Azure CI commit ref 60f3af15697c701d2ea8f3c08ceebd72a33e3dbe

Author: simpeg-bot

en/latest

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-v0.11.1
+v0.11.2

en/v0.11.2/.buildinfo

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+# Sphinx build info version 1
+# This file records the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 2296adff33f16fbd064b2b565386256e
+tags: 645f666f9bcd5a90fca523b33c5a78b7

en/v0.11.2/_downloads/005789fc4d07d603b5f8ac849b9d13b3/discretize-TensorMesh-stencil_cell_gradient_z-1_01_00.pdf

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+# Here we compute the values of a scalar function on the z-faces. We then create
+# an averaging operator to approximate the function at cell centers. We choose
+# to define a scalar function that is strongly discontinuous in some places to
+# demonstrate how the averaging operator will smooth out discontinuities.
+#
+# We start by importing the necessary packages and defining a mesh.
+#
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+#
+h = np.ones(40)
+mesh = TensorMesh([h, h, h], x0="CCC")
+#
+# Create a scalar variable on z-faces
+#
+phi_z = np.zeros(mesh.nFz)
+xyz = mesh.faces_z
+phi_z[(xyz[:, 2] > 0)] = 25.0
+phi_z[(xyz[:, 2] < -10.0) & (xyz[:, 0] > -10.0) & (xyz[:, 0] < 10.0)] = 50.0
+#
+# Next, we construct the averaging operator and apply it to
+# the discrete scalar quantity to approximate the value at cell centers.
+# We plot the original scalar and its average at cell centers for a
+# slice at y=0.
+#
+Azc = mesh.average_face_z_to_cell
+phi_c = Azc @ phi_z
+#
+# And plot the results:
+#
+fig = plt.figure(figsize=(11, 5))
+ax1 = fig.add_subplot(121)
+v = np.r_[np.zeros(mesh.nFx+mesh.nFy), phi_z]  # create vector for plotting
+mesh.plot_slice(v, ax=ax1, normal='Y', slice_loc=0, v_type="Fz")
+ax1.set_title("Variable at z-faces", fontsize=16)
+ax2 = fig.add_subplot(122)
+mesh.plot_image(phi_c, ax=ax2, normal='Y', slice_loc=0, v_type="CC")
+ax2.set_title("Averaged to cell centers", fontsize=16)
+plt.show()
+#
+# Below, we show a spy plot illustrating the sparsity and mapping
+# of the operator
+#
+fig = plt.figure(figsize=(9, 9))
+ax1 = fig.add_subplot(111)
+ax1.spy(Azc, ms=1)
+ax1.set_title("Z-Face Index", fontsize=12, pad=5)
+ax1.set_ylabel("Cell Index", fontsize=12)
+plt.show()