{ "cells": [ { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 55, "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": 56, "metadata": {}, "outputs": [], "source": [ "def show(coordinates, u) -> 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", "\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.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": 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", "\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": 58, "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": "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": 59, "metadata": {}, "outputs": [], "source": [ "def calcul_alpha(x, y):\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", " 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", "\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", " 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": 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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", 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" ] }, "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)\n", "\n", "# on compare avec le résultat théorique exacte\n", "show(coords, u_ex(coords[:, 0], coords[:, 1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partie II : maillage mixte et ajoût des conditions de Neumann\n" ] }, { "cell_type": "code", "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": [ "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": 69, "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": 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 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": 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": [ { "data": { "image/png": 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XfBW62Wzm8OHDZGdnk5GRIek1szXdrfnx9qWsjni7ogciVu1YO+7MzLeu9pGRkS5/fwslju6IRmfgK79+h86Jqc+eaDJQ1+X/BiHWGntr1Mbesfftb3+biooK/vKXv3DFFVdQUlLi9AG6detWWltb3V2jH+gXBOFSf9yz34QuiqJt3K8/YuO+iK+rqwudTsfmzZtddmT117XgVNLN4OCgx/z4hVgI48zMV6vVtLe32/K1XZn5C21FP9E7zJ4/fIxWPGVGW0x66jr8L3THPbq9Y++vf/0r27dvp6CggCeeeILCwkJiYmL8fQsi8C9BEETg/0RR/KOnF/hN6FZxO/tlBbpAxbo3NpvNREdHTwudScEXoYuiaBuDvHHjRo+r0UJY0T2hUqlIS0sjLS1tWosoRzM/EE0iZrOiv1XRxndfqMQim75XFk0GGnu06AxGQpX+61Xv6V51Oh3XX389t9xyi9+u6cAXRFHsEgQhGXhbEITjoih+5O4FfjXdnQnG+jVvwzxShW5tVJiZmUlmZibHjh3zOv7urdA1Gg0TExPk5eW59OQ7shBXdHe4M/MHBwcRxam54wkJCW7NfKn4uqL/6vVynvx3J8hm/r5Fkx6zRaS6tY+NBZmzur9p5/Vwr95+/ny4ftfJ//cLgvAysAmYO6E7wyrYQAi9p6eHlpaWacMTAj3Eobe3l+bmZsLCwiSLHE6PFd0d9mZ+XFwcQ0NDqFQqm5kfERFhM/N9ySv3dkUXRZFb/vgBn3VoEWQzP1uixQSWqc9PWVOXX4XuKTErkAiCEAHIRFEcP/n3i4EHPb0u4EJXKBSYTCavCzPkcrnLjq4Wi4Xjx4+j1+spKSmZFt7wxYknJbxmsVhoaGhgcnKSkpISjhw54vU1Fpp4Z0NISMg0M39iYmJaJ9iYmBhb3FnKQ96bFX180sCXf/M2PZOuxxaLJoPt7+VN3dLelJ+Q4qP62te+xgcffMDg4CCCIHQC/wWEAIii+LggCKnAUSAasAiC8G1gJZAIvHzy/ArgGVEUD3q6J78K3dmb89V7LpfL0ev1M74+OTlJZWUlaWlpFBYWzrhmIDrB6vV6KisriY+Pp7i42PaLnG0hjKvXLvSHguP7FgSByMhIIiMjycrKwmw2Mzo6ilqtpqWlBblcblvt7RtCujunK453qfn6/32CTnS/57YXetmJbr+GBKW0e/bEs88+a//PGeaGKIq9zr4OjAFrPV7AgTkz3b3FWcJMX18fJ06cYNWqVcTGxrp8nT+Fbi2CWb58+bRSVqsVIHVLMt/i9XeHGXfnsxc2nEov7ezsZHx83KmZL8V0/+fRZu5/uQZR5tmxJhpPLRJ9Ixp61OOkJ0iPxLjCkyPSYDDMy5BKT8yJ6e7rim59ndVsnpiYmNGR1RFfMuqcCd3aBaa7u3tGEQx4L9zTfY8+G5xNerHvCxcbG4ter3f7gP6fV4/x1yO9Tp1uzrDYregwZb77S+inWy06LHDT3Ww2TxuesHz5cklVb76s6Pb+AOsARUEQXCY8BKriLRAspFZSrsz8gYEBqqurZ5j5ADc8/j5HunQIghfOOtP0bV95Uzc7Ns1+VvnpmOcOc2S6m0wmn143OTlJaWmp24wzR2Zruk9OTlJRUWEL1/lrH+3seFeCWegruj/3u1Zhh4aGsm7dOsxmM2q1ms7OTroHhnng/X6GzaFeX090WNHL/OSQOx07wMIC3aNbLBba29sZHx/nC1/4glcee1+ntVg7kjQ0NLj1AVjxNj/eUbzd3d309vYSFxdHQkICYWFhc95AwlcCmeuuVCpJTU1l0Kjge8+eQI/3oTrRYgbL9MWlurUXg8mMUjG7st3TcXgDzIHprlAoMBgMTo52jk6no6qqiqioKKKjo70Oy/myRxcEgaGhIdq6+5mURXkUufU1vpjuVn+DVqslLy+P0dFRTpw4gU6ns4WkVCrVgl/RA3FO6+fnH4dO8OMDdZKcbk7PZZr5eTOYzNS197E2L31W93k61qLDAjPd7YcnREdHU1ZW5vX1vDXdjUYjLS0tiKJItxjDj379N2RyOTu2rHL7Ol9Md6PRSGlpKXFxcRQUFGA0GomMjCQjI8PW6siaeWY0GmlrayMhIWFe2kV5IhD3IwgC//2PIzxb2o8g0enmDMf9uZWypu5ZC11KT/czfkV3hhTTXRRFmpubGRoaYsOGDYSGhmKxWHwOy0kdnTw+Pk5VVRXJycnoDQY++agTEwpuefAP/O2/7+LCDa6dN94+UAwGAw0NDRQWFpKcnDzjIWHf6igtLY3GxkaUSqWtXZR1FHF8fPy8h28C0g3GYuHrj75DeZ/RK6ebM5yt6HAyceaiWZ066IxzeQEP4TWDwUBlZSXR0dHTikN8dUjJ5XJ0Op3H47q7u2ltbaWoqAiTycRrh+oY0WiRqSIwjfVz3Y8f5fmffYcvFDlvW+DN/fX19TEwMEBeXp6tvbM7hJONM+0zz8bGxmxOKoD4+HgSEhJcJqAEEn83chwc0/Kd17sYE8P8cj5XK/qR4+2Mjo4SHR3t888sKHRch9dcme7Dw8PU1tba+qp5OpcUPK20FouF+vp6dDodmzZtQqFQMDY2xhs1A2h1egRlGAgCZpORPT/4Nf/4xXfZVJjt9DpSMqSampoYHR0lIyPD544ugiAQExNDTEwMubm5GI1G1Go1XV1djI2NzXlzSH9S3jrAjfs+w4B/RA4zY+hWekcmqGloRm4xEB4ebvuZhYVJv7YUZ5yUh/lcMy+muyiKtLa20t/fz/r16736QXvCndCtU1ITExNZsWKF7WHSP6bjSPsYCQrD1GqqDMein8BkNPCV7z3Ca7/6Hmvzp2cjenLGmUwmqqqqCA8PZ/369TY/gBQ8WQshISGkpKSQkpJiS0AZGhqitrZ2Rg/4QEwq8Zfp/sJnDTz4Wr3PTjdX2GfFOTIhj+SLG/OZnJxErVbT0NCAXq+flpvvrvLMU7faReF1d3oBB9PdaDTaBFBSUuL3D6Irn4DVenA2JfUfR9sIkUHvsAYAQRkO+omp+zXoufyeX/LW775PYXaq7TXuxGiNxWdnZ5Oenu7x+Nlgn4CSnZ2NyWRieHiY/v5+GhsbCQsLw2Kx+HWl94fQ/+vFQ7xYMTgrp5sznIXW7Clv6uai9cuIiIggIiKCJUuWTHOEtrW1IQjCtKQd+8+olJ7ui9Z0twrP2gLZfniCv3Fc0UVRpL29nZ6eHqfWg9FsYf/RNpLC5LSNnjyHKhzz+KljDHot27/1P7z7+/vJz0h2eh0rg4OD1NfXs3r16mmdReYqBVahUJCUlERSUpKtm2lDQwNdXV10dXX5pRX0bB5YRpOZ//jDe1QPmGbtdHOGK0eclbITXTO+5tjz3bo1srZ+DgsLswn/dJy7BuD/n7TjBWQyTCYTbW1t1NXVUVxc7JXIvf1Q2QvQbDZTWVnJ+Pg4mzZtcrpFeLuyg8FxHeEhp0QrU4UD0x9aeu0kF931P7T1qoGZYrS2lWpubmbjxo0z2gfNR7abtZtpdHQ0ubm5rF+/nvj4eNRqNaWlpVRUVNDR0cHk5KTXjSt9WdH7Rye44KE3qB7wPlNSKp6EXtnSi8nsPlpi3RoVFhZSUlJCXl6ebeJOd3c3XV1dDAwMOI3uSDHdb7rpJpKTk1m9erXT7wuCsEIQhM8EQdALgvBdh+9tFwShXhCEE4IgfN/thezwu+nu+IG25qtrNBqXeeOu8GVaizUzztp5ZsmSJWRmum468PdPGqb+Yjll7guCDEEZimjQTjtWO6Hhgr0/4+PHfzjNGWfNjZfL5S7bSi2EohbHHnFarRa1Wk1TUxNarVbyPtV6j95wpKmXW/98GKMQ2NCgK4+7Fa3BSEPnACuzpS02giDYzPzMzExqa2uJiYlhfHyc9vZ2AFt2Y1RUlCTT3dcOsIIgyIHfMxUk7ASOCIJwQBTFWk/vI6B7dOvwhJCQEFatcp+A4gxfhC6TyZicnKS8vHyG+ezIid5RDp3oA2BSN/3pLFNFYHYQOsDE+BjnffNnPP2Da4mMjESn01FeXk5GRobbMTwLMX89LCyMjIyMGQk7bW1tthx0Zwk73q7oT398nIcONoKfnW7O8LSiw9Q+XarQZ5z/ZGtn66ptNBoZHh6mp6eHvXv3UldXx8svv8xVV13F0qXOQ7Oz6AC7CTghimIzgCAIzwG7AI9CD4jpbi3xrKmpoaioyOcED2/z5K3efK1WS0lJicfum09/2mD7+5Bm+kogU7puMDk2OsLXH/orXX2DHDt2jOXLl3uctbUQVnR3WPepS5cuZePGjaxcuRKlUklbWxuHDx+mrq6Ovr4+jEajV0K//5nP+OlbTZLLS2eLpxUdZlfg4rhHDwkJITk5mRUrVvDUU08RFxeHUqnk3nvvZXx83M2ZfCID6LD7d+fJr3nE7z99s9lMdXU1giBMG57gaydYqdln9qOQIyIiPObIT+pN/ONwMwCxYQqGNNP3jVP7dNeMjY7ytZ/+lU8eu19SZd1CXNHd4dgRdnx8nKGhITo7O9HpdGi1WpRKpcuEHaPJzJ7fvcNxtSUgTjdXuIqh2+NPodsjk8kwGAx861vf4t577/X5GoHA77+Bmpoa4uPjWbNmzbRJlr70TZdaoDI2NsaRI0fIzMxk+fLlkq514FgLmpPmemrMzAopQSZHCHFfOTU2OspF3/kVEzrPH66FvqK7QxAEm0Nvw4YNJCUlERoaSldXF4cPH6ampoaenh5b66/e4Qm2/fQNjqv9N89OCqLFAmbP6c8tvWqGNTO3ZVLwlDDjS8djL+gC7E3HzJNf84jfV/SioqIZH1JrLD0QnWC7urpob29n3bp1khMVRFHkGTuzPTLE+S9OporAbHSfTtvX18e5dzzEZ//3I1RK1z9Ob6yZhVbA4ojVzI+Pj5+RsFPZOcojn49ilnlXdegPpJjtViqauznPRXqzO9y1vJqDh/MRYJkgCLlMCXwPcI2UF/p9RXf2Q5hN8wlXQrdYLNTW1jIwMEBJSYlX2UgVbUPUdA6fOpfZ+b15Mt+tdHf3sPWbD2N08x69LWtdSCu6I/b3Zk3Yyc7OpnxUxc8/18yLyEGaI86Kr51hPXV4ldoB9qyzzqK+vt7a3ORmQRBuFwTh9pPnSD3ZGfYe4EeCIHQKghAtiqIJ2Au8BdQBL4iiWCPlvufEQzKbdlLOxKHT6aioqLDFOr1dAW0htZOMTDg349w55Bxp6+jg/Lt+yYePfg+53Hl4TSoLeUUXRZGhcR3tY/2MHO+jb1hD78gEgxNGPmg3OO2xPmf35oXQy074vwW0KIq+dIAF2OdwHlcdYBFF8Q3gDW/vbU6E7muDSGd7dLVaTV1dHYWFhbYuo94wPKHn9bJW279FUaRr0Ll3VJArEBQqySbhieYWvvjtR3jvt9+dIdb5XtFdPTwm9Eba+kZoHxyla3Cc3mEN/WOTDI1pGZnQoTOY0BpN6Awm9EYzRrMZiwhwauWSywSMJgOq5Hy/3rO3eGO6lzd3Y7GIyGRetqhy83sxGAwLtqgoIAkzjsy2QSRML4Sx1qz7wkuHmjCYTgkuNSaU7u5hl8fLVOGYvfgA1TWcYPu9v+bgI9+e0ftcKr4648xmC93qcdr6R+kYHKNnWEPfiIb2viEmDRYmDGY0OiM6gwmDyYLJYmHqMiLYX08QsGYGzrxvGY5fshj1YLGgsOgxyebvg+7Niq7RGmjqGWJZRqLngyWyUAtaYA5Nd1/36EajEZPJRHV1NUqlclaFMBbLdCccQFKEEndGnEwVgXnC9YPAGRU1x9n1/d/z6sN3ThOKYw7+yMgIUVFRXiUETeiNvFXazPvV7dR3DjKs0aLVmzCaLVMPBwcVnnpgiFMzOK0IU/8RrKL2cbcQIojoT74v7dgwIbGpHl4ROCxePJBhap/ujdA99Z5fqN1l4DTYo1tDZ1lZWZLnnVvNZMdfyif1PbQPaqZ9LSzE/SdcqkPOkcPlVVz9X3/khQe/MXUeu3sxmUxUVlYiiiI6nY6QkBBbamp4ePi0h0NDt5oDhxv5vL6b5r5hNFrnq5YoWqZWZauYZ6zKvovZFYIAOr3Odr9mnYYQJw+buUBqaM2e0hNdXLm1SPLxp2vTCVjgpvv4+Dg9PT1s3LjRp3nnjkJ/2mE1Bzy2nRLkIQgKpVdmoZWPDpVy7X//ib/9fzcBUyuCVqulvLycrKwsWxNKa7VU3fEGPm7oo6p3krquEYafKsPsUIARGapEo3NcuYSppJQ51pfZoJ++PRHNWAyTyFRzv6qJZu9/P+XN3jnkTtfhDTCHzjhnc9RcYa0UGhoaIiUlxSuRg/MEnW71BO9Vz8wtGBqb8Hw+ZThmH4QO8PYnh7j15yH8/NbL0Ov1lJaWUlhYSFRUFM09al493Mi/67to6RthbNJw0tQWmG5nn0KjMzDninaCaDEjijPHE5knx+ZH6D78fhq7BhnX6okKk+ZXkNJdZtGs6M7wZkW39pCLiYlhxYoVdHd7HwZxdr3nPmvE4tiQUYDOwTGP55OpIjBPjnh9H1b++e4nGHRaVmcl02UIpfatN+kcGj9ZSONM0As3hg5TD2KL2eDUejPrNSgC0DzS4z15uT+HqZ1OZUsP56zMkXT86doBFhaY6W5tTLFs2TKSk5MZHx/3OSxnv6IbTGae/+zEjOPSopS0j3sOeQk+7tPtef9oDR92msBFcs7phGg2IriwKgTRgkWvQR4aNbf35KZ9lDvKTnT7TeiLfkWXEkfv7Oyko6Nj2kBDX6auwEyhv13VyeD4zFTWUEGa80amUII8xGtnjz1Gs4VQQYYoDwGzGZjbPHB/IVrMiBaz2xXboh2fe6H7uLXyJkPudO0uA3PQYQbch9csFgvV1dUMDQ2xadOmaVNLfZm6Yr2e/eue/qTe6XFx0dLNLF+9744IggByOcjnpmzT31hMRo9muVmnmYoCzCG+mO4Axxo70Wg0kvIWpITXrIMhFxrzukfXarVUVFSQlpZGVlbWjA/QbGarW1f0xt4RDp3od3qcXi99hZYpw7FMjnp9L86whrumVncTC31PbmVK5J6PExCx6DTIw2Y/plgKomhB9NHaGpvU8+/SamJDZURHR5OQkOCyw46UFX1R79Gdme7W8UvuJqX6Q+jPfNro8rj+EY3L780452w9yU5WDEEQEOUKEC3TWlktRETRgmgxSXaymbVjcyd0H812K5OKKL64sZCxsbGpGXxtbchkMluHncjISARBkOSMW6ime0BWdMcUTnvT3dpEcXBwkI0bN7rNDfZ2Yqn96ywWCxN6o625hCMqhYyeYekdQGQhqqkuKW5aCfuCIAggyBEFYUE76kSTcy+7Kyz6SUSLBSEAfeUdma3Qy050sfvsqQm61twGg8HA0NAQ7e3tNpNcFEW3od5Fv0e3Cs9kMlFeXo5er/co8tlgtQQOHD3VXMKRjNhQZ4usW2azT/d0KUGQTTn8BNcx9PlC9OEBNGW++72VklN83Z9bcdZxRqlUkpaWxqpVq9i0aROZmZno9Xq6uro4duwYzc3NjI6OTluI/NQBVhAE4bcnu7xWCoKw3u57ZkEQyk/+OeDNe5yTPbrV7Dl8+DA5OTm2oQaBQiaTodfrefLtCpfHxIR6/9ZlqnAsWs9xd+d4Fu+Uoy5kKp3TYmRBJMaIIhazyaesVrN2HHm4+759/mC2K/rxjn60eiNhKue9Da0ddmJiYoiNjSU6Oprh4WG6u7s5fvw4ERER9PT0MDEx4dEZJ6ED7JeAZSf/bAYeO/l/AK0oiut8eIuBWdEdTbze3l60Wi1r1qwJuMhhyux6t7Se1mHXT3q5D+EtmXIW+3QvFmlBJgO5cl5yxh0RzQafb8Oin5ianBJgZruimy0i1a29no87uUe3NoQsLCxk06ZN5OTkUF9fT3l5OVdddRXf//73mZycdHqOrVu3eiqv3gX8VZzicyBWEIQ0X96XPQE13a0DDbu7u4mIiJiT0ENvby89PT183uNeyBNazxNXHRFCVCDMTWMFQRAQ5CEgkzNfpvxUzNz3MJkgMCfmu2ic3YoOUCohnu7MGWftsLN3717S09N58803Offcc30uo8Z9p9dQQRCOCoLwuSAIu705acCErtfrOXbsGAqFguLiYp9rrKU2bLDmx3d1dZGQtoSPm9Ruj7fOWfP2Xnzfp/smVkEmn5fV3V2aqzeYtYEV+lRobfZCl5I44ynXXavVkpSUxKWXXhqQ4ZZAtiiKG5nqE/drQRAkN70LyN2MjIxw9OhRcnJyWLp0KYIg+C3LzRkmk4mysjJEUWT9+vX8q24Ao9m1sKJCFQyOOTetPN6PnxJnvGE+Vnd3aa7eEGjzXTT5nq1oT9mJLo8LkafqNT/NjXfZ6VUURev/m4EPgGKpJw2I0DUaDcXFxdNmnvujy4wzJiYmOHz4MGlpaRQUFCCK8EpZp9tzpjtp7ywVn4Xuh9ZQp1b3WZ/KLSmxESgV/rmIIAiYfXZgema2+3MrA6MT9KjdWx/u4uj+GiUNHACuO+l93wKMiqLYIwhCnCAIKgBBEBKBc5AwocVKQIS+ZMmSaamsEJhOsAMDA7bRS2lpU/6Kj+t76Bp237M7Sun72xZCwmAOBxLMuL4gTI02CmATxnDBhMHov1XYEkDzfbYed3tKnUxatcdTwowUsTt2gN23bx/2HWCZavzYDJwAngC+efLrhcBRQRAqgPeBh6XMXLMyZwnX/lzRrf3jBgcHKSkpmTaV5ZlPZjaXcGQ2pqQgCMTGxTGiHvL5HLPFmmSTGBVKdFgITb0jfjv3+rwUjta3+e18ABbDJKLZhBCA/P6s+HBaRv1iMFHe1M1lmwtdft+dkKX6n5x0gOXmm29+3O48InCnk/P/G1gj6SJOmJPwGvjeCdZxb28dhazVatmwYcM0kXerJ3ivxvPgilEX7Z2lsGl5JhPMHL/sGf/vrQcnjLSptWxesQSFkxbT3hITrqKp23ldwGwIpPne2t3P8swkEr0oUHKFFIecK6HrdDqnY7kXCnNmg/pquttXsGm1Wo4cOUJCQgIrV66c4fh41klzCUdEUaR7yLcP3YZl6RxpHUYW5kuYMDAba7NF5PCJPrJSE8hJjp3VufJTohke9/0h6I5Ame+iSc/xjkEMJjNrcmbXmLKmrQ+90bc05IXcRgrmWOizMd3VajWlpaUsX77c6bxzg8nMC06aSziSHKVi3EWDRXeszU2hvGNsKsQWGun1Pl0VEtj4e0vfKN2jOjavWOKTU2jlkgSONHR4PtBHLEatzxVmrhBF0bZHH5vUU9XaS0mB79aNwWSmrt03i2Yhd5eBOTTdZyP0vr4+Ghoa2LBhg8tKt39VdjhtLuFIUpT344IKMxOp65u0Gd9KhYIl6clenUO0BD4sZjRbOHyij4IlyaQnSLc6VCFyhse8zyvwBkEQyIrx7x59Zvxc4EhDJ5mJMSRF+RZZKXPhkPO0Bw+u6CdRKBRem+4Wi4WBgQEmJiYoKSlxm23k2K/dFeEe2js7kpcaR8eYEdNJocZHhvLXvRdzYVGuV+exzGEjhobuYUa0ZkoKnE71mcHa7CS6Bv1Ta+8Owc9Zcq4y4lr7RhjTGlmfL609uD2uRipbLDMbYdqzkNtIwQI23fV6PUePHrXN6XYX1mjocd1cwhGzFw+bjIQohvUwaZi67/zUGF74znbC9UOsyEzy8OrpzPXMRK3BxNHmflbnppEU7Tr2n50cw9GG9jm5pxMdPcSp/OercBda05sslJ7oZn1+hstiFWe4cshJafW86IQ+W9N9dHSUo0ePkpeXR3JyssfMOHfNJRxRS8yIS4wOwyRTMaqd2ld+YUU6T++9iKGOJsLDw/nK9vMJUUjfd3tyEgaKmo4h9KKMDfkzi4lkgkCIYMFknhtrQwRSw/33c5CSLFN6opvY8FByU6XN6esaGnPakERKY8ig6Y708Fp3dze1tbUUFxeTmJjoOTNOb+RlF80lZiJKau8cGRqCXKFk4OSe/6otS/n1f2yhsa6azMxMcnJyCA9TsXrpEg9nsrvyPI5BHtcaKG0dpDg/g9iIUz0A1i9NoaFzYE7vZXjYf/kHUpNleoY1tPcNsypTmtidme+nc3cZWEDhNVEUOX78OH19fZSUlEzrBOtO6AeOtaKR2PstPTYMg8n9wyZMqSAtKYGBSTMyQeDuLy5n9zIVR48cJjw8HIVCYbMwtqz2dnro/DaUKG8dQB6iYm1uKknR4VQ1uU8VDgRtPYOzSkG2x5usOLMINZ3DLE+PI0Ll3inozHw/nYc3wALZoxuNRlul27p166Y15nP3OlEUeVpCJpyVxAj3ezWFXEZeZjJNAxoiVCH8320X8NWSbERR5KyzziItLY2+vj4OHTpEdXU1y73cp/ujSGS2qDU6qjrU5MarMPgYM54t6ZGz/znIBHjmP7/CHZedxYol0n8P9d0jhKlUFLgZruhM6J726Au5jRQEsGecI64Eq9FoqKysZOnSpaSkpDh9nas9elnrIHVd0iedumvyLwiwJi+dio4R0uMi+L/bLkChVdPXp2H9+vUoFArCw8NJTExEFMWp4RLIkAmC5P23TJhaWeabgpRIBrVmMuPCGJowotHPreC7u3uA2FmdIz5MRlq4yJ2XbuR7V22jpXuAZ978mMYhA4cbutAaXFt5g2OTDI1NUlKQybHGrhm/v/KmLlpaWklOTrINvTzd9+gBy3V3rD93Fl7r6+ujqamJNWvWuGxK4a63uzerOUxl1rliQ8ESStuGWZudyO9v3kZfezOy0FDWrl0748FlbS20dvVKCnMzqGmWZgILMmCem72mRatoVutRhcgZV0+SEhtBRGgIfaOByYhzRkt3H/kr0+jwUHzkjqUpsYSEhNDU1IRGo8FoNHLdxSVkZGRgNIscOt7O++UneK+iifb+kRmvF4EjDV0sz0xkaGxiWtmywWShZWCM8fExdDodsbGxyOVyt+G1hdzTHebJdBdFkRMnTtDR0UFJSYnbH5ArS0Ct0fFGmXfFFxNG58vp5hVTIr90fQ77vnEe7Y11xMfHU1BQ4DHLzJt9uiDOr+mulMtAEYLRbEGjM5KbnkTPsIZJvYlV2d4lAM2W5LDZmTa5SVFkZGSQn5+PTCYjPz/fliJdV1NFXlwI9115Lh/+8nbe+Z/b+NE1F3L2yuwZWXP1nYMYzBaKcqenz3aM6FmxYgXFxcUkJCTYJvtWVFTQ2dk5Y9GQYrrPsjHk9YIgNJ78c71XPyzmsHrNvhNsVVUV4eHhbNiwwaOQXJnuLx5qwuBFWEghE+gempmwsakgg8Mtau760jpuOncpNdVVLFu2jISEBEnn3bx6GfsOfCDxLubXbl+5JIHy9lOddxLjomnq6mdcq6e+o59NyzI43Oi5KMgfdHR1gSDtZ+yMrIRwNBoNVVVVrFmzZprIJicnGRwcpK6uDqPRSHx8PF/ZsoybLtnIhN7IJ9UtvF/exPsVTQyMTjA2oaeypZdNy5dQdqILo9lCZWsf/3HysxcdHU1cXBwJCQnEx8czPDxMfX09RqORuLg4jEajpBRYXxtDCoIQD/wXsJGpD9ExQRAOiKIoed86Z6a7tSXUkSNHyM7Oltwk0tmKbrGIPOtF7Bym2js3j00X2vr8dCq7x3nkuq2ckxtNTU0Na9as8WqvtWWN9BVdLhMwzkEqrDPW5iRNEzmA0XJqdTOZLRxu6GDT8kyONnYT6Nvs6B1kxeoltAz51uknOVxGVVUVRUVFM35f4eHhZGVlkZWVhclkQq1W09PTY+vYujYjkQvXXoRCsYOatl7eOyn6Iw2d5KbEozcaqWjusVVGjo2N0dvby8qVK1EqlaSkpJCSkoIoioyOjvL444/z4YcfMjIywlVXXcU111zjNItz69attLa2untbtsaQwOeCIFgbQ54HvC2KohpAEIS3ge3AzJpXF8zZij40NMTk5CSbN28mJkZ6C2Bne/SPjnfTMeRdbnZc2PS3uiYnha5RA3/bewlJIXpaW1tZv379tLJXKSTERLFsSSqNHZ67iArz1LM9LTaCE30zrZnWwXEEYXrW3uH6TlbnpNDaN3pyFnvgiFeZafHxtfqhLtZ+Yf2MBieOKBQKkpOTSU5ORhRFNBoNg4ODVFRMtQJPSEjgxguLuHv3OQyNTfJhVTOfVLXQMzzO8PgkSplITU0NRUVFREZGYrFYEEURs9mMxWIhNjaW++67j08//ZQf/OAHHDlyxK3TzgOuGkO6axgpiYALXRRF2tra6OvrIzw83CuRg/NpLVLz2u1RCKfOsTwzAVGu5Nlvb0M71MPopIn169f73O9r8+p8SUKfangxt/t0hUxGRLiKnrGZueyjkwayUhJo652exFLd2kdWUgzR4Sq6PbRXmg0tbR0Q4r1vQAAuPGudR5HPeJ0gEBUVRVRUFLm5ubZpLG1tbWg0GmJiYji3IIVdWwpBkDE2Pk5lde20rYH1M2IVs8Vi4d///jfNzc0UFhaydetWr9/PXBAwZ5w1JFFVVWUrSvF1xJI9XWoN79dIH3VrZWRs6gObkxJLTloyf/nmF1F3NqNUKlm1atWsmvptWb1M0nHz0aZ9fX4qJ3pdF6ykJsQ6/Xr7wCiTOj2FS1zHm2dLz+Aw+Une9+BLiVYRGzX7mLV1GsuaNWvYvHkzaWlpjI6OcuzYMcpKj1FVUU5+fr5bJ1tpaSnf+973+Pzzz6f1SPQRV40hXTaMlErAhK7T6Thy5AixsbE2IfnaCdaeZ/99wqe88cExLYmRStakRXLXuRnUVZWTmppKXl7erJv6bZa4Tw+Z41HJq7MSOdLU5/YYE67NzJEJHSe6Btm4LHBDN2IU3sfwsxP9n5gik8mIi4tj2bJlrFmzBoPBQEZGBp2dnXz++efU19czNDQ07fNbXl7OXXfdxf79+8nOzvbHbThtDAm8BVx8skFkHHDxya9JJmCfvJ6eHgoKCqZNpbCmwfq6h5HaXMKR8BAZglngni+fy4XLE6mtrSU8PJy2tjbGx8dJTk4mJibGZ8GnJ8aRlZpAe6+nPO65258nRIbSNTLpsWquY2jC7feNZgtHGzrZtDyTIw3dfn8HDc2tyMLTvXL+ZSUELjFlcnKSyspKioqKbGFfs9nM8PAwAwMDNDQ0UFZWRn9/P//85z959dVXWbpUWnv1r33ta3zwwQcMDg6SmZnJT37yE4xGI3fcccftoig+zlRjyB1MNYacBG4EEEVRLQjCfwNHTp7qQatjTioBE3pubu4MJ5qvzSesvFXZwZDG+wkrS+LD+d7lZ7MsfirBoqSkhLCwMFvnmq6uLurq6oiOjiY5OZn4+HivH0abVy/zKHQ/tQP2jACpCdHUdHguIBnS6MhIiqNrwH2k5nB9J2vzUmnsUjNp8F8m3eDIOMuSZbSPS7f0shMC01tfq9VSWVnJypUrp+V2yOVyEhMTbVmRIyMjPPPMM8TExHD99dfz9NNPk5eX5/H8zhpDAtx+++2Pg+vGkCe/9yfgTz68LSDA4TVHfBW6NTQnpcOrIxlxEfzy2i8Qohump2eQDRs22HLp5XI5SUlJJCUl2UIl/f39NDU1ERYWRlJSEomJiZI88WetXsaL73zu9hjZHOm8MCVKksitpEsQOkBFcy8ZcRGEKmWoNf7zyMeFQrsXPr/sAKzoWq2WiooKCgsL3Y5Gbmxs5Cc/+QlPP/00a9asYXR01Gun4Hwwp5tGX7rMwJQg6zqHONzkXT+vddkJPHrDF+jvaEZUKFi7dq1Lp5sgCLb52KIoMjExwcDAABUVFQiCQHJyMklJSS47fUrZp8+Fzpelx9HY76WnXCa9MUPX8ATxUWEUpMfT0O2V9eiSxtYO5FGZmCXa7/423XU6nU3k7qJCLS0tXHfddTz11FOsWTPVednbKNJ8MadCn03fuOe83JtfWpzFT65YT0NdDcnJyWRlZUl+rXVwXmRkJLm5ueh0OgYGBmyZVomJiSQlJREVFWWzXLJTE0mKjWTASdOCU+f16i14TWRoCOM6k63tlVS6hr1LWlGPa9FoDaxfmkZpU49Xr3XG8JiGdUvDqet17y+AqYdlQqj/JqPodDrKy8tZsWKFW9G2t7dzzTXXsG/fPoqLJU9CWjCcFqa73izyytFWycfvvXg1N30hl+qqCvLz80lMnF2IKDQ0lCVLlrBkyRJMJhODg4O22GtcXByJiYn09/ezKieND8pdZ+wFukx1WXoCZa3eN5LoG50kNT6aXrX0NtgGk5nSE11sXrGEQ/WdzNZeUVmk+V7iI0LoamvhhFZLXFwcSUlJxMbG+hQetRd5bGysy+O6urrYs2cPjz32GCUlJV5fZyEw56a7L0J/v2HI1rfNHSFyGQ/v2czZOVFUV1ezevVqv9cIKxQKUlNTSU1NxWKxMDQ0RF1dHRaLhdU5qe6FHsASoo35qRxt9r1bTEy4il4fLPFDxzsoXppGXccgulmMcao70YoiNsujNZKbFMXatWttnvD+/n7q6+uJiIiwOcyk+FT0ej3l5eUsX77crch7e3u5+uqr+c1vfsPZZ5/t7dtaMMy56e7NHl0URerr6/lXw4jHY+MjVfzhxnNJDtHT3NxMcXExKpXK4+tmg9FopKWlhfz8fFJTU4lKOsGjr3zs8nghQNG1JYlR1HRKr8t3RnRMHPjYVqqsqYf8tARGJvU+T6kdm5ikcIlA86j7H1JO4tT+3NETbu9TAWzbq4iIiBnWpV6vp6ysjOXLl7tsHw7Q39/PlVdeyS9+8Qu2bdvm0/taKMy56a7XS5t+aTKZqKyspH1cpHPUfauo/JRoHr95Kzp1D+pxHevXr59NvrEkJiYmqKqqmpYrsH7lMhJiIhkadbVP97/SlQo5crkCrcE3gVnpHfM+bGnPiZ4hkmIiyE+L50SPb066SIXnEJszR5yjT8VgMDA4OEhzczMTExM2Ez8uLg6TyUR5eTkFBQVuRT44OMiVV17JT3/6Uy688EKf3s9CYk7Hgko13a11xSkpKXzQ6v4DfO7yVJ658wLUnU3IZDLWrFkTcJEPDw9TVVXF6tWrpyUEAWxa5Tp5wptW01JZm5tC68Ds55p1D0+QGDM7b/bA6ARdgyOsy/NtNFLtiVZUCvcfyax4z6EspVJJeno6RUVFbN68maSkJAYHBzl06BCffvopcXFxbrd0w8PDXHnllfz4xz9m+/btXr+PhcicCl2K6T4yMkJpaSkrVqwgJCKGgxWuxwRduDSKOzbGUF1+jISEBPLz8wOelNLb20tjYyPr1q1z+mHZ7CbvXamUHsaSwtqcZI8prt6QmSytS6o7tAYTFc3dbF7u/fCECZ2e5cnuhextDF0mk5GQkEBubi6CIFBQUIBSqaSyspLDhw/T3NzM+Pi4rQZjdHSUK6+8kvvuu4/LL7/c6/ewUFlQXvfu7m7a2tpYu3YtKpWKJ98/jtFJcwmZIPCD3evZVZRCVVUVsbGxdHd3Mzg4SFJSEsnJyV6Xm3rCWoWnVqttPeSc4a7jjD+97skx4bQM+LeyTO+njDdRnHLSbcjPoLK1z+nv0BUW3TjuPPi+xNANBgPl5eXTIjA5OTkYjUYGBwdpbW2ltbWV559/nvb2dr71rW9xxRVXeH2dhcyCiKNbW0uNj4/bykVFEaex8wiVgl9fdw6FCQrq6upYv/5UTfLk5CT9/f22JBer6Gc7ztbqFDSbzaxbt85tKGdVXibREWGMORnN7K/MOJlMIC4qnPru2TngHNHi34fjsRNdLEuPZ2hch1pi6nJNYwthqcvQOvHgJ0WpPLZqdsRoNFJeXk5eXt6MMGtISAhpaWmkpaWRmZnJk08+SXJyMr/61a8YGBjgnnvu8epaC5mACt1Zg0hHodu3lioqKrIlQnxc30OnenoCRUZcBI/ffC4qwyidnb1s2LCBkJBT5nB4eDg5OTnk5OSg1+ttSS4mk4nExESSk5OdemHdYS21jY6Otpl/7pDJZGxcmcd7R2pmfM9frriS/DQOnfCfyW6lU60hNjKMEY3/GkU2dquJi1CSERdB17DnhBidwUhRchgVXTMdmlnx3q3mRqORsrIycnNz3eZSaLVarr/+er72ta9x8803T92HbnbOyYXGvO7RdTodR48eJSkpiaVLl9pELgjCjDFL67ITeP7uL2Ia7mZycpJ169ZNE7kjKpWKzMxM1q9fT3FxMWFhYTQ1NXHo0CEaGxsZGRnxWBtvMBgoLS0lOTnZq3JWV/Xp/ljRs+JC/bovt0cUISdt1jXVMxieMKDWaMlLlJYTbpxwXj+f5UUxi3Ulz83NdVsnrtPp+PrXv85Xv/pVbrrpJtvX3Q30dIenBpCiKHL33XeTn59PUVERpaWlPl3HW+Zc6NYV3VrgX1BQQGpq6jSRd6o1fFB3qrnEpcVZ7Lt1Kx0n6oiMjKSwsNCrTCiribZ27VpKSkqIiYmhq6uLzz//nLq6uhl1xjAVPistLSUvL09yfzsrm13s02er85hwJVpREdB+bqGhs9vmuEJrMNE6qGFTgeefZU1jC5FOTHSpjjhrCC07O9utyA0GA9dffz07duzgG9/4hl8cuTfccAMHDx50+f0333yTxsZGGhsb+eMf/8gdd9wx62tKYU5Nd2sn2J6eHlpbW1m3bh1KpRJRFKcJ9/nPmmx11HsvXs3N5+ZRVVluG7o4G+Ryua2HmMViYWRkhP7+fhoaGoiKiiI5ORm5XE5DQwOrV6/2qVf32mXZhKmUaPXTK7xm+znKTo6jsn1wdifxwNBE4PrEWcSpcteNyzIob+51mQVnMJlZlhhKmYP5LkXoJpOJsrIysrKy3H5WjEYjN910E9u2beOuu+7yW7TGUwPIV199leuuuw5BENiyZQsjIyMIgpB2ssFEwJjTFR2mspK6u7ttjRgFQZgmcoPJzEuHmlAqZDzy9bO4dnOmrUZ4tiJ3RCaTER8fz4oVK9iyZQtLliyhu7ub8vJyVCoV4+PjGI3S5rrZE6KQs6HQu/npnti0LC3gIgdoHRgnMiywGYVHG6ecdDERrq8z0DMzrOrJ425dybOyspxO/bE/7tZbb2XDhg3ce++9c9cngKm8+SVLTnWFyszMBC8bPfrCnAndbDZTUVGBKIq2clGrqW7Pvyo7EIG/3nEBG9KUNDY2Ulxc7LZG2F+MjIxgsVjYtm0bBQUF6HQ6ysrKOHbsGB0dHZKz+sD5Pt3X8FpuSgzlbYEXOUyNd87LCPwwh7qOASJUIWQlOf+9tvUOEqWanvgUbpl0mYdhFXlmZqZbkZvNZr75zW9SWFjID37wgzkV+XwScNMdTlUJZWRkMDExQW9vL0lJSU5j0UeaB3jh7oswjPQxMDDBhg0bAp7p5ix8Zk2pzMvLQ6vVMjAwQFVVFaIo2sJ27hoOONunCz4ku4cp5RjNU2OC5orw8MDs0x3pHhojKkzJ6uxkqtum9xowmS0sSwyltGvKUx8XHoJZP8GxY+0olUpbU5DQ0FDbIpKRkUFqquusPLPZzN13301mZiYPPPDAvIg8IyODjo5T1kpnZyd42ejRFwIeRx8dHaW6utpW7xsVFUVvby9tbW2EhYWRnJxMYmIiISEhmMwW7vnSGtqaGggLC6OoqCjgvwyz2Ux1dTWRkZEsX77c6fXCwsJsAwEMBgMDAwPU19djMBhISEggJSWFyMjIaa9dvyIXpUKBwW4F8mVFX5mVzLFm7xpuzJaRybkbujiuNVDX3jc1Madhenff8RE1MGXe5yRGkp+fT35+vm0SS01NDSaTCaPRSHp6uluRWywW7r33XuLi4njooYfmbSXfuXMnjz76KHv27OHQoUPExMQQ6P05gOAhxDQr/25XVxcNDQ2sXbvWlqlm3Y9bK476+voYHBxEqVQSHx9Pb28vmZmZZGQEfNuCwWCgoqKC9PR0n65nrU3v7+9nYmKC+Ph4kpOTiY2NRRAEdn/3EY7UNtmOX1lcQsuwdBGtX5pCacvcmOz2KOQyZLoRtBLnzvuLTcszOXaix9ZpRiYIpCxdjXrCwK7iTP7nynXTjjebzZSVlREREYHJZLL1B7AWsFg/axaLhe9///sA/Pa3v51Va29P2DeATElJsTWABLj99tsRRZG9e/dy8OBBwsPD+fOf/8zGjRsD/tQJqNCHhoZQKBS2SZTunqIDAwPU1tYSEhKCSqWyecYDVWpqrT7zZs6aOywWC2q1mv7+fkZHR4mJieH5Dyt58p8f2Y5ZWriGbq00IyotPpIxrYmJORablawIMy19I3N+3dXZKbQNjDKunfL+n1WyntLOCe7+YgHfvKDAdpzVXE9JSbE9pK1RlIGBAdRqNXK5nKNHj9LW1oZer+fxxx8PqMhnQcCFHlDT/bXXXiMvL89j2ujAwABNTU1s3LiRiIiIaXtiwG+prFZGRkaoq6vzOXzmDJlMNqNT6LL06eOUVUolaD3vtRUyGRGhKnpG5m6UsSPJSUnzIvTqtj6WJMUQHaaiSz3OyNAAED7N4+5M5HAqihIfH48oinR3d/PII4/Y8jVeeOEF9uzZM+fvaSEQUKFHR0fz29/+lvr6ei644AJ27dplm9gCU+Z7R0cHAwMD0+ae2e+J9Xo9/f391NbWYjabSUpKIiUlxefOm/39/bS0tFBcXOxz9pMnBEEgLi6OL1+8lR88cQDzyWQcg0EPeK5gW5+fyuEApLh6g8Ywd84/RzoGRokJV1G4JInjLR1kLiuyxdAtFguVlZUkJyd73G79/e9/Jzo6mvb2dgYHB+nt9Tw260wloKa7Fa1Wy8GDB3nppZeoqKhg27ZtXHrppbz22mvs2bNH8twzqyOsv78fg8FAYmIiKSkpkvPX29vbGRgYoKioyG36rL8YGBjgK/f/lqbuqdbLRRs20Tjk3hRfnZVITdewx8ELgUapkGHSqDGafG8PNVtC5DLWLk1HGZvCYzeeS6RKTkVFBYmJidNi0Y6IoshvfvMbysrKeOaZZ/zyuz548CDf+ta3MJvN3HLLLbY9v5X29nauv/56RkZGMJvNPPzww+zYsUPq6U/vPboz9Ho9r7zyCt/97ndJTk6muLiYK664gnPOOcerX4i1xLC/vx+tVmvzftt3ZrW9CVGkoaEBo9HIypUr52Sf1t3dTVdXF/881mKbn752w2YahlxnnsWGhyDIFQwHMDvNG5YlKDneFnCHsEcu3ricx755GZWVlSQkJHgU+WOPPcYnn3zCCy+84JdyZbPZTEFBAW+//TaZmZmUlJTw7LPPsnLlStsxt912G8XFxdxxxx3U1tayY8cOTyOS7Qm40OfcM6FSqaipqeHXv/41n332GVdeeSWvvPIKZ599NnfeeSdvv/02BoPnD7pj/np0dDRtbW22OVnWohWz2UxlZSVyuXzWwxSl0traSl9fH+vXr+ectcttXxfcPTcFSI6JWDAiB4iL9o//YjZEhSn5xiUbqKqqIj4+3qPI9+3bxwcffMDzzz/vt54Ehw8fJj8/n7y8PJRKJXv27OHVV1+ddowgCIyNTXX6GR0d9bo+ItDM7dS/kzz44IO2v19yySVccsklmEwmPv74Y1588UV+8IMfUFxczO7du7ngggs87qXlcrltOL39mKXa2lpMJhMpKSl+GaboCXvLwZr9t2l1vi3n3931Ny1Ln/d9uSPzuU8HiAxV8qfvfAX55CCxsbEee/M/9dRTvP7667z66qt+jdY4S1s9dOjQtGMeeOABLr74Yn73u98xMTHBO++847fr+4MFE2tQKBScf/75/OEPf6CyspJvfOMbfPzxx2zbto0bb7yRV199lclJzw0QrWOWrLXjmZmZmM1mDh06RG1tLYODg7Oe6OoMi8VCdXU1MplsmuUQFxXBiuw0t69dlh5H6RwnxUihZWAcuXx+PiIRoSH86Z4rUOrUxMTEeJxW+vTTT7N//35efvnlgDlZ3fHss89yww030NnZyRtvvMG1114bkM+Zr8zLiu4JuVzOueeey7nnnovFYuHIkSO8+OKLPPzww+Tn57Nz5062b9/uMjQ2OjpKbW0tq1atsuXIW0NefX19NDY22irVEhISZp1ia+1Ym5CQ4PQDuXn1Mupau3Hm8vB1uspcoDWYWJqeREPH3FoaEaEh/OnbV6DSDRMVFUVOTo7b41988UX+/ve/8/rrrwdkDpqztFVHj/++ffts5alnnXUWOp2OwcFBvxdi+cqCWdFdIZPJ2Lx5M7/85S8pKyvjhz/8IfX19Wzfvp09e/bwzDPPMDIyYju+r6+P48ePs27dummFMNaQl32l2ujoKEeOHKGyspLe3l6f5sIZDAbKyspIS0tzuepY896dGe7L0hPoHZldq+ZAEh8b+GIie0JD5Dx6+w7CjKNERUWRm+u+CvCVV17hySef5MCBA34f1mGlpKSExsZGWlpaMBgMPPfcc+zcuXPaMVlZWbz77rsA1NXVodPp3NbCzzVz7nX3F6IoUl1dzUsvvcTrr79ua9ivVCr53//9X8kefFEU0Wg0tlTc0NBQ20BFT+ewTuD0NPapXz1K8X/cz4aSzdQOnHK2zXa6ylywMj2WqoYmzwf6gTClgp9ft41oiwZRFElPTycpKcnl7PrXX3+dX/3qV7z++utue7T7gzfeeINvf/vbmM1mbrrpJn74wx/y4x//mI0bN7Jz505qa2u59dZb0Wg0CILAz3/+cy6++GKppz/zwmuBwGw2c9ttt1FaWopKpSIqKoqdO3dy+eWXk5SU5JUTzj7/XqFQ2FJxHT244+PjVFdXs3LlSkkTNc+99QHi0nOoHZiKoy9JjGJQY0Drx1njgSAsRMbkyCCWAAf2Q5UK9n37CmJEDaGhoeTk5NhSisfGxoiJiSEpKck2u/5f//oXP/vZz3jjjTf8ksI8z5zeKbBzxeTkJGvWrOGJJ55AEASamprYv38/11xzDUqlkp07d7Jr1y5SU1M9ij4iIoK8vDzy8vKmdZWVyWS2VFytVkt9fT1FRUVEREhrb7Rl9TIa1FMi99d0lblAa7SQm55IU1fgLI9QpYInvvVlYkQNKpXKFiGxn11vzWF//PHH+fDDD+nt7eXNN988E0Q+J5wRK7orRFGkvb2d/fv388orr2CxWLj88svZvXs3mZmZXq30Op2O/v5+urq60Gq1ZGVlkZGRITn//qV3D/H3j45TPWCgZFl6wBo8BoKNOXEcqvZubLVUVCEK/vit3STKtISEhHgcwvHhhx/ywAMPcMEFF/DRRx9x//33c9lllwXk3uaQoOnuL0RRpKenxxaC0Wq1XHrppezatUtyjL2zs5Pe3l4KCwttkzxNJpNtpXe3unf2DbH3D/9EHhFHRfuQP99awFmblUBpbYPfz6sKUfDHu3eTpNChUCg8ivyzzz7ju9/9Lq+99prN6z2bOeme0loBXnjhBVuTirVr1/LMM8/4dC0PBIUeKPr7+3n55Zf5xz/+gVqtZseOHezevZuCggKnKbQtLS2MjY3NmO1mNBoZGBigr68PvV5vE71jIwqAW3/zCsc6NYxpF072mxRiI1So+7v9mn+vVMj5v7t3kxKiRy6Xs2zZMreCPXr0KHfffTcHDhzwmDgjBSlprY2NjVx11VW89957xMXF0d/fH6hwWVDoc8HQ0BCvvvoq+/fvp7e3l0suuYQvf/nLFBYWYrFYqKqqQqVSsWLFCrcptPaNKCYnJ0lISCA5OZno6GgEQeCdilb+9tFxDjX2LMi4uTvSw0U6+n2bkuqIUiHnsb27SA812uahuRN5eXk5d9xxBy+//DJ5eXl+uYfPPvuMBx54gLfeeguAn/3sZwDcf//9tmO+973vUVBQwC233OKXa7oh6IybCxISErjpppu46aabGBkZ4Z///CcPPfQQTU1NKBQKLrzwQn784x97zJNXKBSkpqaSmpqK2WxmaGiIjo4OxsfHiY+PZ0NWMhfuvYTRSQPvVrVzsLyVT493Y5jHCjGpRIf5p9pPqZDz+zt3khFmQhTxKPLq6mpuv/12XnrpJb+JHKSltTY0TG1XzjnnHMxmMw888MBpO101KHQHYmNjufbaa9m9eze7du0iJyeH1tZWzjnnHC688EJ27drFxo0bPYresX+8Wq2mu7ub48ePExsby3nLkvnypqVMGsy8X93OWxVtfFjTuWDDbWGRMcDsHIghchmPfvNysiIsWCyiyx59Vurq6rjlllt47rnnKCgocHlcoDCZTDQ2NvLBBx/Q2dnJ1q1bbUM9TzeCQneBTCbj+9//vi3pwVpT/8QTT3DXXXexbds2du3axZYtWzym0Np3n7G2O+rr66OhoYHo6Gi2ZCdzbv56KgpUjIYk8EF9H+9Xd9jaKS0EOtSe56a5I0Qu43ffvJycKDCZzKxYscKtyBsaGrjxxht5+umnp+2b/YWUtNbMzEw2b95MSEgIubm5FBQU0NjYSElJid/vJ9D4ZY/uyXup1+u57rrrOHZsao75888/7zF/eSGj0+l4++23eemllzh27Bhnn302X/7ylznnnHNcjlN2hiiKjI6O2hpixMfHk56eTmJiImYRPqvv5mB5G+9UtTMscRppIEkNM9M1MOL16xRyGb+9/TLyY2UYjUYKCwvdirylpYVrrrmGv/zlLxQXF8/ijl1jMpkoKCjg3XffJSMjg5KSEp555hlWrVplO+bgwYM8++yzPPXUUwwODlJcXEx5eXkgYvcL3xknxXtprUh7/PHHee6553j55Zd5/vnn/XD784/BYOD999/npZde4rPPPmPTpk3s3r2brVu3SqqHHhwcpKmpiaKiIgwGA/39/QwNDdlaYSclJSHIZBxu7OWtijbermijb3R+Em3WZ8VwpLbZq9fIZQI/2fMFSnLibY0/3Im8vb2dq6++mieffDLgK6entFZRFLn33ns5ePAgcrmcH/7wh4HqObfwhS7Fe3nJJZfwwAMPcNZZZ2EymUhNTWVgYOCMm5JhMpn46KOPePHFF/n4449tNfXnn3++09LJvr4+2trabDPorDhrhZ2SkmIbelHW0s/B8lb+VdFG59DM8cKBYn1OAkeqpcfT5TKBh6+/kJwIMxqNhujoaNvDy1m9eFdXF1dddRW///3vOfvss/156wudhe91l+K9tD9GoVAQExPD0NCQ20KQ0xGFQsEFF1zABRdcgNls5tNPP2X//v088MADrFq1it27d/PFL36R8PBwampq0Ol0rF+/foa5LwiCbVLM0qVLmZiYoL+/n7KyMlv+/b2XruMHV2ymumOQt8paeauijeY+5+OG/UXXsPSutHKZwK9uu5RVySomJyfZsGGDrbtvZWUlgM1ZGRYWRm9vL1dffTW/+c1vFpvI54SgMy5AyOVytm7dytatW7FYLBw+fJiXXnqJn/3sZ0RGRiKXy3n++ecl7ekjIiLIzc0lNzcXrVZLf38/lZWVCIJAcnIyd168mnt3bqSxZ5i3ytt4q7yVui7/xLzt6RudJCU+mj71mNvj5DKBR27dweqUUDQaDatXr0YQBMLDw8nOziY7Oxu9Xs/AwACffvop3/ve97BYLPznf/4n5557rt/vO4gfhC7Fe2k9JjMzE5PJxOjo6KIqRpDJZGzZsoUtW7bw4IMP8sknn1BcXMyOHTvIyspi586d7NixQ1IVXFhY2DSx9Pf3U1NTg9lsJjk5mZu2FbD3S+toGxjjXxVtHCxvpbJ1wG+ZT5nJCW6FLhMEfnHLlyhKDWN8fNwmckdUKhWZmZmEhoYSGxvLtm3b+Ne//sWxY8d4/PHH/XS3QazMeo8uxXv5+9//nqqqKpsz7h//+AcvvPCCH27/9OPgwYNcdNFFyOVyW039iy++yBtvvEFSUhK7du3isssuIz4+3qvzWlth9/X1YTQabZVffX19dA6O0apV8a+KNo429c2q5HRDbiKHq+qdfk8mCPz8lu1syIhkbGyM1atXu803GB4e5oorruBHP/oRl19+OTC73HWQlr8OsH//fr761a9y5MgRNm7c6PP1/MTCd8aBZ++lTqfj2muvpaysjPj4eJ577jmPWU6efmH/+7//y5NPPolCoSApKYk//elPHvuKLWREUeT48eO89NJLvPbaa8TExLBz504uu+wyr2vqrfn3LS0tGI1GMjIybK2w1Rodb1e0cbC8jUONPRjN3vU1y4iPoL29fcbXZYLA/9y0nZKsKEZGRlizZo1bkY+OjvKVr3yF7373u1xxxRVe3YMrpESAYKqXwKWXXorBYODRRx8NCp15ynWX8gt7//332bx5M+Hh4Tz22GO2Fr9nAqIo2mrqrR1NL7/8csk19dZutBaLhfz8fNRqNX19fUxMTNjy72NiYhjTGnivqp2D5W18crwLvVFaKm6sTMfQ2KkEGkGAh2/czpacGIaHhz2KfHx8nK9+9avs3buXq6++WtoPRQJSIkAA3/72t7nooov4xS9+wS9/+ctFIfQF2TNOSh/t888/39YIcMuWLdY502cEgiCQn5/Pfffdx6effspf/vIXAG644Qa2b9/O7373Ozo6OnD2kLZaBgArVqwgJCSElJQUioqK2LRpE3FxcXR2dvL555/T097CtmUJPH7bhRx++Bp+c+N57FifS4TKvesmO+1ULzRBgIduuIQtOTGo1WqPIp+YmGDPnj3cdtttfhU5OI8AdXVNHz1eWlpKR0cHl156qV+vvdBZkF53KSE7e/bt28eXvvSlubi1OUcQBLKzs7nnnnv4zne+Y6upv/3229HpdFx22WXs2rWL3Nxc21yyyMhIp7Xd1lbYSUlJWCwWhoeH6e3tpb6+npiYGLbkpPCl4m0YzRY+quvirfJW3qvqmFFWG6JUnbw3+H/XX8w5eXEMDg7aetm7QqvVsmfPHq699lquvfZa//+wPGCxWLjnnntsD87FxIIUujf8/e9/5+jRo3z44YfzfSsBRxAE0tPTueuuu9i7d6+tpv6ee+5heHgYhULBeeedxw9/+EOP5r1MJiMhIYGEhAREUbQ10mhoaCAqKop1aSlcsOoLWBD4rL6bt8pbebuyHbVGx4BGD8CD136RrfkJDAwMeBS5Tqfj61//OldeeSU33nijX38uVjxFgKx9/s477zwAent72blzJwcOHFgI5ntAWZB7dKl7rXfeeYe77rqLDz/8cMH0z54PTCYTV199NRaLBYPBQF9f37Saem8cedb8e2sqbkREBCkpKVPJTYLA0aY+3ipvpSApgi/kx9Pf38/atWvdFvYYDAb+4z/+g4svvpi77rorYBmRUiJA9px33nmLZo++IFd0+z7aGRkZPPfcczNa+JSVlfGNb3yDgwcPLmqRw5RJvGvXLq677jpgav77gQMH+H//7//R1tbGRRddxO7duykqKvJYXisIArGxscTGxiKKIuPj47ZR06GhoWSlpHD/7o309/fT19fnUeRGo5Ebb7yR8847L6Aih6nMxEcffZRLLrnEFgFatWrVtAjQYmVBrujgOWT3xS9+kaqqKtLSpsYdZWVlceDAAbfnPE1jrLNifHyc119/nf3799PQ0GCrqd+wYYPXAyc1Gg39/f10d3djMplYunQpKSkpLot3TCYTN998M8XFxdx///1nXG2DH1mc4bVAcBrHWP3G5OQkb775Jvv376e6utpWU79582bJY6l6enro7u6moKCAoaEh+vv7pzXZsBarmM1mbr/9dvLz823NFYO4JCh0f3Eax1gDgn1NfWlpqa2m/uyzz3aZf28V+bp166Y9GKytsPv7+xkeHubf//43HR0dZGdn89BDDwVF7pnFGUcPBMEY63RCQ0O5/PLLeeqppzh27Bhf/vKX2b9/P2effTZ33XUX77777rQ59b29vXR1dTndk4eGhpKVlcXGjRtZu3Ytx48f5/PPP+fDDz/kz3/+81y/tSBOWJDOuPlgMcdYlUol27dvZ/v27dNq6u+//37Wr19PSkoK4+Pj/PznP3dbbWexWPjlL3/JkiVLePnllxkZGaG1tXXW97fY0qEDgiiK7v6cMfz73/8WL774Ytu/H3roIfGhhx6y/XtkZERMSEgQs7OzxezsbFGlUolpaWnikSNH5uN2FwQmk0n87//+bzEzM1Nct26duGfPHvHZZ58VBwYGxImJiWl/xsfHxe985zvirbfeKprNZr/eQ15entjU1CTq9XqxqKhIrKmpmXbMe++9J05MTIiiKIp/+MMfxKuuuspv158jPOlw1n8WjdCNRqOYm5srNjc32z4w1dXVLo/ftm3boha5KE79zG688UZxZGRENJvN4meffSbec889YlFRkfiVr3xF/Nvf/ib29fWJGo1GvO+++8Trr79eNJlMfr0HTw9oR0pLS8Wzzz7br/cwBwRc6Itmj24fYy0sLOSqq66yxVg9heXccfDgQZYvX05+fj4PP/yw02NeeOEFVq5cyapVq7jmmmt8vtZco1Ao+NOf/kRMTIytpv6RRx6hrKyM+++/n+rqai655BI2bdpEfX09+/btk+y9l4oU34o9Z3I69Kzw8CQI4gYpZmVDQ4O4bt06Ua1Wi6Ioin19ffNxqwHDbDaLr776qjg+Ph6Q87/44ovizTffbPv3X//6V/HOO+90euzf/vY3cfPmzaJOpwvIvQSQ4Iq+kJFSZffEE09w5513EhcXB3DGZfHJZDJ27txJZGRkQM4vpYMRTKVD//SnP+XAgQNOG08udoJCnwVSzMqGhgYaGho455xz2LJlCwcPHpzr2zytsU+HNhgMPPfcczNSWa3p0AcOHDjjHqT+IhheCzBn0lif+UBK/vp//ud/otFouPLKKwFp6dCLjaDQZ8FiG+szX+zYsYMdO3ZM+9qDDz5o+/s777wz17d02hE03WeBFLNy9+7dfPDBB8DUVJaGhga/TgUNEkQKQaHPAikhu0suuYSEhARWrlzJ+eefzy9+8QtJra49he3a29s5//zzKS4upqioiDfeeMPv7y/ImcOiKWo5nZBSaXfbbbdRXFzMHXfcQW1tLTt27PBLummQeSFY1LIYkRK2EwSBsbGpQQqjo6Okp6fPx60GOU0ICn0BIiVs98ADD/D3v/+dzMxMduzYwe9+97u5vk2f8bQt0ev1XH311eTn57N58+agpeIHgkI/TXn22We54YYb6Ozs5I033uDaa6/FYvFuGMN8YDabufPOO3nzzTepra3l2Wefpba2dtox+/btIy4ujhMnTvCd73yH++67b57u9swhKPQFiJSw3b59+7jqqqsAOOuss9DpdAwODs7pffqClG3Jq6++yvXXXw/AV7/6Vd59912nPeyDSCco9AWIlLBdVlYW7777LgB1dXXodDqSkpKcnW5BIWVb4mrMdhDfCQp9ASIlbPfII4/wxBNPsHbtWr72ta/xl7/8JdiyKYhLPIXXgpxBCILwJ+AyoF8UxdVOvi8AvwF2AJPADaIolvr5Hs4CHhBF8ZKT/74fQBTFn9kd89bJYz4TBEEB9AJJYvDD6jPBFX1x8Rdgu5vvfwlYdvLPbcBjAbiHI8AyQRByBUFQAnsAx8T0A8D1J//+VeC9oMhnR1DoiwhRFD8C1G4O2QX89WSN9OdArCAIaX6+BxOwF3gLqANeEEWxRhCEBwVBsDoi9gEJgiCcAO4BnDfgDyKZYFFLEHsygA67f3ee/FqPPy8iiuIbwBsOX/ux3d91wJX+vOZiJ7iiBwmyCAgKPYg9XcASu39nnvxakNOcoNCD2HMAuE6YYgswKoqiX832IPNDcI++iBAE4VngPCBREIRO4L+AEABRFB9nat+8AzjBVHgtMIPMg8w5wTh6kCCLgKDpHiTIIiAo9CBBFgFBoQcJsggICj1IkEVAUOhBgiwCgkIPEmQREBR6kCCLgKDQgwRZBPz/8jjt1aAiCakAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "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)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 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()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.4" } }, "nbformat": 4, "nbformat_minor": 4 }