diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..625b81c --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1,3 @@ +{ + "jupyter.jupyterServerType": "local" +} \ No newline at end of file diff --git a/TP-EDP.ipynb b/TP-EDP.ipynb index 3dc669d..f6e2c5b 100644 --- a/TP-EDP.ipynb +++ b/TP-EDP.ipynb @@ -2,21 +2,17 @@ "cells": [ { "cell_type": "code", - "execution_count": 158, + "execution_count": 54, "metadata": {}, "outputs": [], "source": [ - "import matplotlib.pyplot as plt\n", - "import mpl_toolkits.mplot3d\n", "import numpy as np\n", - "import scipy.sparse as scps\n", - "import scipy.sparse.linalg as ssl\n", - "import math" + "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", - "execution_count": 159, + "execution_count": 55, "metadata": {}, "outputs": [], "source": [ @@ -27,13 +23,13 @@ " Les conditions limites sont de type Dirichlet uniquement -> `neumann=[]`.\n", "\n", " Args:\n", - " n (int): nombre de points par cote du care => Npts points de discretisation au total\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", + " 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", @@ -95,7 +91,7 @@ }, { "cell_type": "code", - "execution_count": 160, + "execution_count": 56, "metadata": {}, "outputs": [], "source": [ @@ -103,9 +99,8 @@ " \"\"\"Fonction d'affichage de la solution u sur le maillage defini par elements3, coordinates.\n", "\n", " Args:\n", - " elements3 : matrice a trois colonnes contenant les elements triangles de la discretisation, identifies par les indices de leurs trois sommets.\n", - " coordinates : matrice a deux colonnes contenant les coordonnes 2D des points de la discretisation.\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", + " 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", "\n", " Returns:\n", " None, plots a figure\n", @@ -122,21 +117,29 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "**Partie I : maillage triangulaire et conditions de Dirichlet**\n" + "## 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": 161, + "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "def f(x, y):\n", - " # return 2 * np.pi ** 2 * np.sin(np.pi * x) * np.sin(np.pi * y)\n", - " try:\n", - " return np.ones(x.shape[0])\n", - " except:\n", - " return 1\n", + " return 2 * np.pi ** 2 * np.sin(np.pi * x) * np.sin(np.pi * y)\n", "\n", "\n", "def u_ex(x, y):\n", @@ -144,62 +147,132 @@ "\n", "\n", "def u_d(x, y):\n", - " # return np.zeros(x.shape[0])\n", - " # return 1\n", - " return np.ones(x.shape[0])\n", - "\n", - "def g(x):\n", - " # return np.cos(x)\n", - " return 1" + " return np.zeros(x.shape[0])" ] }, { "cell_type": "code", - "execution_count": 162, + "execution_count": 58, "metadata": {}, "outputs": [ { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" + "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": [ - "n = 10\n", - "coords, elems3, dirichlet, neumann = maillage_carre(n)\n", - "show(coords, f(coords[:, 0], coords[:, 1]))\n", - "# show(coords, u_ex(coords[:, 0], coords[:, 1]))\n", - "# print(maillage_carre(3))" + "# 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": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "[M^A_T]_{ij} = \\displaystyle \\int_T \\nabla \\eta_i (x, y) \\eta_j (x, y) \\ dx \\ dy\n", + "$$\n" ] }, { "cell_type": "code", - "execution_count": 163, + "execution_count": 59, "metadata": {}, "outputs": [], "source": [ - "def raideur(triangle):\n", - " M = np.zeros((3, 3))\n", - " x = triangle[:, 0]\n", - " y = triangle[:, 1]\n", + "def calcul_alpha(x, y):\n", + " \"\"\"Calcul du coefficient alpha.\n", "\n", - " # calcul de alpha\n", + " Args:\n", + " x (np.array): les coordonnées x du triangle.\n", + " y (np.array): les coordonnées y du triangle.\n", + "\n", + " Returns:\n", + " float: 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", - " alpha = np.linalg.det(mat_alpha)\n", "\n", + " return np.linalg.det(mat_alpha)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "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": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def raideur(triangle):\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", @@ -217,17 +290,160 @@ "\n", " M[i, j] = np.dot(grad_eta_i, grad_eta_j)\n", "\n", - " return M / alpha / 2" + " 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": 164, + "execution_count": 61, + "metadata": {}, + "outputs": [], + "source": [ + "def assemblage(coordinates, elements3):\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": 62, + "metadata": {}, + "outputs": [], + "source": [ + "def second_membre(coordinates, elements3):\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": 63, + "metadata": {}, + "outputs": [], + "source": [ + "def calcul_Ud(coords, dirichlet):\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": 64, + "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": 65, + "metadata": {}, + "outputs": [], + "source": [ + "def untildage(x, dirichlet, U_d):\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": 66, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -251,86 +467,34 @@ } ], "source": [ - "def assemblage(coords, elems3):\n", - " Ns = len(coords)\n", - " A = np.zeros((Ns, Ns))\n", - " for triangle in elems3:\n", - " M = raideur(coords[triangle])\n", - " for i, a in enumerate(triangle):\n", - " for j, b in enumerate(triangle):\n", - " A[a, b] += M[i, j]\n", - " return A\n", - "\n", - "\n", - "def second_membre(coords, elem3, f):\n", - " Ns = len(coords)\n", - " b = np.zeros(Ns)\n", - " for triangle in elem3:\n", - " coords_triangle = coords[triangle]\n", - " centre = np.mean(coords_triangle, 0)\n", - "\n", - " # calcul de alpha\n", - " x = coords_triangle[:, 0]\n", - " y = coords_triangle[:, 1]\n", - " mat_alpha = np.array([[x[1] - x[0], x[2] - x[0]], [y[1] - y[0], y[2] - y[0]]])\n", - " alpha = np.linalg.det(mat_alpha)\n", - "\n", - " b[triangle] += alpha / 6 * f(centre[0], centre[1])\n", - "\n", - " return b\n", - "\n", - "\n", - "def calcul_Ud(coords, dirichlet):\n", - " Ns = len(coords)\n", - " U = np.zeros(Ns)\n", - " # for d in dirichlet:\n", - " # x, y = coords[d].flatten()\n", - " # U[d] = u_d(x, y)\n", - " U[dirichlet.T] = u_d(coords[dirichlet, 0], coords[dirichlet, 1])\n", - "\n", - " return U\n", - "\n", - "\n", - "def tildage(A, b, coords, dirichlet):\n", - " A_tild = np.delete(A, dirichlet, 0)\n", - " A_tild = np.delete(A_tild, dirichlet, 1)\n", - " b_tild = np.delete(b, dirichlet, 0)\n", - " coords_tild = np.delete(coords, dirichlet, 0)\n", - "\n", - " return A_tild, b_tild, coords_tild\n", - "\n", - "\n", - "def untildage(x, dirichlet, U_d):\n", - " x_untild = np.zeros(U_d.shape[0])\n", - " not_dirichlet = np.setdiff1d(range(U_d.shape[0]), dirichlet)\n", - "\n", - " # print(x_untild)\n", - " # print(not_dirichlet)\n", - " # print(dirichlet)\n", - " # print(x)\n", - "\n", - " x_untild[dirichlet] = U_d[dirichlet]\n", - " x_untild[not_dirichlet] = x\n", - "\n", - " return x_untild\n", - "\n", "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", - "b = second_membre(coords, elems3, f)\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", - "# show(coords_tild, x)\n", - "# print(coords.shape, x_untild.shape)\n", - "# print(coords, x_untild)\n", + "# on affiche le résultat\n", "show(coords, x_untild)\n", + "\n", + "# on compare avec le résultat théorique exacte\n", "show(coords, u_ex(coords[:, 0], coords[:, 1]))" ] }, @@ -338,12 +502,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "**Partie II : maillage mixte et ajoût des conditions de Neumann**\n" + "## Partie II : maillage mixte et ajoût des conditions de Neumann\n" ] }, { "cell_type": "code", - "execution_count": 165, + "execution_count": 67, + "metadata": {}, + "outputs": [], + "source": [ + "def f(x, y):\n", + " return 1\n", + "\n", + "\n", + "def u_d(x, y):\n", + " return 1\n", + "\n", + "\n", + "def g(x):\n", + " return 1" + ] + }, + { + "cell_type": "code", + "execution_count": 68, "metadata": {}, "outputs": [], "source": [ @@ -368,29 +550,29 @@ "\n", "ccs = np.array(\n", " [\n", - " [0.0, 0.0],\n", + " [0, 0],\n", " [1 / 3, 0],\n", - " [0.53333333333333, 0.0],\n", + " [16 / 30, 0],\n", " [2 / 3, 1 / 3],\n", - " [1.0, 0.47],\n", + " [1, 14 / 30],\n", " [1, 2 / 3],\n", - " [1.0, 1.0],\n", - " [2 / 3, 1.0],\n", - " [1 / 3, 1.0],\n", - " [0.0, 1.0],\n", - " [0.0, 2 / 3],\n", - " [0.0, 1 / 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, 0.0],\n", + " [1, 0],\n", " ]\n", ")" ] }, { "cell_type": "code", - "execution_count": 166, + "execution_count": 69, "metadata": {}, "outputs": [ { @@ -402,19 +584,26 @@ " [-0.16666667, -0.33333333, -0.16666667, 0.66666667]])" ] }, - "execution_count": 166, + "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def raideur_quadrangle(quadrangle):\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\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", - "\n", " det_J_kk = np.linalg.det(J_kk)\n", "\n", " # on récupère les coefficients\n", @@ -435,26 +624,106 @@ "\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": 167, + "execution_count": 70, + "metadata": {}, + "outputs": [], + "source": [ + "def assemblage_quadrangle(coordinates, elements4):\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": 71, + "metadata": {}, + "outputs": [], + "source": [ + "def second_membre_quadrangle(coordinates, elements4):\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": 72, + "metadata": {}, + "outputs": [], + "source": [ + "def condition_neumann(coordinates, neumann):\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": 73, "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[-0.30555556 1.63888889 -1.67777778 2.11685185 -1.69356874 1.65116133\n", - " -0.30555556 -0.94444444 -0.61111111 -0.30555556 -0.61111111 -0.94444444\n", - " 1.31296296 1.77777778 1.31777778 -0.35296296]\n" - ] - }, { "data": { - 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oFDMyzdz9/hZLHN0dP3jmE/5eM4zVZOJkj4aiAHdcFkWRhIQE0tLSZjn27r77bioqKjhw4ABXXHEF27Ztc+lk3LFjB+3t7Z6uoQbUgiBcFoh7DpjQRVHEYDAELDbuj/i6u7vR6/Vs377dp7HD/grdlnSj0Wi85scvxkIYuVxuN+Nh2sy35ZVrtVr7vjQxMZHw8PAZr12MK7rBZGH/79+iccSKIMiwmo3UdQe+E5DzHt3Rsfe3v/2NXbt2UVRUxGOPPcb69euJjY0N9C2IwD8FQRCB/yeK4v96e0HAhO5paEKwC1RswxMAYmNjfc6C8kfooijaxyBv3rzZ62q0GFZ0b9h6v6enp8/Yl548eRKTyWQ3TxejM65jcJyr/vA+E5bTH2nRbKSmczAQtzcDb/dqMBj4yle+wo033hjwa5/iU6Io9giCkAq8KQjCSVEU/+XpBQE13V0JxvY1X8M8UoXuPDzh+PHjPsfffRW6VqtlcnLSoyffmcW4onvCk5k/NDRk/xl7M/OlMpeHxxuVHXz7uUqsspkTZUWzgfquCSxWK/IAevS93auvnz8/rt9z6v9qQRBeBLYC8yd0V9gEGwyhuxqeEOwhDn19fbS1tRERESFZ5HBmrOiecDTzbcU44eHhksx8Kfi7oj/40gkeP9YPstljo0WTgSnRSmP3EGtypE/v8Ya3xKxgIghCFCATRVF76u+XAD/29rqgC12hUGA2m33OLZbL5W47ulosFrs56Tw8wR8nnpTwmmMX2K1bt3L06FGfr7HYxDsXFAqFWzPfaDTO8OZLWd18XdEtFivXPvwOFf1GBBcPCNFiBnH6d1rW3BNQoXtDio/qS1/6Eu+99x5DQ0MIgtAN/BcQBiCK4iOCIKQDx4FYwCoIwjeBtUAy8OKp8yuAp0RRPOztngIqdFdvzl/vuVwux2AwzPq6rSOruzBWMDrBGgwGKisrSU5OZvXq1fZf5FwLYdy9drE/FJzftyczv729HZlMZl/t3Zn5vvws+0cm+eLv32HEpHAfGTAb7X8va+7hyxfNPcxmP7eEds/eePrppx3/OWtgnyiK/a6+DowDG71ewIl5M919xVXCTH9/P62traxbt464uDi3rwuk0G1FMKtWrZpRr26zAqRuSRZavIHuMOPpfM7efKPRaG//7GjmO/aFk2q6f1DfzR1PlmEWZpvqM+7RfHqRKG/plfK2JOGtW63RaCQszPO9LQTzYrr7u6LbXudoNpeWlnr8QfqTUedK6LbMut7e3llFMOC7cM/0PfpcUCqVM8z8qakpe5aZwWAgPj4eg8Hg9ff20OEqHv6g0+V+3BnHFb1jYISh8UmSY+deI34m1qLDIjfdLRYLOp2Oqqoq0tLS7Gazt9f5s6I7+gMsFgu1tbXIZDJKS0td/mKDVfEWDBZTKylBEIiKiiIqKoply5ZhtVoZGxtjcHCQ2traGe2hYmNj7T+3Wx59n486pxBk0iwoq3nmtq+ipZdPF6/0654dORPz3GGeTHez2ezX66ampigrK2Pt2rX2FkvemKvpPjU1RWVlJdnZ2R5LDQOxorsTzGJf0QMZR5fJZCQkJBAeHs6mTZuwWCz2vu8NDQ2YhTDue72TIZPSp2s6rugA5c3zJ/SzfkV3hT8rutVqpaOjg4mJCc477zyfPPb+TmsRRZHBwUEaGxspKipy6wOw4Wt+vLN4e3t76evrIzExkaSkJCIiIua9gYS/BDPX3bGKrKx1gK//+ROMgu/dYESnFb2suScg93kmDm+AeTDdFQoFRqPRxdGusQ1PiIuLIyYmxuewnD97dEEQGBoaoqNXjU4e41Xkttf4Y7o7+htWrFjB2NgYLS0t6HQ6e+aZSqVa9Ct6MM7p+Pl57L16fvZmM8j8ELnVDNaZn4Gqtj5MZgthirnV55+JteiwyEx3x+EJMTExlJeX+3w9X013k8lEa2srAH1iHN//9eMIMjm7t6/z+Dp/THeTycSJEydITExk1apVmEwmoqOjycrKsu9VNRoNw8PDGI1GOjo6FqxdlDeCcT+2n+ndf/uQfzZpEWT+fTydzXYAvdHMye5B1udJT3JyhZSe7otxRQ/6+EopprsoijQ1NdHW1saWLVvss7j8DctJFbpWq+XYsWOkpKQQGxfHB3XdmFHw1R//kXfKGgJ2HZgOuzQ2NpKbm8uKFStcxv8TEhJYsWIFRUVFdmums7OTo0ePUldXx8DAgM9joYNBMEx3gAm9kd0/O8ybzRNzOr8roQOUNc3dfD9TnXFBF7q38JrBYOD48eMAMyrA/HVISX1A9Pb2Ul1dzYYNG0hOTqa8a4zRCR0yVRRWi5lr/8/v+XdNi9vX+3J//f39DA4OkpeXZ29I6QnhVOPMjIwM1q1bx9atW8nOzrYnC504cYK2tjbGxsYWxMQPhtA7NDoueOAwnRNzP5domp1oBfBBZeOcR16fqUKfl/CaO9Pd1gDBORnF3bmk4G2ltVqt9jRNW/rs+Pg4r9UOotMbEJQRIAhYzCau+u5veOkX32bL6lyX15GSIdXc3Mz4+Lh9vpg/CIJAbGwssbGx5OfnYzKZ0Gg09Pb2cvLkSaKiokhKSlqUPeClcPCTZv7rX6OS4uNScLein+zR2Ke4RkRE2JN2PHUfckaKM07Kw3y+WRCvuyiKtLW1MTQ0xObNm/0qgnCHJ6Hr9XoqKytJTU1lzZo19oeJelzPsc5xkhTG6dVUGYnVMInZZOTz3/kVr/76O2xYkTXjXN6ccWazmaqqKqKioigpKaGtrS1gCTNhYWF2z7Qtz3x4eJi6ujosFos9Dh0XFxeUSSWBXNFtTSKEAIkcZsfQbfSNTJCUsYzVq6PsU1ybm5vR6/XExcXZu8B6Ssjy1q12SXjdXV7AyXR3Hp4Q6A+iO9PdZj2sXr161lSWvx/vIEwG/SPTdqOgjATDJAAmg57L7/k5bz70PQqXnX5SexLj5OQklZWV5Ofnk5GR4fX4ueCYZ56bm4vZbGZ0dBS1Wk1TUxPh4eGIohjQlT4YTSICibsVHaC8uYddW1YRGRlJZGQk2dnZ9p7vGo2Grq4ugBlJO46fUSk93Zes6W4Tnq0FsuPwhEDjvKI79nN3ZT2YLFYOHu8gJUJOx9ipc6gisWhPH2PQ67jkrgd594/fIz8j2eV1bNgiB86dReYrBVahUJCcnExycjKiKKLT6WhsbKSnp4eenp6AtIKe6wPLVZOIQCFaLWB1H+Upa+5l15ZVM77m2PMdpiMxjq2fw8PD7bn7ZrP5jJu7BvPgjJPJZJjNZtrb22loaKCkpMQnkfv6oXIUoM18npycpLS01OUW4c2qLoa0eiLDTotWpooEZj609FOTXHzHg3QPjgKzxWjbjrS2trJly5ZZ7YMWIttNEAQiIyPte/uSkhKSkpLQaDSUlZVRUVFBV1cXk5OTPjeunEuTiM/95r2giBw8r+YgLXEmLCyM1NRUVq9eTWlpKQUFBQA0NzfT19dHd3c3arXaZQREiul+0003kZqaSlFRkcvvC4KwWhCEjwVBMAiC8G2n710qCEKDIAjNgiB81+ubOUXAf9rOH2iz2YxOp0On07kcnuAJf6a12DLjJicnqaqqIicnh6ysLLfHP/Fh4/RfHBIsBEGGoAxHNOpmHDs1oeXC/3iAD//f/5nhjLPlxisUCrfbkcVQ1OJcVabX6xkeHqa1tXVGwk5CQoLXn7k/Qv+/L5/gb0ddN4kIFM4Zcc7UtPdjNFtQSkycsT0sbWZ+XV2dvdOrKzNfiunubwdYQRDkwB+AzwDdwDFBEA6Joljn7X0EdY8+NjZGbW0tYWFhrFmzxufX+yN0mUzG1NQUFRUVXhvzNfePcaR5AIAp/cyns0wVhcVJ6ADa8TF23PYTnv7+tURHW+1tnrOysgKaGz8fhIeHk5WVZU/YGR8fZ3h4mI6ODmQymd2T75ywE+gmEYHE24puNFuo6xhg0wppHYJnnV8UiY+Pt6/ajmb+nXfeSX19PQcPHuSqq66ioKDA5c9pDh1gtwLNoii2AgiC8AywF/Aq9KD81EVRpLOzk7q6OjZu3Oh3fa6vSTOiKNLe3m63Hrx133zyo0b734cnZq4EMqX7kMvY6AjX/ORx+gaHKCsrY9WqVV5nbS2GFd0Ttn3qihUr2LJlC0VFRW4TdnxtErHzJ69SOWCal+w+bys6zC3v3TmO7mjmP/744/Ya+3vvvZeJiQAkBcwkC+hy+Hf3qa95JeArusViobq6GrlcPmN4gr+dYKUmNxiNRqqqqoiJiSEqKsprjvyUwczfj06nvsZHKBiemOnAmd6nu2d0dIRrfvIEHz7yPRLivbfzXYwruieUSuWM+W5arZbh4WF7S22dTkdYWJi9lNQVH57s5fYnjnttEhFIrF5WdJj2vLOr1K/ze0uYMRqN3HXXXdxzzz1+nT9YBHxFr6urIyUlhaKiohmTLP3JRpJaoDI2NsaxY8fIycmhsLBQ0rUOnWhj4pS5nh4320knyOQIYZ7j+yMjI3zm7l9hMHrP5V/sK7onbAk7+fn5bN68mZSUFMLDw+nt7eXYsWPU1NTQ19c3o/XXQ4er+Prj3jvBBBpJK/ocOs54S5jxp+OxD/QAjqZj9qmveSXgK/r69etnfUhtsfRgdILt7u6mq6uLTZs2SU5UEEWRpxzM9mg387lkqigsJr3Hc/X29rHj9gf58OHvEubBl+CLNbPYClicseXl23q8OybsmEwmfvvvQcqHBMlNIgKFaLWCxftDt1+jpXd4nMwk3wcreGp5NQ8P52PASkEQ8pkW+H7gGikvDPiK7uqHMJfmE+6EbrVaqa2tZXh4mNLSUp+ykSo7hqntHjl9LjcfDm/mu42Ozi4uuusXWCzuLQlfy1oX04rujOO92RJ2cnNzyVu5hnvfVFMxLFuQh5WU1dxGeYt/+3RvHV6ldoA955xzaGhoIDs7G0EQbhYE4VZBEG49dY70U51h7wF+IAhCtyAIsaIomoE7gDeAeuA5URRrpdx30DPjYG7tpFyJw5bKmpaWRm5urs8fKntI7RSjk7O96+DZIedMU0sbl9z9K9767bfcdo2RymJf0WHmPRpMZo419nPnM2UYWbjGiN487o6UN/dy2VbfI0Eery+K/nSABTjgdB53HWARRfE14DVf721ehO5vg0hXe/Th4WFOnjzpU3spR0YmDbxa3m7/tyiK9AxpXR4ryBUICpXklaK2oYnd3/4tr/3iG7PEutArupSHx6TBRNfgGD3DWvpGtKhHpxgan0Kj1TGuMzBlMKMzmBif1GG0iBgsVkxmKyIQqVJhiskI6D37ii8rur+ed0+/F6PRuGiLioKSMOPMXBtEwunQmVqtnlMhzAtHWjCaTwsuPS6c3t4Rt8fLVJFYfDEJa+q54vsP8+ID/zHj676u6P4KXRRFRib0dA2N06vRMjAyQUNHD1MmmDRZGZs0oNUZmTCY0BvMGMwWTBYrVttqJIrYswLtt+zJHBUIl4NWO0Z0TCpm5ndf7ogvK3pdxwAGoxmVMnASWKwFLTCPpru/e3STyWSfd65SqXzOrnPEap3phANIiVLiyQcrU0VhmXT/IHDFxycq+dL9j/L0/V9zuv7MHPzR0VFiYmJ8SggSRZF/1XbxRnkrdV2DDI1NMWUwYTRbMVunBeucvmt73am/zPyGYP/PdHGJj7uGMLnApG4KQRDQa0dQxCR7f1GQ8GVFN1msVHf0s2WlSwvZJd56zy/W7jJwBuzRx8fHfZ53bjOTnX8pHzb00Tk0M4khIszzJ1uqQ86Zdz8+zk0/VfLn+66fPo/Dvdhy8EVRRK/XExYWZh+7GxkZOWP1HBqf4uWjTXxQ28XJnmFGJnSztAqOJuWpVVmY/utMIQsQ4P2/Xqez369Fr11QoUuJoTtS1tTjk9DP1KYTsMhN9/Hxcfr6+igtLfVr3rmz0J90Ws0Br62ZBHkYgkLpk1lo47X3/s1/qML44z3TERCrdTpltqKigpycnBnVUhqNhqamJsrbhyjv1VHVNczQ45UYTDMtoXClHL3RwrSKT90jjgIWTq/KQfbpWc2mmc8NsxGryYAsbP73qdOhNd/abPk6weVMHd4A8+iMczVHzR1Wq5WmpiZGRkZIS0vzSeTgOkGnVzPJOzWzHTDD45Pez6eMxOKH0AH+/sb7hIeF8X++8mkMBgNlZWX25pcj2ikOHW3m/dpO6ruH0Wh1p0xvOL0kz2Ra5LbvT7MggTjRimg1z3qwW3VjyMLmv8OKaPH991Pe3ONTxqaU7jJLZkV3hS8rutFopLKykoSEBFatWkVvr+9ZTK6u98zHTQ4imkYmQPfQuNfzyVRRWKZGfb4PG0+98hZG/RQbc5LoNkXy8/feol09xuikfvae2c7ijaPDtJnsSiAW/QSK2AUQug/7cxuDY5N0D42xLCVe0vFnagdYWGSm+9jYGDU1NRQWFpKSkoJWqw1IJ1ij2cKzHzfPOi4jRkmn1nvIS/Bzn+7IoQ/KeCV9laTMrcWO6Ok9WExYjTpkygj3xwQBf7ZWMB1PD5TQF/OKHvTGEyAtjt7V1UVdXR3FxcWkpKQA/k1dgdlCf7O6myHt7FTWcEHank6mUIJ8bokgJsuplknyMIK+eQ4ioii6zSS0YdF5t5ICjbvOr97wJZ7uTeiLtbsMzJPQPYXXLBYLNTU1jIyMsHXr1hkdOf2ZumK7nuPrnvzQdY/2BB+ma/rrfXdGEASQK2Ce88ADhWg2enXcW/TaeU/h9XdF/6SuTXKHHSnhNV/9SfPFgu7RbU0bMjMzWbZs2SyzPxBDHJr6RznSrHZ5nMEg3UsrU0ZinRrz+V5cMR3mkiMKMp89xQuJaLEgip7ngwMIVguicQpBNX/7VX/26ACtA6PUNTQimk3ExsaSlJTktsOOlBV9Se/RXZnutiaKnlJZAyH0pz5qcnucelR6YwDZXD+0LlYMQRAQ5WEgWmfNCltsTJvsrh1wrrDoxuf+M5OIKFoR/XxgWqwi1sgkSguzZ3XYsQ3AtHXYkeKMW6yme1BWdOcUTkfT3bGnu+NkFlf4OrHU8XVWq5VJg8neXMIZlUJG34jrHHeX5wxTgUzhscOoP9hXdwSwmlis+3fR4luHGIt+AkWQRjc5I5rnZhWVNfewbXXOjE6wRqMRjUZDZ2en3SQXRdFj16Ilv0e3Cc9sNlNRUYHRaPQq8rlgswQOHT/dXMKZrPhw95EtN8xln+7tUoJMBnJlwDPXAoFotUy3UfYBQbRiNQS8lZJL/DXbbZQ3zw7hKpVK0tPTZ4zEMhgM9PT0cPz4cVpbW2eNxApQB1hBEITfneryWiUIQonD9yyCIFSc+nPIl/c4L3t0m9lz9OjRGUMNgoVMJsNgMPCnNyvdHhMX7vtbl6kisfrtUfb+VJl21IU59CZfeNFPm+z+9Xuz6saRhwffOTVnobd4TpyxddiJi4sjPj6e2NhYRkZG6O3tpaGhgcjISHp6epicnPTqjJPQAfazwMpTf7YBD5/6P4BOFMVNfrzF4Kzozj+wvr4+dDod69evD7rIYdrserusgfYR9x8AOX6E7ZRz2HP6YD0IMvmiWd1Fi9nvx41FP4ko+j/QUCr+etxtaLQ62ge8Fy7Z9ui2hpBr1qyhtLSUvLw8mpubqaio4KqrruLee+9lamrK5Tl27Nhhb7fthr3A38RpPgHiBUGYs2iCarrbBhr29fURFRU1L6GH/v5++vr6ONLv+QM2qfPcIsoVQpgKhPkJiwmCgCAPOxWGW5gsOdE6nebqLwIiVr10P4i/zHVFB2l5766ccbYOO7fffjuZmZm8/vrr7Ny5k4gIvxOGPHV6DRcE4bggCJ8IgrDPl5MGTei2cchhYWEUFxf7XWMttWGDbcZ6T08PSRnL+FezxuPxtjlrvt6L//t0/8R6enX387JzwF+T3RHLVPCTZ+a6osOpzrBe8JbrrtPpSElJYffu3cFyQuaKoriF6T5xvxEEYYXUFwZF6CMjIxw/fpzly5ezYsUKBEEIWJabK8xmM+Xl5YiiSElJCf+sH8RkcS+smHAFQ+OuTSuv9xOgxBlfEARherrJPK7uVosJIQDXshqmfHbk+YIoigERupQMOW/Va6IoBmJoqNtOr6Io2v7fCrwHFEs9aVCEPjU1RUlJyYyZ54HoMuOKyclJjh49SmZmJoWFhYgivFTe7fGcmS7aO0vFb6HPMVNMEE51VZ1jKq4UYiKUxKgC46cVBLDqgme+B0LkAI3dQ0zoPG8BPMXRAzhK+hBw3Snv+3ZgTBTFPkEQEgRBUAEIgpAMnIeECS02giL07OzsWXuUYHSCHRwcpKKigqKiItLT0wH4oKGPnhHXzR5txCj9f9tCWAQEeMyvT9e35csHcbRRRowcrZcPvS8EM/c9UEK3iiKVbX0ej/GWMCNF7M4dYA8cOIBjB1imGz+2As3Ao4CtJ9ka4LggCJXAu8CDUmau2ZiX8BoEdkW3Jd3YWj07TmV56sPZzSWcmYspKQgCCQkJjGiG/T7HXJlOslGQEa9ELpPRJaHUViprlyVT0+rZIvIVq3Fq2nsvD/zHLSlKQf9QYM5V1tTDeWvz3H7fk5Cl+p9cdIDl5ptvfsThPCJwu4vz/xtYL+kiLpiX8Br43wnWeW9vsVioqqpCr9ezefPmGSLv1UzyTq33vdaYm/bOUigtzEaLPx7VwO+t+8aNDGiNbFs9u07AH8LD5IyMBX71FQQhaKv64LCGLSuzCA+b+0NEiufd3c9Zr9fPxdMedObNBvXXdHesYNPpdBw9epSkpCTWrl07y/HxtIvmEs6IokjvsH8fupIVGRzvGEEe4U+YMDhuc5PFytHmAQqXpZKZNLfw5frcFHr8/Nl4wxKkMJtoNnG8qZfkuCjy0nxv/+1IRUsvVqt/D+TF3EYK5lnoczHdNRoNZWVlrF69muzs2Q39jGYLz7loLuFMaowKrc73fV1RbipVvdrpEFt4tM/7dFVYcOPvjb0jjOosbF2V7VeezfK0eI43dgb+xk4hGnVzzkl3ed5TMfTuoXF6hsYpLZTe7NGZsUk9rf3+bckWc3cZmEfTfS5CHxgYoKmpic2bN7utdPtnVZfL5hLOpMR4nrLqilVZSTQP67E97JUKBcsyfWuXJPq5UviCzmjmWIuadXkZpMRJ/9DJZQKixeRxpNRcEQSB3PjA7tGnQ2unHx4mi5VjjT2sy00jWuVfdMJV3rvtWp4IreinUCgUPpvuVquVwcFBJicn2bJli8ehDc792t0R6aW9szN5afH0as32oQ+J0eH87Y5LuHhDvk/nEecxu622axiDVWBzgbT22CXL02jpC75z0RKgen4b06Wps3+utR1q5DIZa3J8713nLp5utXquw1/MbaRgEZvuBoOBY8eOoVKpyMjI8BjWaOxz31zCGYsPD5uMxGi0JhmTpzqvFqTH8dzdlxJpGGZ1dork8wB+7/38RaszUtY+RHFBFvFR7qsEMxOiqWwOrJfdHa09AyRFBM5X4Sn1dUxnpL5TzdZVy5DLpF/TXYaclFbPS07oczXdx8bGOH78OAUFBaSmpnrNjPPUXMIZjcSMuMTocARFOCNT0/v5T63O5Mk7PsNwVwuRkZF84dILCVNI33d7cxIGi4r2QWRhKjbmp7v8flykAr1p/hpWpqoCtz3wHkMXONrQTW5qPOkJ0hyVTb3DjE/O3gJKaQwZMt2RHl7r7e21N4lMSkrynhlnMPGim+YSsxEltXeOUilQqVT0j0//wq/avoLffGU7TfU1ZGdnk5eXR2SEiqIVy7ycyeHKCzgGeWRCT1WXhs2F2USpTvsoNq9Io7a9f17vRT04GLBzSU2Wae0fZVQ7xapMaV75itbZ+/QzubsMLKLwmq3SbWBggNLSUnuTSG9CP3SinQmJvd8y4yMwmj0/bMLD5GSnpTAwaUEmCNz16VXsW6ni+LGjREZGolAo7BbG9qICSdc9zcL2ai9rVRMTHcnanBQSosOpb/O9Z/5c6R0aIS8pMPUCvnR+1ZutNPSOULQsGaXC88fe1T79TB7eAIskM85kMlFZWUl8fDybNm2aYfp7ep0oijwpIRPORnJU2Iz6P2cUMhkrl6VT2ztGlCqM39ywg1WJcrq6ujjnnHOYmppiYGCAhoYGYmJiWOXjPl0ISJnI3BgYm0I9BluyozjSNLog95CkstAegPP86qu7aGjv4d3KZk52SbEUBGq6hslMjEEVJqfNTQ26K8+7tz361NSUtzrzBSVoPeOccSdYrVZLdXW1fT/u6nXu9ujl7UPU90ifdOppBRAEWL8ik8quUTITovh/t1yEQqdhYGCCkpISFAoFkZGRJCcnI4ri9HAJZMgEQfL+WyaAh6K6eWNlahTDOit5yZEMjBuYMgavuswVre1dCKrUOdX5CMDaZDmfXreF71y1k7beQZ56/QOaho0cbexBZ3Rv5fVqtChkAltWZnG8afbqXdbUTVt7O6kpKfahl2f6Hj1oK7pz/bmr8NrAwAAtLS1s2LDBrdnjqbe7L6s5TGfWuWNL4TJOdIywMTeZP9y8k4HOVmTh4WzcuHHWg8vWWmhj0VrW5GdRKzE3XJABC9zsNTVGRceoEWWYnPGhSTISookOt6Ie9z8t2Ff6h0co2phPk9r73Dt3pMWGExWuoqWlhYmJCUwmE9ddUkpWVhYmi8iRk528W9HMO5UtdKpHZ73ebBU53tRLUW4a3cNjjE6cdsBNGc10DU+gHR9Hr9cTHx+PXC73GF5bzD3dYYHCa6Io0tzcTFdXF6WlpR73Nu4sAc2EntfKO3y6h0mT6yVk2+ppkV9WkseBr19AZ1M9iYmJFBYWes0h92WfLogL2xpKIRNQqlQYzFa0OhN56Un0aLQYTGbW5fi2DZkrMbK5VZ3lJkeRlZVFQUEBMpmMgoICdDodx44do762muUJYdx75fm8/4tbeev/3sIPrrmYc9fmopDP/MjXdKiRCTLW5abN+HrnqIHVq1fbncJarZa+vj4qKyvp7u6etWhI6QA7x8aQ1wuC0HTqz/U+/bCYxz26YyfY6upqIiMj2bx5s1chuTPdnz/SgtGHTC6FTKB3eHa+dWlhNkfbNNz52U3cdP4KamuqWblyJUlJSZLOu61oJQcOvSfxLhbWbl+fm0J5x+nEmJTEeFr7hhibMjDZPcjWlZkcbZofB93JlnbkMdlY/MwvyEmKYmJigurqatavXz9DZFNTUwwNDVFfX4/JZCIxMZEvbF/JTbu2MGkw8WFNG+9WtPBuZQuDY5NotDo02im2rcrhRHM3ZouVqrZ+vnTBJqxWK7GxsSQkJJCUlERiYiIjIyM0NDRgMplISEjAZDJJSoH1tzGkIAiJwH8BW5j+EJ0QBOGQKIqS963zZrrbWkIdO3aM3NxcMjOlZW25WtGtVpGnfYidw3R759bxmR+qkhUZVPeO88vrdnBefiy1tbWsX7/ep73W9vXSV3S5TMA0z4kzNtbnJM8QOYDZwaAzW6wcbeymtDCbspY+vwUolZHxCYpXRFLX75/5nh4tp7q6mg0bNsz6fUVGRpKTk0NOTg5msxmNRkNfXx8nT54kKiqKjVnJXLzxMygUu6nt6OedU6I/2tjFioxEpgwmypt77ZWR4+Pj9Pf3s3btWpRKJWlpaaSlpSGKImNjYzzyyCO8//77jI6OctVVV3HNNde4zOLcsWMH7e3tnt6WvTEk8IkgCLbGkBcAb4qiqAEQBOFN4FJgds2rG+ZtRR8aGmJqaopt27YRFxcn+XWu9uj/OtlL17BvPd8SIma+1aLcVHq1Jh6/YxcpYQba29spKSmZUfYqhaS4GFYuS6epy3s8etp6mX+hp8ZF0jE8W1AdQ7N/hscau1mXm0rXkJbxqcA1n3CF0uK/X0DUDrHxvNIZs/pcoVAoSE1NJTU1FVEUmZiYYGhoiMrK6VbgSUlJ3HjxBu7adx7D41O8X93Kv2vb6RkeY0Q7hVImUltba/cjWa1WRFHEYrFgtVqJj4/n3nvv5aOPPuJ73/sex44d8+i084K7xpCeGkZKIuhCF0WRjo4O1Go1kZGRPokcXE9rkZrX7ohCOH2OVVlJCGEqnrplJ7rhPsamzJSUlPjd72tbUYEkoU83vJjffbpcJpAQHUlD32wrb2TSQE5aEp0DM1f62g412cmxxEWqAtrUwpnapjaUyfn2OgJfOL9kjVeROyMIAjExMcTExJCfn4/RaLSPYJqYmCAuLo7zC9PYu30NCDLGtVqqaupmbA1snxGbmK1WK//+979pbW1lzZo17Nixw+f3Mh8EzRlnC0lUV1fbi1L8HbHkSI9mgndrfd9Hjo5P78/zUuPIy0rlL7d9Gk13K0qlknXr1s2pqd/2opWSjluINu1bCjJcitxGelK8y693D40zOjFFUa7vhSFSmdDpWZ3qX/JMYaY0H4onlEolGRkZrF+/nm3btpGRkcHY2BgnTpygvOwE1ZUVFBQUeHSylZWV8Z3vfIdPPvnEPu57DrhrDOm2YaRUgiZ0vV7PsWPHiI+PtwvJ306wjjz972a/8saHxnUkRStZnxXLnZ/Kor66gvT0dJYvXz7n7izbJO7Tw4LQSskTa7KTONbiudjH6qFPvVZnpL5zgK2FPlmJPiH60ZAiNVZFhDKw9f0ymYyEhARWrlzJ+vXrMRqNZGVl0d3dzSeffEJDQwPDw8MzPr8VFRXceeedHDx4kNzc3EDchsvGkMAbwCWnGkQmAJec+ppkgvbJ6+/vp7CwcEa2kC0N1t89jNTmEs5EhskQLALfumIHFxUmUVdXR2RkJB0dHWi1WlJTU4mLi/Nb8JnJCeSkJ9HptWnB/O3P46JUDGoNXh+K3SOei3wsVpGjDV2UFmZR3tKPOcBOuurGNiIzV/qUtJOTGLzElKmpKaqqqtiwYYM9Lm6xWBgZGWFwcJDGxkbKy8tRq9X84x//4OWXX2bFCmnt1b/0pS/x3nvvMTQ0RHZ2Nj/60Y8wmUzcdtttt4qi+AjTjSF3M90Ycgq4EUAURY0gCP8NHDt1qh/bHHNSCZrQ8/LyZjnR/G0+YeONqi6GJ3yfsLIsMZJ795xLQUIYLS0tlJaWEhERYe9c09PTQ319PbGxsaSmppKYmOjzw2hb0UqvQp+PyaLTF4KclDiqO73XmA+O68hMiqN32HOt+LHGHtYsS6FPM8nolO+/A3cYTCYKIiw0+xBWz00KjtB1Oh1VVVWsXbt2RvKLXC4nOTnZnhU5OjrKU089RVxcHNdffz1PPvkky5cv93p+V40hAW699dZHwH1jyFPf+zPwZz/eFhDk8Joz/grdFpqT0uHVmayEKH5x7acI04/Q1zfE5s2b7UPu5XI5KSkppKSk2EMlarWalpYWIiIiSElJITk5WZIn/pyilTz/1icej/GhLHpOrEmLkSRyG1lpSV6FDlDfNUhKTDgZ8RH0jQYuk05uNQLSox05QRC6TqejsrKSNWvWeByN3NTUxI9+9COefPJJ1q9fz9jYmM9OwYVgXjeN/nSZgWlB1ncPc9TLftOZTblJPHTDp1B3tSIqFGzcuNGt000QBPt8bFEUmZycZHBwkMrKSgRBIDU1lZSUFLedPqXs0+dD58vT4ml2EUrziEx626VBrZ6o8DA25KVR1T7g4925pr6lg/jcNYzrpH02cgNU/WZDr9fbRe4pKtTW1sZ1113HY489xvr1052XfY0iLRTzKvS59I17xse9+WXFOfzoihIa62tJTU0lJydH8mttg/Oio6PJz89Hr9czODhoz7RKTk4mJSWFmJgYu+WSm55MSnw0g6Pu4/vBttwjlQoMFhGTj73f+kZ9G081qTdR097P1sJsjjb65Px1iclipSApnLJuabkRKZGygE1G0ev1VFRUsHr1ao+i7ezs5JprruHAgQMUF0uehLRoOCNMd4NF5KXj7ZKPv+OSIm76VD411ZUUFBTMGA3lD+Hh4Sxbtoxly5ZhNpsZGhqyx14TEhJITk5GrZ5uyvhehfuMPSHIa/rqZSmUtflm9cC00NMSYhgYke4Bt4rTTrrNK7Ooahvw+eHizPjIECBtVJZppI8jR9pJSEggJSWF+Ph4v8KjjiKPj493e1xPTw/79+/n4YcfprS01OfrLAbm3XT3R+jvNg5L8sqGyWU8uH8b5+bFUFNTQ1FRUcCbASgUCtLT00lPT8dqtTI8PEx9fT1Wq5WivHTPQheC53XfvCKdE36I3EZ8lMonods40dTDquxkBsem0PjhKLVR39JJav5aRryY70lRSrZvKbZ7wtVqNQ0NDURFRdkdZlJ8KgaDgYqKClatWuVR5P39/Vx99dX89re/5dxzz/X1bS0a5t1092WPLooiDQ0N/LNx1OuxidEq/njj+aSGGWhtbaW4uBiVyn1TxEBgMploa2ujoKCA9PR0YlKaeeilD9weH6wVPSspmvpe6XX5roiNT4Ru/2YbNXQPkZYQzfL0eFr7R/06h1UUSVUaGdF5Xplzk6cdcc6ecEefCmDfXkVFRc2yLg0GA+Xl5axatcpt+3AAtVrNlVdeyc9//nN27tzp1/taLMy76W4wSMufNpvNVFVV0akV6R7z3CqqIC2WR27egV7Th0arp6SkZC75xpKYnJykurp6Rq5AydqVJMVFMzzmbq8Z+BVdIZehUiqZ8jJY0htq7dzy2gdGJohQhbFpeToVrf71odPpJgHPNd2uPO7OPhWj0cjQ0BCtra1MTk7aTfyEhATMZjMVFRUUFhZ6FPnQ0BBXXnklP/nJT7j44ov9ej+LiXkdCyrVdLfVFaelpfFeu2dH0fmr0nnq9ovQdLcgk8lYv3590EU+MjJCdXU1RUVFs9oHbV3nPnnCl1bTUilenk7rwNz7pXcPT5AYMzdvts5gorK1l21+ZtI1dfR6HWmdKyFZRqlUkpmZyYYNG9i2bRspKSkMDQ1x5MgRPvroIxISEjxu6UZGRrjyyiv54Q9/yKWXXurz+1iMzKvQpZjuo6Oj9tFLYVFxHK503+Xt4hUx3LYljpqKEyQlJVFQUBD0pJT+/n6amprYtGmTyw/LNg9570plYGebr89N4VhLYEJcAMvS5p4/LopwpKGLkhXpKH1oh20jM9rz7y/Hx9CaTCYjKSmJ/Px8BEGgsLAQpVJJVVUVR48epbW1Fa1Wa6/BGBsb48orr+Tee+/l8ssv9/n+FyuLyuve29tLR0cHGzduRKVS8ad3T7r05soEge/tK2HvhjSqq6uJj4+nt7eXoaEhUlJSSE1N9bnc1Bu2KjyNRmPvIecKTx1nArlHT46JoEvjfysmV5gCaHGUNfeyMjOJkUkDQxJ76QP09PQC7k1qf5JljEYjFRUVMyIweXl5mEwmhoaGaG9vp729nWeffZbOzk6+8Y1vcMUVV/h8ncXMooij21pLabVae7moKOIydh6lUvCb685jTZKC+vp6SkpK7JlJU1NTqNVqe5KLTfRzHWdrcwpaLBY2bdrkMZSzbnk2sVERjLsYzRyozDhBEEiJj6a+x6d0Z6/ofchOk0JT7zDJsZEUZCTQ7KGCzpH2PjWrirJoH3b9cPA1/dVkMlFRUcHy5ctnhVnDwsLIyMggIyOD7Oxs/vSnP5Gamsqvf/1rBgcHueeee3y61mImqEJ31SDSWeiOraU2bNhgT4T4oKGPbqcVKyshikduPh+VcYzu7n42b95MWNhpczgyMpK8vDzy8vIwGAz2JBez2UxycjKpqakuvbCesJXaxsbG2s0/T8hkMrasXc47x2pnfS9QrrjSlRkcbQ6cyW6jc3iCuKhwxlxMKvGXofEpxif1rM1KoE5ix94kpet20PGRYcRGSN/+mEwmysvLyc/P95hLodPpuP766/nSl77EzTffDEzH2M8mFnSPrtfrOX78OCkpKaxYscIuckEQZo1Z2pSbxLN3fRrzSC9TU1Ns2rRphsidUalUZGdnU1JSQnFxMREREbS0tHDkyBGampoYHR31WhtvNBopKysjNTXVp3JWd/XpgVjRlyWEczyA+3JHRBHyfJwSKwWjxUpd9zCr06KR0uO5rdO1X8aX1dy2kufn53usE9fr9Xz5y1/mi1/8IjfddJP9654GenrCWwNIURS56667KCgoYMOGDZSVlfl1HV+Zd6HbVnRbgX9hYSHp6ekzRN6tmeC9+tPNJS4rzuHA13bQ1VxPdHQ0a9as8SkTymaibdy4kdLSUuLi4ujp6eGTTz6hvr5+Vp0xTIfPysrKWL58ueT+dja2udmnz3WPHhuhxEgYwWznNtdtjidO9o+zaXm611nxfUMjrEydLWqp+3NbCC03N9ejyI1GI9dffz27d+/m61//ekAcuTfccAOHDx92+/3XX3+dpqYmmpqa+N///V9uu+22OV9TCvNquts6wfb19dHe3s6mTZtQKpWIojhDuM9+3GJ/8N9xSRE3n7+c6qrpfZarIQ++IJfL7T3ErFYro6OjqNVqGhsbiYmJITU1FblcTmNjI0VFRX716t64MpcIlRKdwan2co6ZcfnpCVR2+JfUIhXN5NzaMHujorWP5emJTOpNDIy5dya6agctZUU3m82Ul5eTk5Pj8bNiMpm46aab2LlzJ3feeWfAojXeGkC+/PLLXHfddQiCwPbt2xkdHUUQhIxTDSaCxryu6DCdldTb22tvxCgIwgyRG80WXjjSglIh45dfPodrt2Xba4TnKnJnZDIZiYmJrF69mu3bt7Ns2TJ6e3upqKhApVKh1WoxmaTNdXMkTCFn85rZ89Pn8lEqXZkRdJEDtA9qiY4IrFPOmdZ+DSaLmcIs9+G82obmWVsdb1VrtpU8JyeHtLQ0j8d97WtfY/PmzXzrW9+avz4BTOfNL1t2uitUdnY2+Njo0R/mTegWi4XKykpEUbSXi9pMdUf+WdWFCPzttovYnKGkqamJ4uJijzXCgWJ0dBSr1crOnTspLCxEr9dTXl7OiRMn6OrqkpzVB6736f6a7nmpcVT5UF8+FyxWkfwg7NOd0Wh1tPdr2FyQ4fL741N6ViTNTGGOEYxu8zBsIs/OzvYocovFwn/8x3+wZs0avve9782ryBeSoJvucLpKKCsri8nJSfr7+0lJSXEZiz7WOshzd30G4+gAg4OTbN68OeiZbq7CZ7aUyuXLl6PT6RgcHKS6uhpRFO1hO08NB1zt0/0pagkPk2NFwGCav1lO0ZHzM0PMaLZwoqmHbauWcbSxZ1ZUIko2U9SxchMnTpxAqVTam4KEh4fbF5GsrCzS013PgYdpkd91111kZ2dz//33L4jIs7Ky6Oo67Wzs7u4GHxs9+kPQ4+hjY2PU1NTY631jYmLo7++no6ODiIgIUlNTSU5OJiwsDLPFyj2fXU9HSyMRERFs2LAh6L8Mi8VCTU0N0dHRrFq1yuX1IiIi7AMBjEYjg4ODNDQ0YDQaSUpKIi0tjejo6BmvLVmdj1KhwOiwAvmzoq/LTeVEq/9Vaf4wqg98qq4njjR0sXF5Ok29GqYMp69d19RGWGIuJotIXEQYJUWrgNOTWGprazGbzZhMJjIzMz2K3Gq18q1vfYuEhAQeeOCBBVvJ9+zZw0MPPcT+/fs5cuQIcXFxBHt/DiB4CTHNyXvU09NDY2MjGzdutGeq2fbjtoqjgYEBhoaGUCqVJCYm0t/fT3Z2NllZQd+2YDQaqaysJDMz06/r2WrT1Wo1k5OTJCYmkpqaSnx8PIIgsO/bv+RYXYv9+LXFpbSNSBdR8fI0ytuDvy93RiGXIehG0XuYSBoM8tIS0JvM9I+cdtJt2byZ6t4JirLieOH282ccb7FYKC8vJyoqCrPZbO8PYCtgsX3WrFYr3/3udwH43e9+N6fW3t5wbACZlpZmbwAJcOuttyKKInfccQeHDx8mMjKSv/zlL2zZsiXoT52gCn14eBiFQmGfROnpKTo4OEhdXR1hYWGoVCq7ZzxYpaa26jNf5qx5wmq1otFoUKvVjI2NERcXx7PvV/Gnf/zLfsyKNevp1UkzojLio9AaLUzo51dsNnKiLLQNjM77deOjw0lPiOXkqZLZLUWrqB6G3Rsy+dV++8xBu7melpZmf0jboiiDg4NoNBrkcjnHjx+no6MDg8HAI488ElSRz4GgCz2opvsrr7zC8uXLvaaNDg4O0tLSwpYtW4iKipqxJwYClspqY3R0lPr6er/DZ66QyWSzOoWuzJw5TlmlVILOeycWuUwgOiqcvvHRgNybP6SmpCyI0Ecn9EzqjGwpyOR4cy81ja1EpK+cEVpzJXI4HUVJTExEFEV6e3v55S9/ac/XeO6559i/f/+8v6fFQFCFHhsby+9+9zsaGhq46KKL2Lt3L6WlpTPM966uLgYHB2fMPXPcExsMBtRqNXV1dVgsFlJSUkhLS/O786ZaraatrY3i4mK/s5+8IQgCCQkJfP6SHXzv0UNYTiXjGI0GwHsK5+aC4KS4+sKEcW6toeaCyWLleFM321Yt41hTDxtTI+xCt1qtVFVVkZqa6nW79cQTTxAbG0tnZydDQ0P09/tXJ382EFTT3YZOp+Pw4cO88MILVFZWsnPnTi677DJeeeUV9u/fL3numc0RplarMRqNJCcnk5aWJjl/vbOzk8HBQTZs2OAxfTZQDA4O8oX7fkdL73RobMPmbTQNe05IWZeTTF3PiJRM0aCiUsgxTQxjMs+ft98V6/PSCI+O57tXfopNy+KprKwkOTl5RizaGVEU+e1vf0t5eTlPPfVUQH7Xhw8f5hvf+AYWi4WvfvWr9j2/jc7OTq6//npGR0exWCw8+OCD7N69W+rpz+w9uisMBgMvvfQS3/72t0lNTaW4uJgrrriC8847z6dfiK3EUK1Wo9Pp7N5vx86s9jchijQ2NmIymVi7du287NN6e3vp6enhHyfa7PPTN27eRqMHocdFhCFThDEyGdwpplJZmaTkZEfQHcJeWbMshSfvvZqO5gaSkpK8ivzhhx/mww8/5LnnngtIubLFYqGwsJA333yT7OxsSktLefrpp1m7dq39mFtuuYXi4mJuu+026urq2L17t7cRyY4EXejz7plQqVTU1tbym9/8ho8//pgrr7ySl156iXPPPZfbb7+dN998E6PRexqmc/56bGwsHR0d9jlZtqIVi8VCVVUVcrl8zsMUpdLe3s7AwAAlJSWct3GV/euCp+emAGkJ0YtG5ADxsYHxX8yFmAgl/33dp+lsaSQxMdGryA8cOMB7773Hs88+G7CeBEePHqWgoIDly5ejVCrZv38/L7/88oxjBEFgfHx68uzY2JjP9RHBZn6n/p3ixz/+sf3vu3btYteuXZjNZj744AOef/55vve971FcXMy+ffu46KKLvO6l5XK5fTi945iluro6zGYzaWlpARmm6A1Hy8GW/be1qMCe8+/p+lsLMjkapKo0f5kyLdw+HSA6XMmf7/4Ciqlh4uPjvfbmf+yxx3j11Vd5+eWXAxqtcZW2euTIkRnH3H///VxyySX8/ve/Z3Jykrfeeitg1w8EiybWoFAouPDCC/njH/9IVVUVX//61/nggw/YuXMnN954Iy+//DJTU947ldjGLNlqx7Ozs7FYLBw5coS6ujqGhobmPNHVFVarlZqaGmQy2QzLISEmitW5rtM8bazMSKC8fTDg9zRX2ga1yOUL8xGJCg/jwN1XoNRriIuL8zqt9Mknn+TgwYO8+OKLQXOyeuLpp5/mhhtuoLu7m9dee41rr702KJ8zf1mQFd0bcrmc888/n/PPPx+r1cqxY8d4/vnnefDBBykoKGDPnj1ceumlbkNjY2Nj1NXVsW7dOnuOvC3kNTAwQFNTk71SLSkpac4ptraOtUlJSS4/kNuKVlLf3osrl0eUSsGEwTLnAQjBYMpgZnlmCk1d82tpRIWH8edvXkG4YYSYmBjy8vI8Hv/888/zxBNP8OqrrwZlDpqrtFVnj/+BAwfs5annnHMOer2eoaGhgBdi+cuiWdHdIZPJ2LZtG7/4xS8oLy/n+9//Pg0NDVx66aXs37+fp556itHRUfvxAwMDnDx5kk2bNs0ohLGFvBwr1cbGxjh27BhVVVX09/f7NRfOaDRSXl5ORkaG21XHlvfuynAvzE6mbzSwvd8CSVJc8IuJHAkPk/PQrbuJMI0RExNDfv7sKkBHXnrpJf70pz9x6NChgA/rsFFaWkpTUxNtbW0YjUaeeeYZ9uzZM+OYnJwc3n77bQDq6+vR6/Uea+Hnm3n3ugcKURSpqanhhRde4NVXX7U37FcqlfzqV7+S7MEXRZGJiQl7Km54eLh9oKK3c9gmcHob+6TWjFH8lfvYXLqNusHTjsbp6SqLz2R3ZF1WPFUNLd4PDAARSgX/99qdxIkTiKJIZmYmKSkpbmfXv/rqq/z617/m1Vdf9dijPRC89tprfPOb38RisXDTTTfx/e9/nx/+8Ids2bKFPXv2UFdXx9e+9jUmJiYQBIGf/exnXHLJJVJPf/aF14KBxWLhlltuoaysDJVKRUxMDHv27OHyyy8nJSXFJyecY/69QqGwp+I6e3C1Wi01NTWsXbtW0kTN8792PwmZedQNTqe0LkuOYWjCiM44vwUkvhIZJmNydAhrkAP74UoFB755BXHiBOHh4eTl5dlTisfHx4mLiyMlJcU+u/6f//wnP/3pT3nttdcCksK8wJzZKbDzxdTUFOvXr+fRRx9FEARaWlo4ePAg11xzDUqlkj179rB3717S09O9ij4qKorly5ezfPnyGV1lZTKZPRVXp9PR0NDAhg0biIqSVtK5vWgljZppkSsVcuRyBTqjb1NMF4Ipk5W8jGRae4NneYQrFTz6jc8TJ06gUqnsERLH2fW2HPZHHnmE999/n/7+fl5//fWzQeTzwlmxortDFEU6Ozs5ePAgL730Elarlcsvv5x9+/aRnZ3t00qv1+tRq9X09PSg0+nIyckhKytLcv79C28f4Yl/naRm0EjpysyADl4INlvyEjhS49vYaqmowhT87zf2kSzTERYW5nUIx/vvv8/999/PRRddxL/+9S/uu+8+Pve5zwXl3uaRkOkeKERRpK+vzx6C0el0XHbZZezdu1dyjL27u5v+/n7WrFljn+RpNpvtK72n1b17YJg7/vgP5FEJVM5Tt5hAsTE3ibLaxoCfV6mQ87937SM1zIBCofAq8o8//phvf/vbvPLKK3av91zmpHtLawV47rnn7E0qNm7cyFNPPeXXtbwQEnqwUKvVvPjii/z9739Ho9Gwe/du9u3bR2FhocsU2ra2NsbHx2fNdjOZTAwODjIwMIDBYLCL3rkRBcDXfvsSJ7onGNcFtwFjoImPUjE80Ov9QB9QKuQ8cude0pVG5HI5K1eu9CjY48ePc9ddd3Ho0CGviTNSkJLW2tTUxFVXXcU777xDQkICarU6WOGykNDng+HhYV5++WUOHjxIf38/u3bt4vOf/zxr1qzBarVSXV2NSqVi9erVHlNoHRtRTE1NkZSURGpqKrGxsQiCwFuV7Tz+r5McaerDHMyezUEgM1KkSx2YyTBKhZyH79hLZrjJPg/Nk8grKiq47bbbePHFF1m+fHlA7uHjjz/m/vvv54033gDgpz/9KQD33Xef/ZjvfOc7FBYW8tWvfjUg1/RAyBk3HyQlJXHTTTdx0003MTo6yj/+8Q8eeOABWlpaUCgUXHzxxfzwhz/0mievUChIT08nPT0di8XC8PAwXV1daLVaEhMT2ZyTysV37GJsysjb1Z0crmjno5O9GBe4QkwKMeGBqfZTKuT84fY9ZEWYEUW8irympoZbb72VF154IWAiB2lprY2N09uV8847D4vFwv3333/GTlcNCd2J+Ph4rr32Wvbt28fevXvJy8ujvb2d8847j4svvpi9e/eyZcsWr6J37h+v0Wjo7e3l5MmTxMfHc8HKVD6/dQVTRgvv1nTyRmUH79d2L9pwW2RMHDA3B2KYXMZD/3E5OVFWrFbRbY8+G/X19Xz1q1/lmWeeobCwcE7X9gez2UxTUxPvvfce3d3d7Nixwz7U80wjJHQ3yGQyvvvd79qTHmw19Y8++ih33nknO3fuZO/evWzfvt1rCq1j9xlbu6OBgQEaGxuJjY1le24q5xeUUFmoYiwsifcaBni3pgvtItrLd2nmFgoMk8v4/X9cTl4MmM0WVq9e7VHkjY2N3HjjjTz55JMz9s2BQkpaa3Z2Ntu2bSMsLIz8/HwKCwtpamqitLQ04PcTbAKyR/fmvTQYDFx33XWcODE9x/zZZ5/1mr+8mNHr9bz55pu88MILnDhxgnPPPZfPf/7znHfeeW7HKbtCFEXGxsbsDTESExPJzMwkOTkZiwgfN/RyuKKDt6o7GZlY+KF/6REWegZHfX6dQi7jd7d+joJ4GSaTiTVr1ngUeVtbG9dccw1//etfKS4unsMdu8dsNlNYWMjbb79NVlYWpaWlPPXUU6xbt85+zOHDh3n66ad57LHHGBoaori4mIqKimDE7he/M06K99JWkfbII4/wzDPP8OKLL/Lss88G4PYXHqPRyLvvvssLL7zAxx9/zNatW9m3bx87duyQVA89NDRES0sLGzZswGg0olarGR4etrfCTklJQZDJONrUzxuVHbxZ2cHA2MIk2pTkxHGsrtWn18hlAj/a/ylK8xLtjT88ibyzs5Orr76aP/3pT0FfOb2ltYqiyLe+9S0OHz6MXC7n+9//frB6zi1+oUvxXu7atYv777+fc845B7PZTHp6OoODg2fdlAyz2cy//vUvnn/+eT744AN7Tf2FF17osnRyYGCAjo4O+ww6G65aYaelpdmHXpS3qTlc0c4/KzvoHp6Yt/dXkpfEsRrp8XS5TODB6y8mL8rCxMQEsbGx9oeXq3rxnp4errrqKv7whz9w7rnnBvLWFzuL3+suxXvpeIxCoSAuLo7h4WGPhSBnIgqFgosuuoiLLroIi8XCRx99xMGDB7n//vtZt24d+/bt49Of/jSRkZHU1tai1+spKSmZZe4LgmCfFLNixQomJydRq9WUl5fb8++/ddkmvnfFNmq6hnijvJ03KjtoHRgL6vvrHdVJPlYuE/j1LZexLlXF1NQUmzdvtnf3raqqArA7KyMiIujv7+fqq6/mt7/97VIT+bwQcsYFCblczo4dO9ixYwdWq5WjR4/ywgsv8NOf/pTo6GjkcjnPPvuspD19VFQU+fn55Ofno9PpUKvVVFVVIQgCqamp3H5JEd/as4WmvhHeqOjgjYp26nsCE/N2pH90irTEWAY04x6Pk8sEfvm13RSlhTMxMUFRURGCIBAZGUlubi65ubkYDAYGBwf56KOP+M53voPVauU///M/Of/88z2eO4R/zFnoUryXtmOys7Mxm82MjY0tqWIEmUzG9u3b2b59Oz/+8Y/58MMPKS4uZvfu3eTk5LBnzx52794tqQouIiJihljUajW1tbVYLBZSU1O5aWchd3x2Ex2D4/yzsoPDFe1UtQ8GLPNpWWqSR6HLBIGff/WzbEiPQKvV2kXujEqlIjs7m/DwcOLj49m5cyf//Oc/OXHiBI888kiA7jaEjTnv0aV4L//whz9QXV1td8b9/e9/57nnngvA7Z95HD58mM985jPI5XJ7Tf3zzz/Pa6+9RkpKCnv37uVzn/sciYmJPp3X1gp7YGAAk8lkr/waGBige2icdp2Kf1Z2cLxlYE4lp5vzkzla3eDyezJB4GdfvZTNWdGMj49TVFTkMd9gZGSEK664gh/84AdcfvnlwNxy10Fa/jrAwYMH+eIXv8ixY8fYsmWL39cLEIvfGQfevZd6vZ5rr72W8vJyEhMTeeaZZ7xmOXn7hf3qV7/iT3/6EwqFgpSUFP785z977Su2mBFFkZMnT/LCCy/wyiuvEBcXx549e/jc5z7nc029Lf++ra0Nk8lEVlaWvRW2ZkLPm5UdHK7o4EhTn88trLITo+no7Jj1dZkg8H9vupTSnBhGR0dZv369R5GPjY3xhS98gW9/+9tcccUVPt2DO6REgGC6l8Bll12G0WjkoYceCgmdBcp1l/ILe/fdd9m2bRuRkZE8/PDD9ha/ZwOiKNpr6m0dTS+//HLJNfW2brRWq5WCggI0Gg0DAwNMTk7a8+/j4uIY1xl5p7qTwxUdfHiyR/Jo5niZnuHx0+2vBAEevPFStufFMTIy4lXkWq2WL37xi9xxxx1cffXV0n4oEpASAQL45je/yWc+8xl+/vOf84tf/GJJCH1R9oyT0kf7wgsvtDcC3L59u23O9FmBIAgUFBRw77338tFHH/HXv/4VgBtuuIFLL72U3//+93R1deHqIW2zDABWr15NWFgYaWlpbNiwga1bt5KQkEB3dzeffPIJfZ1t7FyZxCO3XMzRB6/htzdewO6SfKJUnl03uRmne6EJAjxwwy6258Wh0Wi8inxycpL9+/dzyy23BFTk4DoC1NMzc/R4WVkZXV1dXHbZZQG99mJnUXrdpYTsHDlw4ACf/exn5+PW5h1BEMjNzeWee+7h7rvvttfU33rrrej1ej73uc+xd+9e8vPz7XPJoqOjXdZ221php6SkYLVaGRkZob+/n4aGBuLi4tiel8Zni3dislj5V30Pb1S0805116yy2jCl6tS9wf9cfwnnLU9gaGjI3sveHTqdjv3793Pttddy7bXXBv6H5QWr1co999xjf3AuJRal0H3hiSee4Pjx47z//vsLfStBRxAEMjMzufPOO7njjjvsNfX33HMPIyMjKBQKLrjgAr7//e97Ne9lMhlJSUkkJSUhiqK9kUZjYyMxMTFsykjjonWfworAxw29vFHRzptVnWgm9AxOTE+T+fG1n2ZHQRKDg4NeRa7X6/nyl7/MlVdeyY033hjQn4sNbxEgW5+/Cy64AID+/n727NnDoUOHFoP5HlQW5R5d6l7rrbfe4s477+T9999fNP2zFwKz2czVV1+N1WrFaDQyMDAwo6beF0eeLf/eloobFRVFWlradHKTIHC8ZYA3KtopTIniUwWJqNVqNm7c6LGwx2g08pWvfIVLLrmEO++8M2gZkVIiQI5ccMEFS2aPvihXdMc+2llZWTzzzDOzWviUl5fz9a9/ncOHDy9pkcO0Sbx3716uu+46YHr++6FDh/if//kfOjo6+MxnPsO+ffvYsGGD1/JaQRCIj48nPj4eURTRarX2UdPh4eHkpKVx374tqNVqBgYGvIrcZDJx4403csEFFwRV5DCdmfjQQw+xa9cuewRo3bp1MyJAS5VFuaKD95Ddpz/9aaqrq8nImB53lJOTw6FDhzye8wyNsc4JrVbLq6++ysGDB2lsbLTX1G/evNnngZMTExOo1Wp6e3sxm82sWLGCtLQ0t8U7ZrOZm2++meLiYu67776zrrYhgCzN8FowOINjrAFjamqK119/nYMHD1JTU2Ovqd+2bZvksVR9fX309vZSWFjI8PAwarV6RpMNW7GKxWLh1ltvpaCgwN5cMYRbQkIPFGdwjDUoONbUl5WV2Wvqzz33XLf59zaRb9q0acaDwdYKW61WMzIywr///W+6urrIzc3lgQceCIncO0szjh4MQjHWmYSHh3P55Zfz2GOPceLECT7/+c9z8OBBzj33XO68807efvvtGXPq+/v76enpcbknDw8PJycnhy1btrBx40ZOnjzJJ598wvvvv89f/vKX+X5rIVywKJ1xC8FSjrEqlUouvfRSLr300hk19ffddx8lJSWkpaWh1Wr52c9+5rHazmq18otf/IJly5bx4osvMjo6Snt7+5zvb6mlQwcFURQ9/Tlr+Pe//y1ecskl9n8/8MAD4gMPPGD/9+joqJiUlCTm5uaKubm5okqlEjMyMsRjx44txO0uCsxms/jf//3fYnZ2trhp0yZx//794tNPPy0ODg6Kk5OTM/5otVrx7rvvFr/2ta+JFosloPewfPlysaWlRTQYDOKGDRvE2traGce888474uTkpCiKovjHP/5RvOqqqwJ2/XnCmw7n/GfJCN1kMon5+flia2ur/QNTU1Pj9vidO3cuaZGL4vTP7MYbbxRHR0dFi8Uifvzxx+I999wjbtiwQfzCF74gPv744+LAwIA4MTEh3nvvveL1118vms3mgN6Dtwe0M2VlZeK5554b0HuYB4Iu9CWzR3eMsa5Zs4arrrrKHmP1FpbzxOHDh1m1ahUFBQU8+OCDLo957rnnWLt2LevWreOaa67x+1rzjUKh4M9//jNxcXH2mvpf/vKXlJeXc99991FTU8OuXbvYunUrDQ0NHDhwQLL3XipSfCuOnM3p0HPCy5MghAekmJWNjY3ipk2bRI1GI4qiKA4MDCzErQYNi8Uivvzyy6JWqw3K+Z9//nnx5ptvtv/7b3/7m3j77be7PPbxxx8Xt23bJur1+qDcSxAJreiLGSlVdo8++ii33347CQkJAGddFp9MJmPPnj1ER0cH5fxSOhjBdDr0T37yEw4dOuSy8eRSJyT0OSDFrGxsbKSxsZHzzjuP7du3c/jw4fm+zTMax3Roo9HIM888MyuV1ZYOfejQobPuQRooQuG1IHM2jfVZCKTkr//nf/4nExMTXHnllYC0dOilRkjoc2CpjfVZKHbv3s3u3btnfO3HP/6x/e9vvfXWfN/SGUfIdJ8DUszKffv28d577wHTU1kaGxsDOhU0RAgphIQ+B6SE7Hbt2kVSUhJr167lwgsv5Oc//7mkVtfewnadnZ1ceOGFFBcXs2HDBl577bWAv78QZw9LpqjlTEJKpd0tt9xCcXExt912G3V1dezevTsg6aYhFoRQUctSRErYThAExsenBymMjY2RmZm5ELca4gwhJPRFiJSw3f33388TTzxBdnY2u3fv5ve///1836bfeNuWGAwGrr76agoKCti2bVvIUgkAIaGfoTz99NPccMMNdHd389prr3Httdditfo2jGEhsFgs3H777bz++uvU1dXx9NNPU1dXN+OYAwcOkJCQQHNzM3fffTf33nvvAt3t2UNI6IsQKWG7AwcOcNVVVwFwzjnnoNfrGRoamtf79Acp25KXX36Z66+/HoAvfvGLvP322y572IeQTkjoixApYbucnBzefvttAOrr69Hr9aSkpLg63aJCyrbE3ZjtEP4TEvoiRErY7pe//CWPPvooGzdu5Etf+hJ//etfQy2bQrjFW3gtxFmEIAh/Bj4HqEVRLHLxfQH4LbAbmAJuEEWxLMD3cA5wvyiKu079+z4AURR/6nDMG6eO+VgQBAXQD6SIoQ+r34RW9KXFX4FLPXz/s8DKU39uAR4Owj0cA1YKgpAvCIIS2A84J6YfAq4/9fcvAu+ERD43QkJfQoii+C9A4+GQvcDfTtVIfwLEC4KQEeB7MAN3AG8A9cBzoijWCoLwY0EQbI6IA0CSIAjNwD2A6wb8ISQTKmoJ4UgW0OXw7+5TX+sL5EVEUXwNeM3paz90+LseuDKQ11zqhFb0ECGWACGhh3CkB1jm8O/sU18LcYYTEnoIRw4B1wnTbAfGRFEMqNkeYmEI7dGXEIIgPA1cACQLgtAN/BcQBiCK4iNM75t3A81Mh9eCM8g8xLwTiqOHCLEECJnuIUIsAUJCDxFiCRASeogQS4CQ0EOEWAKEhB4ixBIgJPQQIZYAIaGHCLEECAk9RIglwP8HoKTC/hmFoisAAAAASUVORK5CYII=", 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", "text/plain": [ "
" ] @@ -466,86 +735,232 @@ } ], "source": [ - "def assemblage_quadrangle(coords, elems4):\n", - " Ns = len(coords)\n", - " A = np.zeros((Ns, Ns))\n", - " for quadrangle in elems4:\n", - " M = raideur_quadrangle(coords[quadrangle])\n", - " for i, a in enumerate(quadrangle):\n", - " for j, b in enumerate(quadrangle):\n", - " A[a, b] += M[i, j]\n", - " return A\n", - "\n", - "def second_membre_quadrangle(coords, elem4, f):\n", - " Ns = len(coords)\n", - " b = np.zeros(Ns)\n", - " for quadrangle in elem4:\n", - " coords_triangle = coords[quadrangle]\n", - " centre = np.mean(coords_triangle, 0)\n", - "\n", - " # calcul de alpha\n", - " x = coords_triangle[:, 0]\n", - " y = coords_triangle[:, 1]\n", - " mat_alpha = np.array([[x[1] - x[0], x[2] - x[0]], [y[1] - y[0], y[2] - y[0]]])\n", - " alpha = np.linalg.det(mat_alpha)\n", - "\n", - " b[quadrangle] += alpha / 4 * f(centre[0], centre[1])\n", - "\n", - " return b\n", - "\n", - "def condition_neumann(ccs, nns):\n", - " Ns = len(ccs)\n", - " coeffs = np.zeros(Ns)\n", - " for i, j in nns:\n", - " point1 = ccs[i]\n", - " point2 = ccs[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\n", - "\n", - "#------------------------------------------------------------------------------------------------------------------------\n", - "\n", + "# calcul de premier membre de l'équation\n", "A3 = assemblage(ccs, e3)\n", "A4 = assemblage_quadrangle(ccs, e4)\n", - "\n", - "b3 = second_membre(ccs, e3, f)\n", - "b4 = second_membre_quadrangle(ccs, e4, f)\n", - "\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", - "# print(A)\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", - "print(b)\n", "\n", - "# print(b3)\n", - "# print(b4)\n", - "\n", - "# A_tild, b_tild, ccs_tild = tildage_quadrangle(A, b, ccs, dds, nns)\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", - "# print(x)\n", + "\n", + "# on remet les conditions aux bords (Dirichlet)\n", "x_untild = untildage(x, dds, U_d)\n", "\n", - "# print(A)\n", - "# print(b)\n", - "# print(U_d)\n", - "show(ccs, x_untild)\n", - "# show(ccs, u_ex(ccs[:, 0], ccs[:, 1]))" + "# on affiche le résultat\n", + "show(ccs, x_untild)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Compléments d'analyse du système**\n" + "## Compléments d'analyse du système\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analyse de l’ordre du schéma de discrétisation dans le cas d'éléments Triangle\n" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [], + "source": [ + "def f(x, y):\n", + " return 2 * np.pi ** 2 * np.sin(np.pi * x) * np.sin(np.pi * y)\n", + "\n", + "\n", + "def u_ex(x, y):\n", + " return np.sin(np.pi * x) * np.sin(np.pi * y)\n", + "\n", + "\n", + "def u_d(x, y):\n", + " return np.zeros(x.shape[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "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": 76, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "regression linéaire: \n", + "2.078 x - 0.0363\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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": [ + "### Résolution du système linéaire par une méthode directe\n" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "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": 78, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "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()" ] } ], @@ -565,7 +980,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.2" + "version": "3.10.4" } }, "nbformat": 4,