TP-equation-derivees-partie.../TP-EDP.ipynb
2022-04-03 22:42:26 +02:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 134,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {},
"outputs": [],
"source": [
"def maillage_carre(n: int):\n",
" \"\"\"\n",
" Une discrétisation possible d'une EDP elliptique sur le domaine ]0,1[ x ]0,1[.\n",
" Le carre [0,1]x[0,1] est maille uniquement avec des triangles.\n",
" Les conditions limites sont de type Dirichlet uniquement -> `neumann=[]`.\n",
"\n",
" Args:\n",
" n: nombre de points par cote du care => Npts points de discretisation au total\n",
"\n",
" Returns:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" elements3: matrice a trois colonnes. Chaque ligne contient les indices des sommets d'un element triangle, dans le sens antihoraire.\n",
" dirichlet: vecteur colonne des indices des sommets de la frontiere de Dirichlet.\n",
" neumann: matrice a deux colonnes. Chaque ligne contient les indices des deux sommets d'une arete de la frontiere de Neumann. (neumann est vide sur cet exemple)\n",
" \"\"\"\n",
"\n",
" h = 1 / (n - 1)\n",
" n_pts = n * n\n",
" n_elm = 2 * (n - 1) * (n - 1)\n",
" coordinates = np.zeros((n_pts, 2))\n",
" elements3 = np.zeros((n_elm, 3), dtype=int)\n",
" neumann = []\n",
" dirichlet = np.zeros((4 * n - 4, 1), dtype=int)\n",
"\n",
" # Coordonnees et connectivites :\n",
" e = -1\n",
" p = -1\n",
" x = np.zeros((n + 1, 1))\n",
" x[n, 0] = 1.0\n",
"\n",
" for l in range(n + 1):\n",
" x[l, 0] = l * h\n",
"\n",
" for j in range(n):\n",
" for i in range(n):\n",
" p = p + 1\n",
" coordinates[p, 0] = x[i, 0]\n",
" coordinates[p, 1] = x[j, 0]\n",
" if (i != n - 1) & (j != n - 1):\n",
" p1 = p\n",
" p2 = p1 + 1\n",
" p3 = p1 + n\n",
" p4 = p2 + n\n",
" e = e + 1\n",
" elements3[e, 0] = p1\n",
" elements3[e, 1] = p2\n",
" elements3[e, 2] = p3\n",
" e = e + 1\n",
" elements3[e, 0] = p4\n",
" elements3[e, 1] = p3\n",
" elements3[e, 2] = p2\n",
"\n",
" # Liste des sommets de la frontiere de Dirichlet:\n",
" p = -1\n",
" for j in range(n):\n",
" p = p + 1\n",
" dirichlet[p, 0] = j\n",
"\n",
" for j in range(n * 2 - 1, n * (n - 1), n):\n",
" p = p + 1\n",
" dirichlet[p, 0] = j\n",
"\n",
" for j in range(n * n - 1, n * n - n - 1, -1):\n",
" p = p + 1\n",
" dirichlet[p, 0] = j\n",
"\n",
" for j in range(n * n - 2 * n, n - 1, -n):\n",
" p = p + 1\n",
" dirichlet[p, 0] = j\n",
"\n",
" return coordinates, elements3, dirichlet, neumann\n"
]
},
{
"cell_type": "code",
"execution_count": 136,
"metadata": {},
"outputs": [],
"source": [
"def show(coordinates, u, title) -> None:\n",
" \"\"\"Fonction d'affichage de la solution u sur le maillage defini par elements3, coordinates.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" u: vecteur colonne de longueur egale au nombre de lignes de coordinates contenant les valeurs de la solution a afficher aux points de la discretisation.\n",
" title: le titre de la figure\n",
"\n",
" Returns:\n",
" None, plots a figure\n",
" \"\"\"\n",
"\n",
" ax = plt.figure().add_subplot(projection=\"3d\")\n",
" ax.plot_trisurf(\n",
" coordinates[:, 0], coordinates[:, 1], u, linewidth=0.2, antialiased=True\n",
" )\n",
" plt.title(title)\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Partie I : maillage triangulaire et conditions de Dirichlet\n",
"\n",
"$$\n",
"\\left\\{\n",
"\\begin{array}{rll}\n",
"\n",
"\\displaystyle -\\delta u (x, y) &= f(x, y) &\\text{sur } \\Omega \\\\\n",
"\\displaystyle u (x, y) &= u_d(x, y) &\\text{sur } \\partial\\Omega_d \\\\\n",
"\\displaystyle \\frac{\\partial u (x, y)}{\\partial n} &= g(x, y) &\\text{sur } \\partial\\Omega_n\n",
"\n",
"\\end{array}\n",
"\\right.\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": 137,
"metadata": {},
"outputs": [],
"source": [
"def f(x, y) -> np.ndarray:\n",
" return 2 * np.pi ** 2 * np.sin(np.pi * x) * np.sin(np.pi * y)\n",
"\n",
"\n",
"def u_ex(x, y) -> np.ndarray:\n",
" return np.sin(np.pi * x) * np.sin(np.pi * y)\n",
"\n",
"\n",
"def u_d(x, y) -> np.ndarray:\n",
" return np.zeros(x.shape[0])"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"coords = [[0. 0. ]\n",
" [0.5 0. ]\n",
" [1. 0. ]\n",
" [0. 0.5]\n",
" [0.5 0.5]\n",
" [1. 0.5]\n",
" [0. 1. ]\n",
" [0.5 1. ]\n",
" [1. 1. ]]\n",
"\n",
"elems3 = [[0 1 3]\n",
" [4 3 1]\n",
" [1 2 4]\n",
" [5 4 2]\n",
" [3 4 6]\n",
" [7 6 4]\n",
" [4 5 7]\n",
" [8 7 5]]\n",
"\n",
"dirichlet = [[0]\n",
" [1]\n",
" [2]\n",
" [5]\n",
" [8]\n",
" [7]\n",
" [6]\n",
" [3]]\n",
"\n",
"neumman = []\n"
]
}
],
"source": [
"# affichage d'un petit maillage\n",
"coords, elems3, dirichlet, neumann = maillage_carre(3)\n",
"print(\n",
" f\"coords = {coords}\",\n",
" f\"elems3 = {elems3}\",\n",
" f\"dirichlet = {dirichlet}\",\n",
" f\"neumman = {neumann}\",\n",
" sep=\"\\n\\n\"\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 139,
"metadata": {},
"outputs": [],
"source": [
"def calcul_alpha(x, y) -> float:\n",
" \"\"\"Calcul du coefficient alpha.\n",
"\n",
" Args:\n",
" x (np.array): les coordonnées x du triangle.\n",
" y (np.array): les coordonnées y du triangle.\n",
"\n",
" Returns:\n",
" alpha: le coefficient alpha.\n",
" \"\"\"\n",
" mat_alpha = np.array(\n",
" [\n",
" [x[1] - x[0], x[2] - x[0]],\n",
" [y[1] - y[0], y[2] - y[0]]\n",
" ]\n",
" )\n",
"\n",
" return np.linalg.det(mat_alpha)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$[M^A_T]_{ij} = \\displaystyle \\int_T \\nabla \\eta_i (x, y)^\\top \\eta_j (x, y) \\ dx \\ dy$$"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1. , -0.5, -0.5],\n",
" [-0.5, 0.5, 0. ],\n",
" [-0.5, 0. , 0.5]])"
]
},
"execution_count": 140,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def raideur(triangle) -> np.ndarray:\n",
" \"\"\"Construction de la matrice de raideur ́elementaire relative à un ́élément triangle.\n",
"\n",
" Args:\n",
" triangle: les coordonnées x et y des trois points formant le triangle.\n",
"\n",
" Returns:\n",
" M: La matrice de raideur ́elementaire.\n",
" \"\"\"\n",
" M = np.zeros((3, 3))\n",
" x = triangle[:, 0]\n",
" y = triangle[:, 1]\n",
"\n",
" alpha = calcul_alpha(x, y)\n",
"\n",
" # calcul de la matrice M\n",
" for i in range(3):\n",
" grad_eta_i = np.array(\n",
" [\n",
" y[(i+1)%3] - y[(i+2)%3],\n",
" x[(i+2)%3] - x[(i+1)%3]\n",
" ]\n",
" )\n",
" for j in range(3):\n",
" grad_eta_j = np.array(\n",
" [\n",
" y[(j+1)%3] - y[(j+2)%3],\n",
" x[(j+2)%3] - x[(j+1)%3]\n",
" ]\n",
" )\n",
"\n",
" M[i, j] = np.dot(grad_eta_i, grad_eta_j)\n",
"\n",
" return M / alpha / 2\n",
"\n",
"# on affiche la première matrice de raideur pour vérifier\n",
"raideur(coords[elems3[0]])"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {},
"outputs": [],
"source": [
"def assemblage(coordinates, elements3) -> np.ndarray:\n",
" \"\"\"Assemblage de la matrice A dans le cas d'un maillage constitué uniquement d'éléments triangles.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" elements3: matrice a trois colonnes. Chaque ligne contient les indices des sommets d'un element triangle, dans le sens antihoraire.\n",
"\n",
" Returns:\n",
" A: matrice nécéssaire à la résolution de la formulation variationnelle du problème.\n",
" \"\"\"\n",
" Ns = len(coordinates)\n",
" A = np.zeros((Ns, Ns))\n",
"\n",
" for triangle in elements3:\n",
" M = raideur(coordinates[triangle])\n",
" for i, a in enumerate(triangle):\n",
" for j, b in enumerate(triangle):\n",
" A[a, b] += M[i, j]\n",
" \n",
" return A"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {},
"outputs": [],
"source": [
"def second_membre(coordinates, elements3) -> np.ndarray:\n",
" \"\"\"Calcul le second membre.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" elements3: matrice a trois colonnes. Chaque ligne contient les indices des sommets d'un element triangle, dans le sens antihoraire.\n",
"\n",
" Returns:\n",
" b: vecteur b nécéssaire à la résolution de la formulation variationnelle du problème, sans les conditions de Dirichlet.\n",
" \"\"\"\n",
" Ns = len(coordinates)\n",
" b = np.zeros(Ns)\n",
" for triangle in elements3:\n",
" coords_triangle = coordinates[triangle]\n",
" centre = np.mean(coords_triangle, 0)\n",
" x = coords_triangle[:, 0]\n",
" y = coords_triangle[:, 1]\n",
"\n",
" alpha = calcul_alpha(x, y)\n",
"\n",
" # approximation pour la quadrature du second membre\n",
" b[triangle] += alpha / 6 * f(centre[0], centre[1])\n",
"\n",
" return b"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {},
"outputs": [],
"source": [
"def calcul_Ud(coords, dirichlet) -> np.ndarray:\n",
" \"\"\"Calcul le vecteur Ud nécéssaire à l'application des conditions de Dirichlet.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" dirichlet: vecteur colonne des indices des sommets de la frontiere de Dirichlet.\n",
"\n",
" Returns:\n",
" Ud: vecteur pour appliquer les conditions de Dirichlet.\n",
" \"\"\"\n",
" Ns = len(coords)\n",
" U = np.zeros(Ns)\n",
"\n",
" U[dirichlet.T] = u_d(coords[dirichlet, 0], coords[dirichlet, 1])\n",
"\n",
" return U"
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {},
"outputs": [],
"source": [
"def tildage(A, b, coordinates, dirichlet):\n",
" \"\"\"Permet de retirer les parties de A et b soumis au conditions de Dirichlet, nécéssaire avant la résolution numérique.\n",
"\n",
" Args:\n",
" A: La matrice A de la résolution numérique.\n",
" b: Le vecteur b de la résolution numérique.\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" dirichlet: vecteur colonne des indices des sommets de la frontiere de Dirichlet.\n",
"\n",
" Returns:\n",
" A: La matrice A de la résolution numérique tildée.\n",
" b: Le vecteur b de la résolution numérique tildé.\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation non soumis ausx conditions de Dirichlet. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" \"\"\"\n",
" A_tild = np.delete(A, dirichlet, 0)\n",
" A_tild = np.delete(A_tild, dirichlet, 1)\n",
" \n",
" b_tild = np.delete(b, dirichlet, 0)\n",
" \n",
" coords_tild = np.delete(coordinates, dirichlet, 0)\n",
"\n",
" return A_tild, b_tild, coords_tild"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {},
"outputs": [],
"source": [
"def untildage(x, dirichlet, U_d) -> np.ndarray:\n",
" \"\"\"Opération inverse de la fonction tildage, place dans le vecteur x aux coordonnées de dirichlet les valeurs des conditions\n",
"\n",
" Args:\n",
" x: le vecteur solution trouvé après résolution.\n",
" dirichlet: vecteur colonne des indices des sommets de la frontiere de Dirichlet.\n",
" Ud: vecteur pour appliquer les conditions de Dirichlet.\n",
"\n",
" Returns:\n",
" x: le vecteur solution complet, avec les conditions aux bords.\n",
" \"\"\"\n",
" x_untild = np.zeros(U_d.shape[0])\n",
" not_dirichlet = np.setdiff1d(range(U_d.shape[0]), dirichlet)\n",
"\n",
" x_untild[dirichlet] = U_d[dirichlet]\n",
" x_untild[not_dirichlet] = x\n",
"\n",
" return x_untild"
]
},
{
"cell_type": "code",
"execution_count": 146,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"n = 50\n",
"coords, elems3, dirichlet, neumann = maillage_carre(n)\n",
"\n",
"# calcul du premier membre de l'équation\n",
"A = assemblage(coords, elems3)\n",
"\n",
"# calcul du second membre de l'équation\n",
"b = second_membre(coords, elems3)\n",
"\n",
"# calcul du vecteur des conditions de dirichlet\n",
"U_d = calcul_Ud(coords, dirichlet)\n",
"\n",
"# on modifie b pour vérifier les conditions \n",
"b -= np.dot(A, U_d)\n",
"\n",
"# on enlève les conditions aux bords avant résolution\n",
"A_tild, b_tild, coords_tild = tildage(A, b, coords, dirichlet)\n",
"\n",
"# on résoud le système\n",
"x = np.linalg.solve(A_tild, b_tild)\n",
"\n",
"# on remet les conditions aux bords\n",
"x_untild = untildage(x, dirichlet, U_d)\n",
"\n",
"# on affiche le résultat\n",
"show(coords, x_untild, \"solution calculée\")\n",
"\n",
"# on compare avec le résultat théorique exacte\n",
"show(coords, u_ex(coords[:, 0], coords[:, 1]), \"résultat théorique\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Partie II : maillage mixte et ajoût des conditions de Neumann\n"
]
},
{
"cell_type": "code",
"execution_count": 147,
"metadata": {},
"outputs": [],
"source": [
"def f(x, y) -> int:\n",
" return 1\n",
"\n",
"\n",
"def u_d(x, y) -> int:\n",
" return 1\n",
"\n",
"\n",
"def g(x) -> int:\n",
" return 1"
]
},
{
"cell_type": "code",
"execution_count": 148,
"metadata": {},
"outputs": [],
"source": [
"# Création d'un maillage mixte\n",
"\n",
"e3 = np.array(\n",
" [[1, 2, 12], [2, 3, 12], [3, 4, 14], [4, 5, 14], [2, 15, 3], [3, 15, 4]]\n",
").astype(int)\n",
"\n",
"e4 = np.array(\n",
" [\n",
" [0, 1, 12, 11],\n",
" [11, 12, 13, 10],\n",
" [12, 3, 14, 13],\n",
" [10, 13, 8, 9],\n",
" [13, 14, 7, 8],\n",
" [14, 5, 6, 7],\n",
" ]\n",
").astype(int)\n",
"\n",
"dds = np.array([2, 15, 4, 6, 7, 8, 9, 10, 11, 0]).astype(int)\n",
"\n",
"nns = np.array([[4, 5], [5, 6], [0, 1], [1, 2]]).astype(int)\n",
"\n",
"ccs = np.array(\n",
" [\n",
" [0, 0],\n",
" [1 / 3, 0],\n",
" [16 / 30, 0],\n",
" [2 / 3, 1 / 3],\n",
" [1, 14 / 30],\n",
" [1, 2 / 3],\n",
" [1, 1],\n",
" [2 / 3, 1],\n",
" [1 / 3, 1],\n",
" [0, 1],\n",
" [0, 2 / 3],\n",
" [0, 1 / 3],\n",
" [1 / 3, 1 / 3],\n",
" [1 / 3, 2 / 3],\n",
" [2 / 3, 2 / 3],\n",
" [1, 0],\n",
" ]\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 149,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.66666667, -0.16666667, -0.33333333, -0.16666667],\n",
" [-0.16666667, 0.66666667, -0.16666667, -0.33333333],\n",
" [-0.33333333, -0.16666667, 0.66666667, -0.16666667],\n",
" [-0.16666667, -0.33333333, -0.16666667, 0.66666667]])"
]
},
"execution_count": 149,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def raideur_quadrangle(quadrangle) -> np.ndarray:\n",
" \"\"\"Construction de la matrice de raideur ́elementaire relative à un ́élément quadrangle.\n",
"\n",
" Args:\n",
" quadrangle: les coordonnées x et y des quatres points formant le quadrangle.\n",
"\n",
" Returns:\n",
" M: La matrice de raideur ́elementaire.\n",
" \"\"\"\n",
" x = quadrangle[:, 0]\n",
" y = quadrangle[:, 1]\n",
"\n",
" # calcul de la jacobienne et de son déterminant\n",
" J_kk = np.array([[x[1] - x[0], x[3] - x[0]], [y[1] - y[0], y[3] - y[0]]])\n",
" det_J_kk = np.linalg.det(J_kk)\n",
"\n",
" # on récupère les coefficients\n",
" coeffs = np.linalg.inv(np.matmul(J_kk.T, J_kk))\n",
" a = coeffs[0, 0]\n",
" b = coeffs[0, 1]\n",
" c = coeffs[1, 1]\n",
"\n",
" # on calcul M (on a calculé toutes les intégrales au préalable)\n",
" M = np.array(\n",
" [\n",
" [2 * a + 3 * b + 2 * c, -2 * a + c, -a - 3 * b - c, a - 2 * c],\n",
" [-2 * a + c, 2 * a - 3 * b + 2 * c, a - 2 * c, -a + 3 * b - c],\n",
" [-a - 3 * b - c, a - 2 * c, 2 * a + 3 * b + 2 * c, -2 * a + c],\n",
" [a - 2 * c, -a + 3 * b - c, -2 * a + c, 2 * a - 3 * b + 2 * c],\n",
" ]\n",
" )\n",
"\n",
" return det_J_kk / 6 * M\n",
"\n",
"# on affiche la première matrice de raideur pour vérifier\n",
"raideur_quadrangle(ccs[e4[0]])"
]
},
{
"cell_type": "code",
"execution_count": 150,
"metadata": {},
"outputs": [],
"source": [
"def assemblage_quadrangle(coordinates, elements4) -> np.ndarray:\n",
" \"\"\"Assemblage de la matrice A dans le cas d'un maillage constitué uniquement d'éléments quadrangles.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" elements4: matrice a quatre colonnes. Chaque ligne contient les indices des sommets d'un element quadrangle, dans le sens antihoraire.\n",
"\n",
" Returns:\n",
" A: matrice nécéssaire à la résolution de la formulation variationnelle du problème.\n",
" \"\"\"\n",
" Ns = len(coordinates)\n",
" A = np.zeros((Ns, Ns))\n",
"\n",
" for quadrangle in elements4:\n",
" M = raideur_quadrangle(coordinates[quadrangle])\n",
" for i, a in enumerate(quadrangle):\n",
" for j, b in enumerate(quadrangle):\n",
" A[a, b] += M[i, j]\n",
" \n",
" return A"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {},
"outputs": [],
"source": [
"def second_membre_quadrangle(coordinates, elements4) -> np.ndarray:\n",
" \"\"\"Calcul le second membre.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" elements4: matrice a quatre colonnes. Chaque ligne contient les indices des sommets d'un element quadrangle, dans le sens antihoraire.\n",
"\n",
" Returns:\n",
" b: vecteur b nécéssaire à la résolution de la formulation variationnelle du problème, sans les conditions de Dirichlet.\n",
" \"\"\"\n",
" Ns = len(coordinates)\n",
" b = np.zeros(Ns)\n",
" for quadrangle in elements4:\n",
" coords_quadrangle = coordinates[quadrangle]\n",
" centre = np.mean(coords_quadrangle, 0)\n",
" x = coords_quadrangle[:, 0]\n",
" y = coords_quadrangle[:, 1]\n",
"\n",
" alpha = calcul_alpha(x, y)\n",
"\n",
" b[quadrangle] += alpha / 4 * f(centre[0], centre[1])\n",
"\n",
" return b"
]
},
{
"cell_type": "code",
"execution_count": 152,
"metadata": {},
"outputs": [],
"source": [
"def condition_neumann(coordinates, neumann) -> np.ndarray:\n",
" \"\"\"Calcul le vecteur nécéssaire à l'application des conditions de Neumann.\n",
"\n",
" Args:\n",
" coordinates: matrice a deux colonnes. Chaque ligne contient les coordonnes 2D d'un des points de la discretisation. Ces sommets seront identifies a l'indice de la ligne correspondante dans la matrice coordinates.\n",
" neumann: vecteur colonne des indices des sommets de la frontiere de Neumann.\n",
"\n",
" Returns:\n",
" Ud: vecteur pour appliquer les conditions de Neumann.\n",
" \"\"\"\n",
" Ns = len(coordinates)\n",
" coeffs = np.zeros(Ns)\n",
" for i, j in neumann:\n",
" point1 = coordinates[i]\n",
" point2 = coordinates[j]\n",
" \n",
" valeur = np.linalg.norm(point1 - point2) / 2 * g((point1 + point2) / 2)\n",
" coeffs[i] += valeur\n",
" coeffs[j] += valeur\n",
"\n",
" return coeffs"
]
},
{
"cell_type": "code",
"execution_count": 153,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# calcul de premier membre de l'équation\n",
"A3 = assemblage(ccs, e3)\n",
"A4 = assemblage_quadrangle(ccs, e4)\n",
"A = A3 + A4\n",
"\n",
"# calcul du second membre de l'équation\n",
"b3 = second_membre(ccs, e3)\n",
"b4 = second_membre_quadrangle(ccs, e4)\n",
"b = b3 + b4\n",
"\n",
"# calcul de Ud pour les conditions de Dirichlet\n",
"U_d = calcul_Ud(ccs, dds)\n",
"\n",
"# modifiction de b pour vérifier Dirichlet\n",
"b -= np.dot(A, U_d)\n",
"\n",
"# modification de b pour vérifier Neumann\n",
"b += condition_neumann(ccs, nns)\n",
"\n",
"# on enlève les conditions aux bords (Dirichlet) avant résolution\n",
"A_tild, b_tild, ccs_tild = tildage(A, b, ccs, dds)\n",
"\n",
"# on résoud le système\n",
"x = np.linalg.solve(A_tild, b_tild)\n",
"\n",
"# on remet les conditions aux bords (Dirichlet)\n",
"x_untild = untildage(x, dds, U_d)\n",
"\n",
"# on affiche le résultat\n",
"show(ccs, x_untild, \"résultat numérique\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Compléments d'analyse du système\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Analyse de lordre du schéma de discrétisation dans le cas d'éléments Triangle\n"
]
},
{
"cell_type": "code",
"execution_count": 154,
"metadata": {},
"outputs": [],
"source": [
"def f(x, y) -> np.ndarray:\n",
" return 2 * np.pi ** 2 * np.sin(np.pi * x) * np.sin(np.pi * y)\n",
"\n",
"\n",
"def u_ex(x, y) -> np.ndarray:\n",
" return np.sin(np.pi * x) * np.sin(np.pi * y)\n",
"\n",
"\n",
"def u_d(x, y) -> np.ndarray:\n",
" return np.zeros(x.shape[0])"
]
},
{
"cell_type": "code",
"execution_count": 155,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"98/98\r"
]
}
],
"source": [
"erreurs = []\n",
"hs = []\n",
"range_n = range(3, 100, 5)\n",
"\n",
"for n in range_n:\n",
" print(f\"{n}/{max(range_n)}\", end=\"\\r\")\n",
" coords, elems3, dirichlet, neumann = maillage_carre(n)\n",
"\n",
" A = assemblage(coords, elems3)\n",
" b = second_membre(coords, elems3)\n",
" U_d = calcul_Ud(coords, dirichlet)\n",
" b -= np.dot(A, U_d)\n",
"\n",
" A_tild, b_tild, coords_tild = tildage(A, b, coords, dirichlet)\n",
"\n",
" x = np.linalg.solve(A_tild, b_tild)\n",
" x_untild = untildage(x, dirichlet, U_d)\n",
" x_ex = u_ex(coords[:, 0], coords[:, 1])\n",
"\n",
" v = x_untild - x_ex\n",
" h = np.sqrt(1/len(v))\n",
" hs.append(h)\n",
" erreur = h * np.linalg.norm(v)\n",
" erreurs.append(erreur)"
]
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"regression linéaire: \n",
"2.078 x - 0.0363\n"
]
},
{
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"log_hs = np.log(hs)\n",
"log_erreurs = np.log(erreurs)\n",
"\n",
"# affichage des erreurs\n",
"plt.plot(log_hs, log_erreurs, label=\"numérique\")\n",
"\n",
"# regression linéaire\n",
"coeffs = np.polyfit(log_hs, log_erreurs, 1)\n",
"reg = np.poly1d(coeffs)\n",
"\n",
"# affichage de la regression linéaire\n",
"plt.plot(log_hs, reg(log_hs), alpha=0.5, label=\"regression\")\n",
"plt.xlabel(\"log(h)\")\n",
"plt.ylabel(\"log(erreur)\")\n",
"plt.grid()\n",
"plt.legend()\n",
"\n",
"print(f\"regression linéaire: {reg}\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On observe alors que l'on obtient un ordre de discrétisation d'environ 2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Résolution du système linéaire par une méthode directe\n"
]
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"98/98\r"
]
}
],
"source": [
"zeros_A = []\n",
"zeros_L = []\n",
"range_n = range(3, 100, 5)\n",
"\n",
"for n in range_n:\n",
" print(f\"{n}/{max(range_n)}\", end=\"\\r\")\n",
" coords, elems3, dirichlet, neumann = maillage_carre(n)\n",
"\n",
" A = assemblage(coords, elems3)\n",
"\n",
" A_tild = np.delete(A, dirichlet, 0)\n",
" A_tild = np.delete(A_tild, dirichlet, 1)\n",
"\n",
" L = np.linalg.cholesky(A_tild)\n",
"\n",
" zeros_A.append(len(np.where(A == 0)[0]))\n",
" zeros_L.append(len(np.where(L == 0)[0]))"
]
},
{
"cell_type": "code",
"execution_count": 158,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7faf9ef04850>"
]
},
"execution_count": 158,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(range_n, zeros_A, label=\"A\")\n",
"plt.plot(range_n, zeros_L, label=\"L\")\n",
"plt.xlabel(\"n\")\n",
"plt.ylabel(\"#zéros\")\n",
"plt.grid()\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On observe que la matrice L possède moins de zeros que la matrice A, il n'est donc pas bénéfique de l'utiliser pour gagner en espace mémoire lors d'un stockage creux (surtout pour n très grand)."
]
}
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