ls
README.md demo_nonlinear-poisson.py.rst Untitled.ipynb demo_poisson.ipynb __pycache__/ demo_poisson.py.rst aneurysm.xml.gz demo_singular-poisson-rst.ipynb box_with_dent.xml.gz demo_singular-poisson-rst.py.rst convert.py dolfin-1.6.0/ demo_auto-adaptive-poisson.ipynb dolfin-1.6.0.tar.gz demo_auto-adaptive-poisson.py.rst dolfin_fine.xml.gz demo_biharmonic.ipynb dolfin_fine_subdomains.xml.gz demo_biharmonic.py.rst environment.yml demo_built-in-meshes.ipynb generate-notebooks.py demo_built-in-meshes.py.rst jupyter_converter.py demo_cahn-hilliard.ipynb lshape.xml.gz demo_cahn-hilliard.py.rst rst-to-ipynb-demos.py demo_eigenvalue.ipynb split-cell-example.ipynb demo_eigenvalue.py.rst splitcell.py demo_hyperelasticity.ipynb test.py demo_hyperelasticity.py.rst unitsquare_32_32.xml.gz demo_maxwell-eigenvalues.ipynb unitsquare_32_32_c00.xml.gz demo_maxwell-eigenvalues.py.rst unitsquare_32_32_c01.xml.gz demo_nonlinear-poisson.ipynb unitsquare_32_32_c11.xml.gz
import nbformat
nb = nbformat.read('demo_maxwell-eigenvalues.ipynb', as_version=4)
for cell in nb.cells:
print(cell.cell_type)
print(' %s...' % cell.source.splitlines()[0])
markdown
Stable and unstable finite elements for the Maxwell eigenvalue problem...
code
diagonal mesh...
markdown
Note that the eigenvalues calculated using the Nédélec elements are all...
code
crossed mesh...
markdown
Again the Nédélec elements are accurate. The Lagrange elements also...
code
from dolfin import *...
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Specifying matplotlib as backend:...
code
%matplotlib inline...
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**Function eigenvalues.** The function `eigenvalues` takes the finite...
code
def eigenvalues(V, bcs):...
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We start by defining the bilinear forms on the right- and left-hand...
code
#...
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Next we assemble the bilinear forms `a` and `b` into PETSc matrices `A`...
code
#...
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We zero out the rows of $B$ corresponding to constrained boundary...
code
#...
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Now we solve the generalized matrix eigenvalue problem using the SLEPc...
code
#...
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We specify that we want 12 eigenvalues nearest in magnitude to a target...
code
#...
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Finally we collect the computed eigenvalues in list which we convert to...
code
#...
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**Function print\_eigenvalues.** Given just a mesh, the function...
code
def print_eigenvalues(mesh):...
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First we define the Nédélec edge element space and the essential...
code
#...
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Then we do the same for the vector Lagrange elements. Since the Lagrange...
code
#...
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The true eigenvalues are just the 12 smallest numbers of the form...
code
#...
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Finally we print the results:...
code
#...
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**Calling the functions.** To complete the program, we call...
code
mesh = RectangleMesh(Point(0, 0), Point(pi, pi), 40, 40)...
cell3 = nb.cells[3]
cell3
{'cell_type': 'code',
'execution_count': None,
'metadata': {'attributes': {'classes': ['sourceCode', 'none'], 'id': ''}},
'outputs': [],
'source': 'crossed mesh\nNédélec: [ 1.00 1.00 2.00 4.00 4.00 5.00 5.00 7.99 9.00 9.00 10.00 10.00]\nLagrange: [ 1.00 1.00 2.00 4.00 4.00 5.00 5.00 6.00 8.01 9.01 9.01 10.02]\nExact: [ 1.00 1.00 2.00 4.00 4.00 5.00 5.00 8.00 9.00 9.00 10.00 10.00]'}
cell3.metadata.attributes.classes
['sourceCode', 'none']
cell1 = nb.cells[1]
new_source = '\n'.join(['```', cell1.source, '````'])
new_cell = nbformat.v4.new_markdown_cell(new_source)
nb.cells[1] = new_cell
new_cell
{'cell_type': 'markdown',
'metadata': {},
'source': '```\ndiagonal mesh\nNédélec: [ 1.00 1.00 2.00 4.00 4.00 5.00 5.00 8.01 8.98 8.99 9.99 9.99]\nLagrange: [ 5.16 5.26 5.26 5.30 5.39 5.45 5.53 5.61 5.61 5.62 5.71 5.73]\nExact: [ 1.00 1.00 2.00 4.00 4.00 5.00 5.00 8.00 9.00 9.00 10.00 10.00]\n````'}
nbformat.write(nb, 'demo_maxwell-eigenvalues.ipynb')
md =
nbformat.v4.new_markdown_cell('some markdown')
{'cell_type': 'markdown', 'metadata': {}, 'source': 'some markdown'}