 8 quadratic forward 0 {}'.format(a0, a0 + smax1, smax2))
+#end_python:
+
+#waveform: gaussiandotnorm 1 9.42e9 mypulse
+#hertzian_dipole: z 0.013 0.013 0.014 mypulse
+#rx: 0.038 0.114 0.013
+
+#plate: 0.013 0.013 0.013 0.038 0.113 0.013 pec
+
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_f f
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_n n
--- a/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_MRIPML-1.in
+++ b/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_MRIPML-1.in
@@ -0,0 +1,36 @@
+#title: Response from an elongated thin PEC plate
+#domain: 0.051 0.126 0.026
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 2100
+#time_step_stability_factor: 0.99
+
+################################################
+## PML parameters
+## CFS (alpha, kappa, sigma)
+## sigma_max = (0.8 * (m + 1)) / (z0 * d * np.sqrt(er * mr))
+## z0 = 376.73, d = 0.001
+################################################
+
+#pml_cells: 10
+
+######################
+## 1st order MRIPML ##
+######################
+#pml_formulation: MRIPML
+
+#python:
+import numpy as np
+
+# Parameters from Antonis' MATLAB script (M3Dparams.m)
+smax = 1.1 * ((4 + 1) / (150 * np.pi * 0.001))
+print('#pml_cfs: constant forward 0.05 0.05 quartic forward 1 8 quartic forward 0 {}'.format(smax))
+#end_python:
+
+#waveform: gaussiandotnorm 1 9.42e9 mypulse
+#hertzian_dipole: z 0.013 0.013 0.014 mypulse
+#rx: 0.038 0.114 0.013
+
+#plate: 0.013 0.013 0.013 0.038 0.113 0.013 pec
+
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_f f
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_n n
--- a/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_MRIPML-2.in
+++ b/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_MRIPML-2.in
@@ -0,0 +1,39 @@
+#title: Response from an elongated thin PEC plate
+#domain: 0.051 0.126 0.026
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 2100
+#time_step_stability_factor: 0.99
+
+################################################
+## PML parameters
+## CFS (alpha, kappa, sigma)
+## sigma_max = (0.8 * (m + 1)) / (z0 * d * np.sqrt(er * mr))
+## z0 = 376.73, d = 0.001
+################################################
+
+#pml_cells: 10
+
+######################
+## 2nd order MRIPML ##
+######################
+#pml_formulation: MRIPML
+
+#python:
+import numpy as np
+
+# Parameters from http://dx.doi.org/10.1109/TAP.2018.2823864
+smax1 = 0.65 * ((4 + 1) / (150 * np.pi * 0.001))
+smax2 = 0.65 * ((2 + 1) / (150 * np.pi * 0.001))
+print('#pml_cfs: quadratic reverse 0 0.15 quartic forward 1 12 quartic forward 0 {}'.format(smax1))
+print('#pml_cfs: linear reverse 0 0.8 constant forward 0 0 quadratic forward 0 {}'.format(smax2))
+#end_python:
+
+
+#waveform: gaussiandotnorm 1 9.42e9 mypulse
+#hertzian_dipole: z 0.013 0.013 0.014 mypulse
+#rx: 0.038 0.114 0.013
+
+#plate: 0.013 0.013 0.013 0.038 0.113 0.013 pec
+
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_f f
+geometry_view: 0 0 0 0.051 0.126 0.026 0.001 0.001 0.001 pml_3D_pec_plate_n n
--- a/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_ref.in
+++ b/tests/models_pmls/pml_3D_pec_plate/pml_3D_pec_plate_ref.in
@@ -0,0 +1,34 @@
+#title: Standard PML of response from an elongated thin PEC plate
+#domain: 0.201 0.276 0.176
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 2100
+#time_step_stability_factor: 0.99
+
+################################################
+## PML parameters
+## CFS (alpha, kappa, sigma)
+## sigma_max = (0.8 * (m + 1)) / (z0 * d * np.sqrt(er * mr))
+## z0 = 376.73, d = 0.001
+################################################
+
+#pml_cells: 10
+
+#############
+## CFS PML ##
+#############
+#python:
+import numpy as np
+
+# Parameters from http://dx.doi.org/10.1109/TAP.2018.2823864
+smax = 1.1 * ((4 + 1) / (150 * np.pi * 0.001))
+print('#pml_cfs: constant forward 0.05 0.05 quartic forward 1 8 quartic forward 0 {}'.format(smax))
+#end_python:
+
+#waveform: gaussiandotnorm 1 9.42e9 mypulse
+#hertzian_dipole: z 0.088 0.088 0.089 mypulse
+#rx: 0.113 0.189 0.088
+
+#plate: 0.088 0.088 0.088 0.113 0.188 0.088 pec
+
+geometry_view: 0 0 0 0.201 0.276 0.176 0.001 0.001 0.001 pml_3D_pec_plate_ref_f f
+geometry_view: 0 0 0 0.201 0.276 0.176 0.001 0.001 0.001 pml_3D_pec_plate_ref_n n
--- a/tests/models_pmls/pml_off.in
+++ b/tests/models_pmls/pml_off.in
@@ -0,0 +1,10 @@
+#title: PML test none
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 0
--- a/tests/models_pmls/pml_x0/pml_x0.in
+++ b/tests/models_pmls/pml_x0/pml_x0.in
@@ -0,0 +1,26 @@
+#title: PML test x0 slab
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 10 0 0 0 0 0
+
+#pml_formulation: HORIPML
+
+## Built-in 1st order PML
+#pml_cfs: constant forward 0 0 constant forward 1 1 quartic forward 0 None
+
+## PMLs from http://dx.doi.org/10.1109/TAP.2011.2180344
+## Standard PML
+pml_cfs: constant forward 0 0 quartic forward 1 11 quartic forward 0 7.427
+
+## CFS PML
+pml_cfs: constant forward 0.05 0.05 quartic forward 1 7 quartic forward 0 11.671
+
+## 2nd order RIPML
+pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 0.5836
+pml_cfs: constant forward 0.05 0.05 cubic forward 1 8 quadratic forward 0 5.8357
--- a/tests/models_pmls/pml_xmax/pml_xmax.in
+++ b/tests/models_pmls/pml_xmax/pml_xmax.in
@@ -0,0 +1,26 @@
+#title: PML test xmax slab
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 0 0 0 10 0 0
+
+#pml_formulation: HORIPML
+
+## Built-in 1st order PML
+#pml_cfs: constant forward 0 0 constant forward 1 1 quartic forward 0 None
+
+## PMLs from http://dx.doi.org/10.1109/TAP.2011.2180344
+## Standard PML
+pml_cfs: constant forward 0 0 quartic forward 1 11 quartic forward 0 7.427
+
+## CFS PML
+pml_cfs: constant forward 0.05 0.05 quartic forward 1 7 quartic forward 0 11.671
+
+## 2nd order RIPML
+pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 0.5836
+pml_cfs: constant forward 0.05 0.05 cubic forward 1 8 quadratic forward 0 5.8357
--- a/tests/models_pmls/pml_y0/pml_y0.in
+++ b/tests/models_pmls/pml_y0/pml_y0.in
@@ -0,0 +1,26 @@
+#title: PML test y0 slab
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 0 10 0 0 0 0
+
+#pml_formulation: HORIPML
+
+## Built-in 1st order PML
+#pml_cfs: constant forward 0 0 constant forward 1 1 quartic forward 0 None
+
+## PMLs from http://dx.doi.org/10.1109/TAP.2011.2180344
+## Standard PML
+pml_cfs: constant forward 0 0 quartic forward 1 11 quartic forward 0 7.427
+
+## CFS PML
+pml_cfs: constant forward 0.05 0.05 quartic forward 1 7 quartic forward 0 11.671
+
+## 2nd order RIPML
+pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 0.5836
+pml_cfs: constant forward 0.05 0.05 cubic forward 1 8 quadratic forward 0 5.8357
--- a/tests/models_pmls/pml_ymax/pml_ymax.in
+++ b/tests/models_pmls/pml_ymax/pml_ymax.in
@@ -0,0 +1,26 @@
+#title: PML test ymax slab
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 0 0 0 0 10 0
+
+#pml_formulation: HORIPML
+
+## Built-in 1st order PML
+#pml_cfs: constant forward 0 0 constant forward 1 1 quartic forward 0 None
+
+## PMLs from http://dx.doi.org/10.1109/TAP.2011.2180344
+## Standard PML
+pml_cfs: constant forward 0 0 quartic forward 1 11 quartic forward 0 7.427
+
+## CFS PML
+pml_cfs: constant forward 0.05 0.05 quartic forward 1 7 quartic forward 0 11.671
+
+## 2nd order RIPML
+pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 0.5836
+pml_cfs: constant forward 0.05 0.05 cubic forward 1 8 quadratic forward 0 5.8357
--- a/tests/models_pmls/pml_z0/pml_z0.in
+++ b/tests/models_pmls/pml_z0/pml_z0.in
@@ -0,0 +1,26 @@
+#title: PML test z0 slab
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 0 0 10 0 0 0
+
+#pml_formulation: HORIPML
+
+## Built-in 1st order PML
+#pml_cfs: constant forward 0 0 constant forward 1 1 quartic forward 0 None
+
+## PMLs from http://dx.doi.org/10.1109/TAP.2011.2180344
+## Standard PML
+pml_cfs: constant forward 0 0 quartic forward 1 11 quartic forward 0 7.427
+
+## CFS PML
+pml_cfs: constant forward 0.05 0.05 quartic forward 1 7 quartic forward 0 11.671
+
+## 2nd order RIPML
+pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 0.5836
+pml_cfs: constant forward 0.05 0.05 cubic forward 1 8 quadratic forward 0 5.8357
--- a/tests/models_pmls/pml_zmax/pml_zmax.in
+++ b/tests/models_pmls/pml_zmax/pml_zmax.in
@@ -0,0 +1,26 @@
+#title: PML test zmax slab
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.050 0.050 0.050 myWave
+#rx: 0.070 0.070 0.070
+
+#pml_cells: 0 0 0 0 0 10
+
+#pml_formulation: HORIPML
+
+## Built-in 1st order PML
+#pml_cfs: constant forward 0 0 constant forward 1 1 quartic forward 0 None
+
+## PMLs from http://dx.doi.org/10.1109/TAP.2011.2180344
+## Standard PML
+pml_cfs: constant forward 0 0 quartic forward 1 11 quartic forward 0 7.427
+
+## CFS PML
+pml_cfs: constant forward 0.05 0.05 quartic forward 1 7 quartic forward 0 11.671
+
+## 2nd order RIPML
+pml_cfs: constant forward 0 0 constant forward 1 1 sextic forward 0 0.5836
+pml_cfs: constant forward 0.05 0.05 cubic forward 1 8 quadratic forward 0 5.8357