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Add plots, remove extra changes #20

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Add plots, remove extra changes #20

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42cff1a
Add solution plots to poisson solver notebook
anushkasinghh Mar 10, 2025
92be763
Add solution plotting function
anushkasinghh Mar 11, 2025
269fc63
Merge pull request #1 from anushkasinghh/anushka
anushkasinghh Mar 11, 2025
b5792df
Reverting incorrect changes
Mar 11, 2025
169331d
cleaned nb
Mar 12, 2025
4ccca1f
Merge branch 'pyccel:master' into anushka
anushkasinghh Mar 13, 2025
2698e29
nan
Mar 13, 2025
464d966
nan
Mar 13, 2025
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100 changes: 99 additions & 1 deletion chapter1/poisson.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -257,7 +257,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "d829e410",
"id": "827c3e69-77ac-4312-a4dd-a1c26a40b27c",
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I think that this id can be changed by hand to its original value using a text editor (or from the GitHub web interface). If it causes a problem, our CI build will spot it.

"metadata": {},
"outputs": [],
"source": [
Expand All @@ -273,6 +273,104 @@
"# print the result\n",
"print(h1_error)"
]
},
{
"cell_type": "markdown",
"id": "14d92a71-8c0f-4a91-8f56-c405f3fc76d1",
"metadata": {},
"source": [
"### Visualization\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2a33eab4-f4b8-428d-ae35-2d086d5645c3",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
"from sympy import lambdify\n",
"\n",
"def refine_array_1d(breaks, N):\n",
" \"\"\"Refine a 1D array by inserting N points between each pair of original values.\"\"\"\n",
" refined = np.concatenate([np.linspace(breaks[i], breaks[i+1], N+1)[:-1] for i in range(len(breaks)-1)])\n",
" return np.append(refined, breaks[-1]) # Add the last point\n",
"\n",
"def plot_solutions(Vh, uh, phi_exact, N=10):\n",
" \"\"\"\n",
" Refine the grid, evaluate solutions, compute errors, and plot results.\n",
"\n",
" Parameters:\n",
" Vh: The finite element space (must have `spaces` attribute with `breaks`).\n",
" uh: The numerical solution function.\n",
" phi_exact: The exact solution function (callable).\n",
" N: Number of points to insert between breaks (default: 10).\n",
" \"\"\"\n",
" # Generate refined grid for visualization\n",
" eta1 = refine_array_1d(Vh.spaces[0].breaks, N)\n",
" eta2 = refine_array_1d(Vh.spaces[1].breaks, N)\n",
"\n",
" # Evaluate numerical solution on the refined grid\n",
" num = np.array([[uh(e1, e2) for e2 in eta2] for e1 in eta1])\n",
"\n",
" # Compute exact solution\n",
" ex = np.array([[phi_exact(e1, e2) for e2 in eta2] for e1 in eta1])\n",
" err = num - ex\n",
"\n",
" # Generate physical grid coordinates\n",
" xx, yy = np.meshgrid(eta1, eta2, indexing='ij')\n",
"\n",
" # Create figure with 3 subplots\n",
" fig, axes = plt.subplots(1, 3, figsize=(12.8, 4.8))\n",
"\n",
" def add_colorbar(im, ax):\n",
" \"\"\"Add a colorbar to the given axis.\"\"\"\n",
" divider = make_axes_locatable(ax)\n",
" cax = divider.append_axes(\"right\", size=0.2, pad=0.2)\n",
" cbar = ax.get_figure().colorbar(im, cax=cax)\n",
" return cbar\n",
"\n",
" # Plot exact solution\n",
" ax = axes[0]\n",
" im = ax.contourf(xx, yy, ex, 40, cmap='jet')\n",
" add_colorbar(im, ax)\n",
" ax.set_xlabel(r'$x$', rotation='horizontal')\n",
" ax.set_ylabel(r'$y$', rotation='horizontal')\n",
" ax.set_title(r'$\\phi_{exact}(x,y)$')\n",
" ax.set_aspect('equal')\n",
"\n",
" # Plot numerical solution\n",
" ax = axes[1]\n",
" im = ax.contourf(xx, yy, num, 40, cmap='jet')\n",
" add_colorbar(im, ax)\n",
" ax.set_xlabel(r'$x$', rotation='horizontal')\n",
" ax.set_ylabel(r'$y$', rotation='horizontal')\n",
" ax.set_title(r'$\\phi(x,y)$')\n",
" ax.set_aspect('equal')\n",
"\n",
" # Plot numerical error\n",
" ax = axes[2]\n",
" im = ax.contourf(xx, yy, err, 40, cmap='jet')\n",
" add_colorbar(im, ax)\n",
" ax.set_xlabel(r'$x$', rotation='horizontal')\n",
" ax.set_ylabel(r'$y$', rotation='horizontal')\n",
" ax.set_title(r'$\\phi(x,y) - \\phi_{exact}(x,y)$')\n",
" ax.set_aspect('equal')\n",
"\n",
" # Show figure\n",
" plt.tight_layout()\n",
" fig.show()\n",
"\n",
"# Define the exact solution as a symbolic expression (example: phi_exact = x^2 + y^2)\n",
"ue = sin(np.pi*x)*sin(np.pi*y)\n",
"\n",
Comment on lines +367 to +369
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ue was already defined in the section titled "Computing the L^2 norm", as it was needed to define the error norms. Please remove its definition from this place, and move the comment line (which is useful) to the previous definition.

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By the way, I have just realized that the same section redefines u, which was previously defined in the section titled "Formal Model". Could you please remove the second definition?

"# Convert the symbolic expression to a callable function using lambdify\n",
"phi_exact = lambdify((x, y), ue, 'numpy')\n",
"plot_solutions(Vh, uh, phi_exact, N=10)"
]
}
],
"metadata": {},
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