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Small fixes in Krylov example #2322

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Sep 11, 2023
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Small fixes in Krylov example #2322

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Update krylov_example.rst
germa89 Sep 8, 2023
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[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Sep 8, 2023
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Merge branch 'main' into doc/small-fixes-in-krylov-example
germa89 Sep 11, 2023
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67 changes: 35 additions & 32 deletions doc/source/examples/extended_examples/Krylov/krylov_example.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -34,7 +34,7 @@ These are the main steps required:

Perform required imports
------------------------
Perform required imports and launch MAPDL.
Perform required imports and launch MAPDL.

.. code:: ipython3

Expand Down Expand Up @@ -224,22 +224,33 @@ Get the first 10 natural frequency modes of the acoustic duct.
A = mm.mat(k.nrow, nev)
eigenvalues = mm.eigs(nev, k, M, phi=A, fmin=1.0)

for each_freq in range(10):
print(f"Freq = {eigenvalues[each_freq]:8.2f} Hz") # Eigenfrequency (Hz)

The first ten modes are:

+-------------+----------------+
| Mode number | Frequency (Hz) |
+=============+================+
| 1 | 83.33 |
+-------------+----------------+
| 2 | 250.00 |
+-------------+----------------+
| 3 | 416.67 |
+-------------+----------------+
| 4 | 583.34 |
+-------------+----------------+
| 5 | 750.03 |
+-------------+----------------+
| 6 | 916.74 |
+-------------+----------------+
| 7 | 1083.49 |
+-------------+----------------+
| 8 | 1250.32 |
+-------------+----------------+
| 9 | 1417.26 |
+-------------+----------------+
| 10 | 1584.36 |
+-------------+----------------+

.. parsed-literal::

Freq = 83.33 Hz
Freq = 250.00 Hz
Freq = 416.67 Hz
Freq = 583.34 Hz
Freq = 750.03 Hz
Freq = 916.74 Hz
Freq = 1083.49 Hz
Freq = 1250.32 Hz
Freq = 1417.26 Hz
Freq = 1584.36 Hz


Run harmonic analysis using Krylov method
Expand Down Expand Up @@ -273,15 +284,11 @@ frequency-sweep Krylov method.

Obtain the shape of the generated subspace.

.. code:: ipython3

print(Qz.shape)


.. parsed-literal::
.. code:: pycon

>>> print(Qz.shape)
(3240, 10)


**Step 3**: Reduce the system of equations and solve at each frequency
from 0 Hz to 1000 Hz with ramped loading.
Expand All @@ -292,15 +299,11 @@ from 0 Hz to 1000 Hz with ramped loading.

Obtain the shape of the reduced solution generated.

.. code:: ipython3

print(Yz.shape)


.. parsed-literal::
.. code:: pycon

>>> print(Yz.shape)
(10, 100)


**Step 4**: Expand the reduced solution back to the FE space.

Expand Down Expand Up @@ -340,12 +343,12 @@ Load the last result substep to get the pressure for each of the selected nodes.
# Get pressure at the node
pressure = get_pressure_at(each_node, substep_index)['x'][0]

#Calculate amplitude at 60 deg
# Calculate amplitude at 60 deg
magnitude = abs(pressure)
phase = math.atan2(pressure.imag, pressure.real)
pressure_a = magnitude * np.cos(np.deg2rad(60)+phase)

# Store result for later plotting
# Store result for later plotting
x_data.append(loc[0]) # X-Coordenate
y_data.append(pressure_a) # Nodal pressure at 60 degrees

Expand Down Expand Up @@ -435,4 +438,4 @@ Plot the frequency response function for the selected node.
plt.show()


.. image:: files/file_38_0.png
.. image:: files/file_38_0.png