{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Adaptive PDE discretizations on Cartesian grids\n", "## Volume : Non-divergence form PDEs\n", "## Part : Monotone numerical schemes\n", "## Chapter : Linear partial differential equations\n", "\n", "This notebook illustrates the use of monotone finite difference schemes to compute viscosity solutions of PDEs, in two space dimensions. We address both first order and second order problems, but focus on linear equations.\n", "\n", "In the second order case, our numerical schemes are adaptive and depend on Selling's decomposition of the diffusion tensors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Non-Divergence form PDEs, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. A first order linear equation](#1.-A-first-order-linear-equation)\n", " * [1.1 Vector fields in the upper quadrant](#1.1-Vector-fields-in-the-upper-quadrant)\n", " * [1.2 General vector field](#1.2-General-vector-field)\n", " * [1.3 Mock boundary conditions](#1.3-Mock-boundary-conditions)\n", " * [2. A second order linear equation](#2.-A-second-order-linear-equation)\n", " * [2.1 Varadhan's formula](#2.1-Varadhan's-formula)\n", " * [3. Second-order scheme with upwind first order differences](#3.-Second-order-scheme-with-upwind-first-order-differences)\n", "\n", "\n", "\n", "**Acknowledgement.** Some of the experiments presented in these notebooks are part of \n", "ongoing research with Ludovic Métivier and Da Chen.\n", "\n", "Copyright Jean-Marie Mirebeau, Centre Borelli, ENS Paris-Saclay, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:02.811152Z", "iopub.status.busy": "2024-04-30T08:47:02.811009Z", "iopub.status.idle": "2024-04-30T08:47:02.816481Z", "shell.execute_reply": "2024-04-30T08:47:02.816178Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; print(TocTools.displayTOC('LinearMonotoneSchemes2D','NonDiv'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:02.818168Z", "iopub.status.busy": "2024-04-30T08:47:02.818043Z", "iopub.status.idle": "2024-04-30T08:47:02.859426Z", "shell.execute_reply": "2024-04-30T08:47:02.859130Z" }, "tags": [ "ExportCode" ] }, "outputs": [], "source": [ "from agd import Selling\n", "from agd import LinearParallel as lp\n", "from agd import AutomaticDifferentiation as ad\n", "from agd import Domain" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:02.861026Z", "iopub.status.busy": "2024-04-30T08:47:02.860905Z", "iopub.status.idle": "2024-04-30T08:47:03.059340Z", "shell.execute_reply": "2024-04-30T08:47:03.058901Z" }, "tags": [ "ExportCode" ] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.linalg " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some utility functions" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.061009Z", "iopub.status.busy": "2024-04-30T08:47:03.060889Z", "iopub.status.idle": "2024-04-30T08:47:03.063051Z", "shell.execute_reply": "2024-04-30T08:47:03.062814Z" }, "tags": [ "ExportCode" ] }, "outputs": [], "source": [ "norm = ad.Optimization.norm\n", " \n", "def streamplot_ij(X,Y,VX,VY,subsampling=1,*varargs,**kwargs):\n", " def f(array): return array[::subsampling,::subsampling].T\n", " return plt.streamplot(f(X),f(Y),f(VX),f(VY),*varargs,**kwargs) # Transpose everything" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. A first order linear equation\n", "\n", "We numerically compute the *viscosity* solution of the equation\n", "$$\n", " 1-<\\nabla u(x), \\omega(x)>=0\n", "$$\n", "over some domain, with dirichlet boundary conditions.\n", "In general, there exists no classical solution. The viscosity solution therefore has a jump over part of the domain boundary.\n", "In addition, a technical condition is required for the existence of a viscosity solution: the equation\n", "$$\n", " \\gamma'(t) = \\omega(\\gamma(t)),\n", "$$\n", "solved *backwards in time* from a point $x$, must lead to some point $x_*$ of the domain boundary in finite time $T(x)$. Then \n", "$$\n", "u(x) = T(x) + b(x_*),\n", "$$\n", "where $b$ denotes the boundary condition." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First let us define the discretization grid." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.064419Z", "iopub.status.busy": "2024-04-30T08:47:03.064321Z", "iopub.status.idle": "2024-04-30T08:47:03.066229Z", "shell.execute_reply": "2024-04-30T08:47:03.065989Z" } }, "outputs": [], "source": [ "#Define the square [-1,1]^2, sampled on a cartesian grid\n", "aX0 = np.linspace(-1,1); aX1 = aX0\n", "X = np.array(np.meshgrid(aX0,aX1,indexing='ij'))\n", "shape = X.shape[1:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the boundary conditions, by choosing a domain, an adequate value, and the grid." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.067614Z", "iopub.status.busy": "2024-04-30T08:47:03.067514Z", "iopub.status.idle": "2024-04-30T08:47:03.069549Z", "shell.execute_reply": "2024-04-30T08:47:03.069309Z" } }, "outputs": [], "source": [ "bc_domain = Domain.Ball([0,0],0.9)\n", "def bc_value(x): return 0.3*np.sin(2*np.pi*(x[0]+x[1]))\n", "\n", "bc = Domain.Dirichlet(bc_domain,bc_value,X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Vector fields in the upper quadrant\n", "\n", "We assume here that $\\omega_0(x)\\geq 0$ and $\\omega_1(x)\\geq 0$, where $\\omega(x) = (\\omega_0(x),\\omega_1(x))$.\n", "\n", "A monotone numerical scheme for the considered PDE, at a point $x=(x0,x1)$ in the interior of the domain, is \n", "$$\n", " 1 - \\omega_0(x) \\frac{u(x_0+h,x_1)-u(x)} h - \\omega_1(x) \\frac{u(x_0,x_1+h)-u(x)} h= 0.\n", "$$\n", "\n", "If $(x_0+h,x_1)$ falls out of the domain, then the adequate value on $\\partial \\Omega$ is extracted from the boundary conditions, as explained in notebook [subsets of R^d](../Notebooks_Algo/SubsetRd.ipynb)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.070907Z", "iopub.status.busy": "2024-04-30T08:47:03.070813Z", "iopub.status.idle": "2024-04-30T08:47:03.072688Z", "shell.execute_reply": "2024-04-30T08:47:03.072457Z" } }, "outputs": [], "source": [ "def Scheme(u,omega,bc):\n", " omega0,omega1 = omega\n", " residue = 1. - omega0*bc.DiffUpwind(u,(1,0)) - omega1*bc.DiffUpwind(u,(0,1)) # 1- = 0\n", " return np.where(bc.interior,residue,u-bc.grid_values) # Placeholders outside the interior" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.073992Z", "iopub.status.busy": "2024-04-30T08:47:03.073899Z", "iopub.status.idle": "2024-04-30T08:47:03.075753Z", "shell.execute_reply": "2024-04-30T08:47:03.075513Z" } }, "outputs": [], "source": [ "omega = np.stack( (1.3+np.sin(np.pi*X[1]), np.cos(np.pi*(X[0]+X[1])/4)) )" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.077059Z", "iopub.status.busy": "2024-04-30T08:47:03.076962Z", "iopub.status.idle": "2024-04-30T08:47:03.238363Z", "shell.execute_reply": "2024-04-30T08:47:03.238092Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal')\n", "streamplot_ij(*X,*omega*bc.interior);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can evaluate the scheme on an arbitrary guess numpy array, which produces a non-zero residue." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.240072Z", "iopub.status.busy": "2024-04-30T08:47:03.239961Z", "iopub.status.idle": "2024-04-30T08:47:03.363213Z", "shell.execute_reply": "2024-04-30T08:47:03.362922Z" } }, "outputs": [ { "data": { "text/plain": [ "(-1.0, 1.0, -1.0, 1.0)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = np.zeros(bc.shape) # Arbitrary guess (here zero)\n", "residue = Scheme(u,omega,bc)\n", "\n", "plt.title(\"Scheme residue of arbitrary guess\")\n", "plt.contourf(*X,residue); plt.colorbar(); plt.axis('equal')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order solve the scheme, we evaluate it on a function featuring automatic differentiation information, here of sparse type, and solve the residue for zero." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.364852Z", "iopub.status.busy": "2024-04-30T08:47:03.364745Z", "iopub.status.idle": "2024-04-30T08:47:03.369934Z", "shell.execute_reply": "2024-04-30T08:47:03.369699Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(constant=u) # Initial guess (here zero), with autodiff information\n", "residue_ad = Scheme(u_ad,omega,bc)\n", "solution = u + residue_ad.solve()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.371471Z", "iopub.status.busy": "2024-04-30T08:47:03.371372Z", "iopub.status.idle": "2024-04-30T08:47:03.435777Z", "shell.execute_reply": "2024-04-30T08:47:03.435488Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title('Solution to 1- = 0')\n", "plt.contourf(*X,solution);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 General vector field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the vector field $\\omega$ does not remain in a fixed quadrant, then the numerical scheme needs to be adaptive, and use upwind finite differences:\n", "$$\n", " 1 - |\\omega_0(x)| \\frac{u(x_0+s_0(x)h,x_1)-u(x)} h - |\\omega_1(x)| \\frac{u(x_0+s_1(x)h,x_1)-u(x)} h= 0,\n", "$$\n", "where $s_0(x)$ denotes the sign of $\\omega_0(x)$, and likewise for $s_1(x)$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.437456Z", "iopub.status.busy": "2024-04-30T08:47:03.437347Z", "iopub.status.idle": "2024-04-30T08:47:03.439624Z", "shell.execute_reply": "2024-04-30T08:47:03.439398Z" } }, "outputs": [], "source": [ "def Scheme(u,omega,bc):\n", " \n", " # Compute the scheme coefficients and offsets\n", " coefs = np.abs(omega)\n", " coefs = bc.as_field(coefs)\n", " \n", " basis = bc.as_field(np.eye(len(omega)))\n", " offsets = np.sign(omega)*basis\n", " \n", " # Compute the first order finite differences\n", " du = bc.DiffUpwind(u,offsets.astype(int))\n", " \n", " # 1- = 0 in interior\n", " residue = 1.-lp.dot_VV(coefs,du)\n", " \n", " # Placeholders on boundary\n", " return np.where(bc.interior,residue,u-bc.grid_values) " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.440994Z", "iopub.status.busy": "2024-04-30T08:47:03.440898Z", "iopub.status.idle": "2024-04-30T08:47:03.442715Z", "shell.execute_reply": "2024-04-30T08:47:03.442477Z" } }, "outputs": [], "source": [ "omega2 = np.stack( (1.3+np.sin(np.pi*X[1]), np.cos(np.pi*(2*X[0]+X[1])/2)) )" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.444057Z", "iopub.status.busy": "2024-04-30T08:47:03.443964Z", "iopub.status.idle": "2024-04-30T08:47:03.599814Z", "shell.execute_reply": "2024-04-30T08:47:03.599540Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal')\n", "streamplot_ij(*X,*omega2*bc.interior);" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.601491Z", "iopub.status.busy": "2024-04-30T08:47:03.601376Z", "iopub.status.idle": "2024-04-30T08:47:03.606157Z", "shell.execute_reply": "2024-04-30T08:47:03.605849Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(bc.shape)\n", "residue_ad = Scheme(u_ad,omega2,bc)\n", "solution = residue_ad.solve()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.607622Z", "iopub.status.busy": "2024-04-30T08:47:03.607541Z", "iopub.status.idle": "2024-04-30T08:47:03.671301Z", "shell.execute_reply": "2024-04-30T08:47:03.671020Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title('Solution to 1- = 0')\n", "plt.contourf(*X,solution);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3 Mock boundary conditions\n", "\n", "A different way of implementing Dirichlet boundary conditions, simpler and cruder, is to extend them to the full domain complement. We refer to this approach as mock boundary conditions." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.672829Z", "iopub.status.busy": "2024-04-30T08:47:03.672726Z", "iopub.status.idle": "2024-04-30T08:47:03.677292Z", "shell.execute_reply": "2024-04-30T08:47:03.677039Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(bc.shape)\n", "residue_ad = Scheme(u_ad,omega2,bc.Mock) # Mock boundary conditions, extended to the whole domain complement\n", "solution = residue_ad.solve()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.678715Z", "iopub.status.busy": "2024-04-30T08:47:03.678634Z", "iopub.status.idle": "2024-04-30T08:47:03.744672Z", "shell.execute_reply": "2024-04-30T08:47:03.744358Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title('Solution to 1- = 0. (Mock boundary conditions)')\n", "plt.contourf(*X,solution);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also directly construct the mock boundary conditions, by providing an array of values to be used as boundary conditions, and the grid scale." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.746240Z", "iopub.status.busy": "2024-04-30T08:47:03.746136Z", "iopub.status.idle": "2024-04-30T08:47:03.747949Z", "shell.execute_reply": "2024-04-30T08:47:03.747729Z" } }, "outputs": [], "source": [ "bc_mock_grid_values = bc.value(X) # Evaluate the boundary conditions on the full grid\n", "bc_mock_grid_values[bc.interior]=np.nan # Specify domain interior by NaNs\n", "\n", "bc_mock = Domain.MockDirichlet(bc_mock_grid_values, bc.gridscale)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.749997Z", "iopub.status.busy": "2024-04-30T08:47:03.749894Z", "iopub.status.idle": "2024-04-30T08:47:03.815815Z", "shell.execute_reply": "2024-04-30T08:47:03.815522Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u_ad = ad.Sparse.identity(bc_mock.shape)\n", "residue_ad = Scheme(u_ad,omega2,bc_mock) # Mock boundary conditions, extended to the whole domain complement\n", "solution = residue_ad.solve()\n", "\n", "plt.axis('equal'); plt.title('Solution to 1- = 0. (Mock boundary conditions)')\n", "plt.contourf(*X,solution);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. A second order linear equation\n", "\n", "We consider the linear second order equation\n", "$$\n", " c(x) + m(x) u(x) + <\\omega(x),\\nabla u(x)> - \\mathrm{Tr}(D(x)\\nabla^2 u(x)) = 0,\n", "$$\n", "with Dirichlet boundary conditions. For monotony, one needs to assume that $a$ is non-negative, and $D$ is positive semi-definite.\n", "\n", "In contrast with the first order examples:\n", "* There exists a classical solution. Hence there is no discontinuity in the viscosity solution.\n", "* We can use a centered finite difference scheme for the first order term, since the it is dominated by the monotony of the second order term.\n", "\n", "We use adaptive finite differences, determined by a decomposition of the tensor field\n", "$$\n", " D(x) = \\sum_{1 \\leq i \\leq n} \\mu_i(x) e_i(x) e_i(x)^T,\n", "$$\n", "where $\\mu_i(x)$ is non-negative, and $e_i(x)$ has integer offsets.\n", "This induces a decomposition of the vector field\n", "$$\n", " \\omega(x) = \\sum_{1 \\leq i \\leq n} \\nu_i(x) e_i(x)\n", "$$\n", "where $\\nu_i(x) = \\mu_i(x)$.\n", "The numerical scheme eventually reads:\n", "$$\n", " a(x) u(x) \n", " {+} \\sum_{1 \\leq i \\leq n} \\nu_i(x) \\frac{u(x+h e_i(x))-u(x-h e_i(x))} {2 h} \n", " {-} \\sum_{1 \\leq i \\leq n} \\mu_i(x) \\frac{u(x+h e_i(x))-2 u(x)+ u(x-h e_i(x))} {h^2}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.817429Z", "iopub.status.busy": "2024-04-30T08:47:03.817327Z", "iopub.status.idle": "2024-04-30T08:47:03.820283Z", "shell.execute_reply": "2024-04-30T08:47:03.820059Z" }, "tags": [ "ExportCode" ] }, "outputs": [], "source": [ "def SchemeCentered(u,cst,mult,omega,diff,bc,ret_hmax=False):\n", " \"\"\"Discretization of a linear non-divergence form second order PDE\n", " cst + mult u + - tr(diff hess(u)) = 0\n", " Second order accurate, centered yet monotone finite differences are used for \n", " - bc : boundary conditions. \n", " - ret_hmax : return the largest grid scale for which monotony holds\n", " \"\"\"\n", " # Decompose the tensor field\n", " coefs2,offsets = Selling.Decomposition(diff)\n", " \n", " # Decompose the vector field\n", " scals = lp.dot_VA(lp.solve_AV(diff,omega), offsets.astype(float))\n", " coefs1 = coefs2*scals\n", " if ret_hmax: return 2./norm(scals,ord=np.inf)\n", " \n", " # Compute the first and second order finite differences \n", " du = bc.DiffCentered(u,offsets)\n", " d2u = bc.Diff2(u,offsets)\n", " \n", " # In interior : cst + mult u + - tr(diff hess(u)) = 0\n", " coefs1,coefs2 = (bc.as_field(e) for e in (coefs1,coefs2)) \n", " residue = cst + mult*u +lp.dot_VV(coefs1,du) - lp.dot_VV(coefs2,d2u)\n", " \n", " # On boundary : u-bc = 0\n", " return np.where(bc.interior,residue,u-bc.grid_values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve a $1-\\Delta u = 0$ over a square domain, with null Dirichlet boundary conditions. \n", "(The mathematician's preferred numerical problem, according to B.M.)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.821644Z", "iopub.status.busy": "2024-04-30T08:47:03.821535Z", "iopub.status.idle": "2024-04-30T08:47:03.823236Z", "shell.execute_reply": "2024-04-30T08:47:03.823000Z" } }, "outputs": [], "source": [ "# Define the problem parameters\n", "cst=1.\n", "mult=0.\n", "omega = np.zeros(2)\n", "diff = np.eye(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the PDE is solved on the whole grid, mock boundary conditions will be enough for our purposes.\n", "Note that:\n", "* First argument is the shape of the domain. Equivalently, provide an array full of NaNs with this shape.\n", "* A padding is specified for values falling outside the grid." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.824570Z", "iopub.status.busy": "2024-04-30T08:47:03.824485Z", "iopub.status.idle": "2024-04-30T08:47:03.826174Z", "shell.execute_reply": "2024-04-30T08:47:03.825941Z" } }, "outputs": [], "source": [ "bc_whole = Domain.MockDirichlet(bc.shape, bc.gridscale, padding=0.)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.827527Z", "iopub.status.busy": "2024-04-30T08:47:03.827451Z", "iopub.status.idle": "2024-04-30T08:47:03.835621Z", "shell.execute_reply": "2024-04-30T08:47:03.835376Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(bc.shape)\n", "residue_ad = SchemeCentered(u_ad,cst,mult,omega,diff,bc_whole)\n", "solution = residue_ad.solve()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.837114Z", "iopub.status.busy": "2024-04-30T08:47:03.837033Z", "iopub.status.idle": "2024-04-30T08:47:03.938495Z", "shell.execute_reply": "2024-04-30T08:47:03.938221Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title(\"Delta u=1 over a square\")\n", "plt.contourf(*X,solution); plt.colorbar();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Varadhan's formula\n", "\n", "We turn to Varadhan's formula for more interesting examples.\n", "First we solve \n", "$$\n", " u - \\epsilon^2 \\mathrm{Tr}(D \\nabla^2 u) = 0\n", "$$\n", "with $u(x_0)=1$ at some given point $x_0$, and null boundary conditions on the square boundary. \n", "Then we apply the following change of unknown, related with the *Hopf-Cole transformation*\n", "$$\n", " v(x) := -\\epsilon \\ln u_\\epsilon(x).\n", "$$\n", "The function $v$ approximates the Riemmanian distance from $x_0$, for the metric $M:=D^{-1}$ defined by the inverses of the diffusion tensors.\n", "\n", "We reproduce some examples from [I Computing distance maps and geodesics using Varadhan's formulas](http://nbviewer.jupyter.org/urls/rawgithub.com/Mirebeau/AdaptiveGridDiscretizations/master/Notebooks/VaradhanGeodesics.ipynb).\n", "A number of small differences distinguish the implementation presented in that other notebook:\n", "* The laplacian is in divergence form. (Presumably better)\n", "* The boundary conditions are of Neumann type. (Presumably better)\n", "* The numerical scheme is not defined in the notebook, but in an external routine. (Less pedagogical, but presumably faster) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Metric specified in terms of eigenvectors and eigenvalues.**\n", "In this example, the metric tensors are specified as \n", "$$\n", " M(x) = \\lambda_1(x)^{-2} v_1(x) v_1(x)^T + \\lambda_2(x)^{-2} v_2(x) v_2(x)^T.\n", "$$\n", "The scalars $\\lambda_1$ and $\\lambda_2$ appearing in this expression should be regarded as the local velocity in the direction of $v_1$ and $v_2$ respectively." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.940087Z", "iopub.status.busy": "2024-04-30T08:47:03.939983Z", "iopub.status.idle": "2024-04-30T08:47:03.942363Z", "shell.execute_reply": "2024-04-30T08:47:03.942129Z" } }, "outputs": [], "source": [ "# Create the domain\n", "aX0 = np.linspace(-1,1,100); aX1=aX0;\n", "X = np.array(np.meshgrid(aX0,aX1,indexing='ij'))\n", "\n", "gridscale = aX0[1]-aX0[0]\n", "bc_grid_values = np.full(X.shape[1:],np.nan)\n", "bc_grid_values[X.shape[1]//2,X.shape[2]//2] = 1\n", "\n", "bc = Domain.MockDirichlet(bc_grid_values,gridscale,padding=0.) # Shape, gridscale, padding" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.943738Z", "iopub.status.busy": "2024-04-30T08:47:03.943642Z", "iopub.status.idle": "2024-04-30T08:47:03.946270Z", "shell.execute_reply": "2024-04-30T08:47:03.946042Z" } }, "outputs": [], "source": [ "# Generate the metric\n", "eig1 = np.stack((np.ones(bc.shape),(np.pi/2)*np.cos(2*np.pi*X[0])))\n", "eig1 /= scipy.linalg.norm(eig1,axis=0) \n", "eig2 = np.stack( (eig1[1],-eig1[0]) ) # Rotate eig1 by pi/2\n", "lambda1, lambda2 = 0.8, 0.2\n", "metric = lambda1**-2*lp.outer_self(eig1) + lambda2**-2*lp.outer_self(eig2)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:03.947651Z", "iopub.status.busy": "2024-04-30T08:47:03.947548Z", "iopub.status.idle": "2024-04-30T08:47:04.149811Z", "shell.execute_reply": "2024-04-30T08:47:04.149550Z" } }, "outputs": [], "source": [ "# Relaxation parameter\n", "epsilon=2*bc.gridscale\n", "\n", "# Generate the PDE parameters\n", "cst=0.\n", "mult=1.\n", "omega=bc.as_field(np.array([0.,0]))\n", "diff = epsilon**2 * lp.inverse(metric)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.151296Z", "iopub.status.busy": "2024-04-30T08:47:04.151213Z", "iopub.status.idle": "2024-04-30T08:47:04.214309Z", "shell.execute_reply": "2024-04-30T08:47:04.213975Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(bc.shape)\n", "residue_ad = SchemeCentered(u_ad,cst,mult,omega,diff,bc)\n", "solution = residue_ad.solve()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.216079Z", "iopub.status.busy": "2024-04-30T08:47:04.215986Z", "iopub.status.idle": "2024-04-30T08:47:04.282007Z", "shell.execute_reply": "2024-04-30T08:47:04.281764Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "distance = -epsilon*np.log(solution)\n", "plt.axis('equal'); plt.title(\"Riemannian distance, approximated using Varadhan's formula\")\n", "plt.contourf(*X,distance);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Zermelo's navigation problem.**\n", "\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.283480Z", "iopub.status.busy": "2024-04-30T08:47:04.283398Z", "iopub.status.idle": "2024-04-30T08:47:04.285645Z", "shell.execute_reply": "2024-04-30T08:47:04.285388Z" } }, "outputs": [], "source": [ "# Generate the metric\n", "metric = bc.as_field(np.eye(2))\n", "drift = 0.8*np.sin(2*np.pi*X[0])*np.sin(2*np.pi*X[1]) * X / norm(X,ord=2,axis=0)\n", "#metric = np.array( ((1,0),(0,1)) ); drift = 0.5*np.array( (1,1) )/np.sqrt(2) # Alternatively : constant drift" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.287082Z", "iopub.status.busy": "2024-04-30T08:47:04.286984Z", "iopub.status.idle": "2024-04-30T08:47:04.492129Z", "shell.execute_reply": "2024-04-30T08:47:04.491836Z" } }, "outputs": [], "source": [ "# Relaxation parameter\n", "epsilon=3*bc.gridscale\n", "\n", "# Generate the PDE parameters\n", "cst=0.\n", "mult=1.\n", "omega=2*epsilon*drift\n", "diff = epsilon**2 * (lp.inverse(metric) - lp.outer_self(drift))" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.493850Z", "iopub.status.busy": "2024-04-30T08:47:04.493755Z", "iopub.status.idle": "2024-04-30T08:47:04.552370Z", "shell.execute_reply": "2024-04-30T08:47:04.552070Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(bc.shape)\n", "residue_ad = SchemeCentered(u_ad,cst,mult,omega,diff,bc)\n", "solution = residue_ad.solve()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.553964Z", "iopub.status.busy": "2024-04-30T08:47:04.553866Z", "iopub.status.idle": "2024-04-30T08:47:04.653294Z", "shell.execute_reply": "2024-04-30T08:47:04.653036Z" } }, "outputs": [ { "data": { "image/png": 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MzEwkJyfj/fffR0JCAgIDA/Hoo4+iuLjY6mPqqhvUAZgOIK7d5u15b0yePBl6vd507Mf333+PI0eOSN5rlly+fBnBwcFm0y1NmzRpEpYtW4bHH38cO3fuxFdffYUjR46gXbt2Dr9P7d2O668z4OZ6s/X5LW3HISEhqKqqMhu8628X9vbV2nPVzsuSy5cv4/r163j77bfNtuf77rsPgPl7yp7PLgCS9w65F8/u+T9r1qyBEAKffvopPv30U7P7P/jgA7z66qvw8vIyTWvomie2Xg+l9hvq2rVr8eSTT2Lt2rUICwtDYmKiqc2WLVtw7do1bNq0CeHh4abp+fn5Nj2HuwUFBaFt27bYsWOHxfv9/f1N//fr1w/9+vVDTU0Njh49irfffhspKSkIDg42Vbhs1bZtW1y/fh0XL16UfGgKIVBcXIy77rpL0t7ea9g888wzyM3NxYoVK5CQkGC1XVBQEO644w787W9/s3h/7WDvaD9sERQUBD8/P6sHUAYFBVl9bNu2bVFUVGQ2/eeff270sUFBQVi8eDEWL16MwsJCfPbZZ3j++edRUlJidXuwhz3vjTZt2mDMmDFYt24dXn31Vaxduxa+vr4WKyJ1tW3bFl999ZXZ9PpBq7S0FP/85z8xb948PP/886bplZWV+PXXX+1cMunz27MdN5WlAFlcXAwfHx+zU/vrb6v29tXac9XOy5I2bdrAy8sLSUlJePrppy22iYyMtDid1IeVFNzcxfLBBx+gc+fO2LNnj9nfc889h6KiImzfvl2W558yZQoOHz6ML7/8Ep9//jmSk5MthqG6p6EKIfDee+85/Jz2fLNqqpEjR+Ly5cuoqalBr169zP66du1q9hgvLy/07t3b9I3YWum3Iffeey8A4KOPPpJMz8rKwrVr10z3O+L999/HqlWrMGXKFDz11FMNth05ciS+++47dO7c2eLy1w8pchg5ciR++ukntG3b1mIfGrp42L333ovvv//e7DVYt24ddDodBg0aZFMfOnXqhBkzZmDIkCEOvZ6W2PvemDJlCn7++WdkZ2fjo48+wv3334/WrVs3+BwDBgxAWVmZ2fu/tvpZty9CCLPTxd9//32z3ST1K0INkXM7tmTTpk2SSkJZWRk+//xz9OvXT/K55Iy+njhxAsePH5dMW79+Pfz9/SVnN9bVokULDBo0CHl5ebjjjjssbs/WAg6pDyspALZv346ff/4ZCxcutHilyejoaCxbtgyrV6+26QqJ9nr44YeRmpqKhx9+GJWVlWb7c4cMGQIfHx88/PDD+Mtf/oKKigqsXLkSV65ccfg5e/TogU2bNmHlypWIi4tDs2bN0KtXryYuiWUTJ07Exx9/jPvuuw8zZ87E3XffDW9vb5w/fx579uzBmDFjcP/99+Odd97BF198gREjRqBTp06oqKgwffMfPHiw3c87ZMgQDB06FHPmzIHRaETfvn3xzTffYN68eYiJiUFSUpJDy/PVV19hxowZCAkJwaOPPmq2/7tW586d0a5dOyxYsAA5OTno06cPnn32WXTt2hUVFRU4c+YMsrOz8c4778h+/ZyUlBRkZWWhf//+mDVrFu644w7cuHEDhYWF2LVrF5577jmr1wOaNWsW1q1bhxEjRmDBggUIDw/Htm3bsGLFCjz11FNWj+MpLS3FoEGDMGnSJERFRcHf3x9HjhzBjh078MADDzhluex9byQmJqJDhw7485//jOLi4kZ39QBAcnIy/vGPf+CRRx7Bq6++ittuuw3bt2/Hzp07AQDNmt38rhcQEID+/fvjjTfeQFBQECIiIrBv3z6sXr3aLAjVHgOzatUq+Pv7w9fXF5GRkRYHV7m2Y2u8vLwwZMgQpKam4saNG1i4cCGMRqNNp+Tb29ewsDCMHj0aaWlpCA0NxUcffYScnBwsXLiwwWuuLFmyBH/84x/Rr18/PPXUU4iIiEBZWRl+/PFHfP755w0eJ0Uq464jdpVk7NixwsfHx3QKoCUTJ04UzZs3F8XFxaajzeueJler9qj32tMNLd1nyaRJkwQA0bdvX4v3f/7556Jnz57C19dX3HLLLeL/+//+P7F9+3azMwRsPbvn119/FQ899JBo3bq10Ol0kn7Bytk99c8Msbasls60qa6uFm+++aZpGVq1aiWioqLEk08+KU6fPi2EuHkq8f333y/Cw8OFXq8Xbdu2FQMGDBCfffZZo8tj6TmFuHlmw5w5c0R4eLjw9vYWoaGh4qmnnjI7pTk8PFyMGDGi0eepu9yN/dU9G+HixYvi2WefFZGRkcLb21sEBgaKuLg48eKLL4ry8nIhhHBou7K23AMGDBDdu3eXTCsvLxcvvfSS6Nq1q/Dx8TGdwjlr1ixRXFwsWRd1z+4RQoizZ8+KSZMmibZt2wpvb2/RtWtX8cYbb4iamhqr66miokJMnz5d3HHHHSIgIED4+fmJrl27innz5pnO3LDG2vLWbosFBQWmaba+N2q98MILplNtLfW//tk9QghRWFgoHnjgAdGqVSvh7+8vHnzwQZGdnS0AiK1bt5ranT9/Xjz44IOiTZs2wt/fXwwbNkx89913Ftfp4sWLRWRkpPDy8pJsL5bew03dji0tU32129/ChQvF/PnzRYcOHYSPj4+IiYkRO3fulLRt6HPO3r5++umnonv37sLHx0dERESYnS1o6eye2ul/+tOfxC233CK8vb1Fu3btRJ8+fcSrr75qalN7ds8nn3wieay9n2nkPjohhJA/ChERactrr72Gl156CYWFhaq4knRjzpw5g8jISLzxxhuYPXu2u7tDBIC7e4iIGrVs2TIAQFRUFKqrq/HFF19g6dKleOSRRzQRUIiUiiGFiKgRLVq0wD/+8Q+cOXMGlZWV6NSpE+bMmYOXXnrJ3V0j0jTu7iEiIiJFkvUU5P3792PUqFEICwuDTqfDli1bGn3Mvn37EBcXZ/qxqXfeecesTVZWFrp16wa9Xo9u3bph8+bNMvSeiIhI29LT03HXXXfB398f7du3x9ixYyVXZbbGVWO1rCHl2rVr6Nmzp2l/bmMKCgpw3333oV+/fsjLy8MLL7yAZ599FllZWaY2ubm5mDBhApKSknD8+HEkJSVh/PjxOHz4sFyLQUREpEn79u3D008/jUOHDiEnJwfXr19HYmJig7+O7sqx2mW7e3Q6HTZv3oyxY8dabTNnzhx89tlnkt+4mD59Oo4fP47c3FwAN39W3Wg0Si6sNGzYMLRp0wYbNmyQrf9ERERad/HiRbRv3x779u1D//79LbZx5VitqANnc3NzJZeDB4ChQ4di9erVqK6uhre3N3JzczFr1iyzNosXL7Y638rKSlRWVppu37hxA7/++ivatm0ryyXIiYhIO4QQKCsrQ1hYmOnifXKoqKhAVVVVk+cjhDAb2/R6vdnVkC2p/bHb+r9rVJdcY7UligopxcXFZj/aFRwcjOvXr+PSpUsIDQ212qahHyxLT0+36WqJRERE1pw7d062U84rKirQqVNLXLx4o8nzatWqldmPQc6bNw9paWkNPk4IgdTUVPzxj39s8JfB5RqrLVFUSAHMf7Cqdm9U3emW2jRUEZk7dy5SU1NNt0tLS9GpUyecO3cOAQEBNvft9HnLl/921Jayno03ktGeX5y7PE1V+LP1H6oj7esUZv2XmJWI26t7OGM7yR5o+cc+rTEajejYsaPkx1CdraqqChcv3sDew+3RqpXjFf7ycoGBvUvMxjdbqigzZszAN998gy+//LLRtnKM1ZYoKqSEhISYpaySkhI0b97c9JsW1tpY+tn0WtbKXAEBAXaFlFb+zinzfWq8+cNZvq0aaSijnOIoNG/pvuev68z5m7+W2szPzR0htzp/5eY31IgOF93cE+tqt1WA26u71G4ngOPbij2f+3W54vCAVq10TRxrblZi7B3fnnnmGXz22WfYv39/o9UiucZqSxT1K8gJCQnIycmRTNu1axd69eoFb2/vBtv06dPHZf1sitqA4i45xVHIKY5yax9qnTnfTvKhTwQob7uo7Y+S+kQ38XVpOiEEZsyYgU2bNuGLL75AZGRko49x5VgtayWlvLwcP/74o+l2QUEB8vPzERgYiE6dOmHu3Lm4cOEC1q1bB+Dm0cHLli1Damoqpk2bhtzcXKxevVpyJPDMmTPRv39/LFy4EGPGjMHWrVuxe/dum8pT7uTucKI0/GChxtRuI+6orHD7VBd3bitq9/TTT2P9+vXYunUr/P39TdUPg8EAP7+b5UJ3jtWyVlKOHj2KmJgYxMTEAABSU1MRExODV155BQBQVFSEwsJCU/vIyEhkZ2dj7969uPPOO/HXv/4VS5cuxYMPPmhq06dPH2zcuBFr167FHXfcgYyMDGRmZlr9mXklUEpAUVIFhchWrtxe+M1c3fja2W/lypUoLS3FwIEDERoaavrLzMw0tXHnWO2Rl8U3Go0wGAwoLS21a5/dqXNhdj8XA4oUP0SoKeT6psztUlsa20723vumXfNzdMxw5DmOnghu0jEp5WU30Kv7L7L21ZUUdUyK1igloCgFBwJqKmdvQ6ycaBNfU+1gSPEASqii8EPDdvpCH3d3QdGcESwYTrSPr682KOoUZC1hFeV/+GFhf/Cwp31lp6ZfoVKN7D1Yktuh5zlzvh0PplU5hhQZMKD8jycODK6uhFh6Pk8KLg2FFU/c/oi0hCHFyZQWUJSwq8cTKG0XTd3+eEpgYSAhS1hNUTeGFCdSWkBxN60PGkoLJtZ4YmAhIm3ggbNEdtIX+qgmoNSn5r4TOUrrX5i0jJUUJ2EVRUqLHwpaGtxZXSEiNWBIcQIGFG3TUjixpHb5GFaISGm4u0fDeNBs03jarhFPWlbyPFqs7noChpQmYhXFnBY+DDx1wPa0YEZEysaQ0gQMKNrDQfomrgMiUgKGFKL/w4FZioGNtEYLVV5Pw5DiIFZRLFPrhwAHY+u4bojIXRhSyONxEG4c1xFphVq/SHkqhhQHsIqiHRx8bcfdP0Tkagwp5LE44DqG642IXIUXc7MDKygNU1MZlQNt0+gLfXjxNyKSHSsp5HEYUJyD65GI5MaQQh6FA6tzcX0SkZwYUshjcECVB9crEcmFx6QQUZPxGBX3cCQg8nUiNWFI0bAhIT+47EcGlX7QLL/ty49BRT7O3H6tzYuvHSkRQwppHgOK6zCoOIc7ttm6z8nXkJSCIYWInIpBxTFKCtMMLKQUDCmkaUr64CeqTw3bZ20fGVbIHRhSiMjpWE2xTg3BxBKGFXIHhhTSLLUOBlrBoPI/WtoWGVbIlXidFCKSjZYGZ0do+UcZtbpcpCwMKaRJ/ABVDk98LbQcTurylOUk92FIoSZT+jVSyP08ZSDz1EHbE5eZXIMhRcNcdSE3peEHpjJp+XXx1HBSl6cvP8mDIYWIyEEMJ1JcF+RsDCmkKfyQVDatvD4MJ9ZxvZAzMaQQkUupeRBjOLEN1xE5i0tCyooVKxAZGQlfX1/ExcXhwIEDVts+9thj0Ol0Zn/du3c3tcnIyLDYpqKiwhWLowqeejwKqYPaBjGGE/txfanH/v37MWrUKISFhUGn02HLli0NtnflOC17SMnMzERKSgpefPFF5OXloV+/fhg+fDgKCwsttl+yZAmKiopMf+fOnUNgYCDGjRsnaRcQECBpV1RUBF9fX7kXhxSMH4rqoobXi+Gkabju1OHatWvo2bMnli1bZlN7V47Tsl9xdtGiRZg6dSoef/xxAMDixYuxc+dOrFy5Eunp6WbtDQYDDAaD6faWLVtw5coVTJkyRdJOp9MhJCRE3s6rFKsopBZKvSotB1fyJMOHD8fw4cNtbu/KcVrWSkpVVRWOHTuGxMREyfTExEQcPHjQpnmsXr0agwcPRnh4uGR6eXk5wsPD0aFDB4wcORJ5eXlW51FZWQmj0Sj505qc4ijTnyvxGinUVEoKBKycOB/Xp3vUH/MqKytley5njNPWyFpJuXTpEmpqahAcHCyZHhwcjOLi4kYfX1RUhO3bt2P9+vWS6VFRUcjIyECPHj1gNBqxZMkS9O3bF8ePH0eXLl3M5pOeno758+c3bWFkwIqH8/CDUN3cXVHh9iMvd7++arKlrCd8hbfDj68orwawCx07dpRMnzdvHtLS0prWOQucNU5b45IfGNTpdJLbQgizaZZkZGSgdevWGDt2rGR6fHw84uPjTbf79u2L2NhYvP3221i6dKnZfObOnYvU1FTTbaPRaPYCyoVBhMg27hjIGE5Iq86dO4eAgADTbb1eL8vzOGuctkbWkBIUFAQvLy+zqklJSYlZdaU+IQTWrFmDpKQk+Pg0/EHSrFkz3HXXXTh9+rTF+/V6vWwvkCUMJkSOcVVQYThxPVZTXCsgIEASUuTgzHHa6uOa0sHG+Pj4IC4uDjk5OZLpOTk56NOnT4OP3bdvH3788UdMnTq10ecRQiA/Px+hoaFN6m9TueOYEOKAozVyvp485oTIeVwxTsu+uyc1NRVJSUno1asXEhISsGrVKhQWFmL69OkAbu6KuXDhAtatWyd53OrVq9G7d29ER0ebzXP+/PmIj49Hly5dYDQasXTpUuTn52P58uVyL45VDCdEzlMbJJz1zZvBRBlYTVGm8vJy/Pjjj6bbBQUFyM/PR2BgIDp16uTWcVr2kDJhwgRcvnwZCxYsQFFREaKjo5GdnW06CrioqMjsmimlpaXIysrCkiVLLM7z6tWreOKJJ1BcXAyDwYCYmBjs378fd999t9yLY8aTwwnP7CG5NSWsMJgQ2ebo0aMYNGiQ6XbtMZzJycnIyMhw6zitE0IIO5dH9YxGIwwGA0pLS+3aZ/e3EyMltz05oADKCSkcjDyLtcDC7UA93F1NOZM8x672jo4ZjjzHS4cS4duqaWf3vBq/S9a+upJLzu4hkgsHJs/D15zIc/AHBh3k6VUUIiIiuTGkOIABRTm7eohIfVgNI1txd48dGE6IiIhch5UUIiIiUiSGFLIbd/UQUVNxlw/ZgiGFVIsfckRE2saQQnZhFYWIiFyFB84SeRj/s9av31gW3vivkxMRuQpDCtmMVRR1aSiMOPIYBhgicjWGFLIJA4o6OBJMmjJvBhdqCv7gIDWGIYUaxYCibHIGE3ufm6GFiJyJIYUaxICiXO4MJ9YwtBCRMzGkkFVKDiiefvqxEgOKJQwtRNQUDClkRsnhxNOpJZxYw+NaiMgeDClkwnCibGoPKNZYWy6GFyJiSPFwDCbqoNWA0hCeDk1EDCkehqFEXTwxnNjC1euFoYjIPRhSNIphRP0YUJTD1teCYYbIuRhSVI5hhEg5eDYTkXMxpKgIA4nnYBVFGxhaiJqGIUWhGEg8FwOKdtV9bRlYiBrHkKIQDCUEMKB4ktrXmmGFyDqGFDdiMHGMVq82y4DimRhWiKxjSHEDhhMiqo9hhcgcQ4oLMZyQNayiUC3/s4JBhej/MKS4AMMJNYQBherzlKpKZacqd3eBFI4hRUYMJ0TUFKyqkKdr5u4OaBUDCtmCVRRqDLcR8mSspDgZwwkRORsrKuSpWElxIgYUsge/IZM9uL2QJ2JIISJSCS0FFR40S7ZgSHESVlHIHloabMi1uO2QJ2FIcQIGFCIiIudjSGkiBhTX0uol8YnswWoKeQqXhJQVK1YgMjISvr6+iIuLw4EDB6y23bt3L3Q6ndnfDz/8IGmXlZWFbt26Qa/Xo1u3bti8ebPci0HkFBxgyBnUvB3xeBRl2b9/P0aNGoWwsDDodDps2bKlwfauHKdlDymZmZlISUnBiy++iLy8PPTr1w/Dhw9HYWFhg487deoUioqKTH9dunQx3Zebm4sJEyYgKSkJx48fR1JSEsaPH4/Dhw/LvTgSrKIQEZHaXbt2DT179sSyZcvsepwrxmmdEELWON67d2/ExsZi5cqVpmm33347xo4di/T0dLP2e/fuxaBBg3DlyhW0bt3a4jwnTJgAo9GI7du3m6YNGzYMbdq0wYYNGxrtk9FohMFgQGlpKQICAmxeloH/mi25zZDielrY3aPmb8CkPGq8foq7KylnkufY1d7RMcOR53jpUCJ8W3k7PJ+K8mq8Gr/L4b7qdDps3rwZY8eOtdrGFeN0LVkrKVVVVTh27BgSExMl0xMTE3Hw4MEGHxsTE4PQ0FDce++92LNnj+S+3Nxcs3kOHTrU6jwrKythNBolf03FgOJ6DChE6ufugOIp6o95lZWVTn8OZ47T1sh6xdlLly6hpqYGwcHBkunBwcEoLi62+JjQ0FCsWrUKcXFxqKysxIcffoh7770Xe/fuRf/+/QEAxcXFds0zPT0d8+fPd8ISEREpC69Gqy17fvkDmpfrHX789WuVAHahY8eOkunz5s1DWlpa0zr3f+QYp61xyWXxdTrpG0gIYTatVteuXdG1a1fT7YSEBJw7dw5vvvmmaeHtnefcuXORmppqum00Gs1eQHuwikJEREp27tw5ye4evd7x4FOfHOO0NbLu7gkKCoKXl5dZciopKTFLWA2Jj4/H6dOnTbdDQkLsmqder0dAQIDkj9SFu3qIrFPLtsVdPa5Tf8xzZkixpKnjtDWyhhQfHx/ExcUhJydHMj0nJwd9+vSxeT55eXkIDQ013U5ISDCb565du+yapyPOnG/HKgoREVE9co3Tsu/uSU1NRVJSEnr16oWEhASsWrUKhYWFmD59OoCbu2IuXLiAdevWAQAWL16MiIgIdO/eHVVVVfjoo4+QlZWFrKws0zxnzpyJ/v37Y+HChRgzZgy2bt2K3bt348svv5R7ccgNtFBFISJSqvLycvz444+m2wUFBcjPz0dgYCA6derk1nFa9pAyYcIEXL58GQsWLEBRURGio6ORnZ2N8PBwAEBRUZHkmilVVVWYPXs2Lly4AD8/P3Tv3h3btm3DfffdZ2rTp08fbNy4ES+99BJefvlldO7cGZmZmejdu7fci0MuxoDiOQw/3Tz7oLSzvGVprVL6AbTc1aNcR48exaBBg0y3a4/hTE5ORkZGhlvHadmvk6JEjp7zHvHBQhl7RXVpMZyo5bgBZ6sNH87GMGOOIcU2Sr5OSt+tM9C8ZdPO7vn3mGWy9tWVXHJ2D5GttBhOAM8JKHIFElufi8FFmZQUUEhdGFJIEbQaTjyBK4NJY+r3xdNCi9J3+RDZiyGFXI6BRP2UFEwaUrefnhZYiLSAIYVkwSCiTWoJJ5bwwFz34K4eagqGFHIYg4jnUHM4qY9hhUg9GFKoUQwjnktL4aQ+rYYVJR2XwioKNRVDCkkwkDifGs/s0XI4qU+rYYUsi+hw0d1dIDswpHg4hhKqy5PCSX0MK87FKgo5A0OKB2IwIUs8OaDUZfipkkFFo1hFUR+GFA/BYEINYUCRYlWlaVhFIWdhSNE4hhNqCMNJw1hVIXIvhhQNYjAhWzCg2IZBxT6sopAzNXN3B8h59IU+DChkEwYU+3B9qR+PR1EnhhSNYDghW3HAdYya1pu7TntnFYWcjSFF5Vg9IXuoaaBVIq4/ItdiSFEphhOyFwdY5+B6tEzJVRTu6lEvhhQVYjghe3FgdS6uTyLXYEhRGQYUdVHCJfE5oMqD6/V/lFxFIXVjSFEJ7t4hR3AglRfXr/JxV4+6MaSoAMMJESkVqygkJ4YUhWNAIUfxW75rcD0TyYchRcEYUMhRHDhdy1PXt9KrKNzVo34MKQrFgEKO8tQBk1xL6QGFtIEhRYEYUIjUh+FQWVhF0QaGFIVhQKGm4EDpXp6y/llFIVdhSCHSCE8ZIIkawyqKdjCkKAirKETqp/WwyCoKuRJDikIwoFBTaH1gJLIVqyjawpCiAAwoRKQGrKKQqzGkEKkcqyjKw9fEPVhF0R6GFDdjFYWagoMhuQqrKOQODClERDJggHQtVlG0iSHFjVhFoabgIEhEWseQQkREDeKuHnIXhhQ3YRVF+/zPCtnmzSqKOvB1Imoal4SUFStWIDIyEr6+voiLi8OBAwestt20aROGDBmCdu3aISAgAAkJCdi5c6ekTUZGBnQ6ndlfRUWF3ItCRESkKfv378eoUaMQFhYGnU6HLVu2NNjeleO07CElMzMTKSkpePHFF5GXl4d+/fph+PDhKCwstNh+//79GDJkCLKzs3Hs2DEMGjQIo0aNQl5enqRdQEAAioqKJH++vr5yL45TsIpCTcFv5+RK3NWjfdeuXUPPnj2xbNkym9q7cpxubldrByxatAhTp07F448/DgBYvHgxdu7ciZUrVyI9Pd2s/eLFiyW3X3vtNWzduhWff/45YmJiTNN1Oh1CQkJk7TuRo+Tc1UPqYvipEqWd9e7uBpFVw4cPx/Dhw21u78pxWtZKSlVVFY4dO4bExETJ9MTERBw8eNCmedy4cQNlZWUIDAyUTC8vL0d4eDg6dOiAkSNHmiW4uiorK2E0GiV/RGrEKgoR2aL+mFdZKd9nhzPGaWtkraRcunQJNTU1CA4OlkwPDg5GcXGxTfN46623cO3aNYwfP940LSoqChkZGejRoweMRiOWLFmCvn374vjx4+jSpYvZPNLT0zF//vymLYyTcFeP9rGKQkSOKvw5CM38HD904cbvN4/56Nixo2T6vHnzkJaW1pSuWeWMcdoa2Xf3ADdLPnUJIcymWbJhwwakpaVh69ataN++vWl6fHw84uPjTbf79u2L2NhYvP3221i6dKnZfObOnYvU1FTTbaPRaPYCEjkDz+ghIiU4d+4cAgICTLf1enl2OTprnLZG1pASFBQELy8vs6pJSUmJWXWlvszMTEydOhWffPIJBg8e3GDbZs2a4a677sLp06ct3q/X62V7gYhqMaCQkvifFSgLb/zLoFacOd+OV52tIyAgQBJS5ODMcdrq45rSwcb4+PggLi4OOTk5kuk5OTno06eP1cdt2LABjz32GNavX48RI0Y0+jxCCOTn5yM0NLTJfSayh/9ZYfojskatIZNn9pA1rhqnZd/dk5qaiqSkJPTq1QsJCQlYtWoVCgsLMX36dAA3d8VcuHAB69atA3BzwR999FEsWbIE8fHxpiqMn58fDAYDAGD+/PmIj49Hly5dYDQasXTpUuTn52P58uVyL06T8HgUdXNXEFHrAEfqpy/0UVVQYTXFMeXl5fjxxx9NtwsKCpCfn4/AwEB06tTJreO07CFlwoQJuHz5MhYsWICioiJER0cjOzsb4eHhAICioiLJNVPeffddXL9+HU8//TSefvpp0/Tk5GRkZGQAAK5evYonnngCxcXFMBgMiImJwf79+3H33XfLvTikUayEEJGnOnr0KAYNGmS6XXsMZ+24685xWieE8LhPZ6PRCIPBgNLSUrv22UV8sLBJz8tKinupMYiwiqId7rhWijOOSVFTJaVWY9WUvfe+adf8HB0zHHmOjivTmnx2z7mn0mTtqyu55OweIldTYyAhIufgbh/tYEgh1dNqIGEVhYg8HX8F2UW4q8e5tH5WDQMKKYVaP7vOnG/n7i6QEzCkkGpoPZiQtjF4uh6Divpxdw8pmicGEg5m5CzOuqCb2k5FJu1gSCFF8sRwAig3oPj8cL7RNlVRHVzQEyL78CBadWNIIUXx1HACKCug2BJKGnsMQ4u2sJpC7sCQQorgyeEEUEZAcSSY2DI/hhXtUGtQYTVFvXjgLLkdA4r2Akr9ecs5f3IttZ7tQ+rEkEJuwzN13B9QXBkgGFa0Q41BhWf6qBNDCrmFp4cTwL0BxZ2BgUHFteR6r6kxqJD6MKSQS7F6cpO7A4q7KaEP1HRqCyqspqgPD5wll2E4YTipy+eH8zyoVgPUdjAtg4q6sJJCLsGAwoBiiVL7RfZRW0WF1IMhhWTHgMKA0hCl989ZSjvr3d0FWTGokBwYUkhWnh5QDD9VMqDYQC39VCtXvQ8ZVMjZGFJcRE37bJ2FAcX9pxcTuZq+0IdhhZyGIYXIydxdPQHUGVDU2GeyjkGFnIEhhWThqVUUd4cTQN2DvZr7TuYYVKipGFLI6TwxoCihegJwkCfr3PW+ZFChpuB1UsipPC2gKCGY1GJAIaVS27VUSDlYSSFyEAOKPLS0LLW0fvqxLVhRIUcwpLiQ1r9JeFIVhQGFyH4884fsxZBCZAelHHtSiwGF7KGULxIMKmQrhhRyCqV8+MlJSeFE6xi+tI9BhWzBkEJkAyUGFA7k6sDjUaxjUKHGMKS4mBaPS9FyFUVpu3dqMaCQVjCoUEMYUoisUGI4IWoqJX6pYFAhaxhS3ECL1RStUXJAYRVFPbirx3YMKmQJQwpRPQwoRO7BoEL1MaRQkyixdNwUSg4oRJ6AQYXqYkhxE+7yUR6lBxRWUdSFu3ocx6BCtRhSiKD8gELkTFqrgJJ2MaS4EaspyqCGgMIqirqwitJ0rKYQwJBCTaCFb2NqCChEnopBhRhS3IzVFCJzVVEd3N0Fh7GK4lwMKp7NJSFlxYoViIyMhK+vL+Li4nDgwIEG2+/btw9xcXHw9fXFrbfeinfeecesTVZWFrp16wa9Xo9u3bph8+bNcnWfNEotVRTu6iEiOe3fvx+jRo1CWFgYdDodtmzZ0uhjXDVOyx5SMjMzkZKSghdffBF5eXno168fhg8fjsLCQovtCwoKcN9996Ffv37Iy8vDCy+8gGeffRZZWVmmNrm5uZgwYQKSkpJw/PhxJCUlYfz48Th8+LDciyMLVlNcTy0BhdSFVRR5sJoir2vXrqFnz55YtmyZTe1dOU7rhBCyHljQu3dvxMbGYuXKlaZpt99+O8aOHYv09HSz9nPmzMFnn32GkydPmqZNnz4dx48fR25uLgBgwoQJMBqN2L59u6nNsGHD0KZNG2zYsMFsnpWVlais/N+gZDQa0bFjR5SWliIgIMDmZYn4YKHNbe2lxjehWo9JUVtA8cRKilp396gtpJSF69zdBbs46wvdmeQ5drU3Go0wGAx2jxmOPEfHlWlo5ufr8Hxu/F6Bc0+l4dy5c5K+6vV66PWNb586nQ6bN2/G2LFjrbaRY5y2RtZKSlVVFY4dO4bExETJ9MTERBw8eNDiY3Jzc83aDx06FEePHkV1dXWDbazNMz09HQaDwfTXsWNHRxdJNqymEN3EgEKezOecD/SFjv/5nLv5hbdjx46Scc9SUcBRcozT1sgaUi5duoSamhoEBwdLpgcHB6O4uNjiY4qLiy22v379Oi5dutRgG2vznDt3LkpLS01/586dc3SRZMWgIj9WUUgODCiuocaKs7ucO3dOMu7NnTvXafOWY5y2pnnTumobnU5aUhRCmE1rrH396fbM09YyF2mb2gKKJ1JrFYVcR1/owy90NggICJBt1xTg/HHaGlkrKUFBQfDy8jJLTiUlJWYJq1ZISIjF9s2bN0fbtm0bbGNtnmrCNx+RurCKQp7GleO0rCHFx8cHcXFxyMnJkUzPyclBnz59LD4mISHBrP2uXbvQq1cveHt7N9jG2jzVhkHF+VhFUT41VlEYUNyDu33cy5XjtOy7e1JTU5GUlIRevXohISEBq1atQmFhIaZPnw7g5vEiFy5cwLp16wDcPEJ42bJlSE1NxbRp05Cbm4vVq1dLjgaeOXMm+vfvj4ULF2LMmDHYunUrdu/ejS+//FLuxSEiAsCAQtpRXl6OH3/80XS7oKAA+fn5CAwMRKdOndw6TsseUiZMmIDLly9jwYIFKCoqQnR0NLKzsxEeHg4AKCoqklwzJTIyEtnZ2Zg1axaWL1+OsLAwLF26FA8++KCpTZ8+fbBx40a89NJLePnll9G5c2dkZmaid+/eci+Oy1R2quK3BSdhFUX51FZFYUBxPx6b4jxHjx7FoEGDTLdTU1MBAMnJycjIyHDrOC37dVKUyNFz3uW8Too1Sg4qarlOippDiiec3cOA4j5qu05KfY6GFCVfJ6XzC6/By9fx66TUVFTgp9dekLWvrsTf7lE4flNoGjUHFFIeLQUUIjVgSFEBpQYVtX8LI/dTUxWFAUV5lFxpJudgSFEJpQYVJdNCFUVNg7i91LRsWgwo/JJBasCQoiIMKkSup8WAoiWspmgbQwoRuZxaqigMKETuxZCiMqym2EYLu3q0igGFiGzFkKJCDCqeRS2Dui3UsCylnfUMKEQKwZCiUgwqpDZqCSieQGsHzfK4FO1iSFExJQQVJX7YaXFXjxoG+Iaoof+eElCI1ET2y+KTvHj5fFI6pQcUhhMi5WIlRQMqO1UpoqpC8lL6YG+J0vvsiQFFidVPImsYUjSEQUX7lD7o16qK6qDovvLgWO1hRVmbuLtHY7j7h9xN6eHEk7GKQmrDSooGeXJFRYsHzdan5BCg5L55ekAhUiOGFDtEdLiIiA4X3d0Nm7gyqPDbmespLQwoefcOd+3cxPcpqRFDioZ5ckXFEyglFCilH/UxnBCpH0OKA9RSTQEYVLTOnQFBqdUThhNzrKKQWvHAWQ/Ag2m1rTYo+Pxw3qXPpzQMJpYxoJCasZLiIVhR0T65wwMrJ6R0/DKmPaykOCiiw0WcOd/O3d2wCysq2lc3RDirsqLEYAKwcmILVlFI7RhSPIxcQaUsXAf/s8Lp8yXHORpYlBpK6mJAaRwDCmkBQ0oTqLGaQp5JDcHDFgwntmFAIa3gMSlNpKYzfWrx+BRSGx53YjsGFNIShhQPxaBCasFwYjsGFNIahhQnUGM1BWBQIeVjQLEdAwppEUOKk6g1qBApFQOKbcrCdQwopFkMKU6kxqDizGoKPyjJGXj8ie34niOtY0hxMjUGFSKlYDixDasn5CkYUmSgtqDCY1NICRhQGsdwQp6GIUUmagsqRO7EgNI4hpPG8QuX9jCkyEhNQYVvbiLlqa2cMKCQp2JIkZmaggqRO7CKYo7BhOgmhhQXYFBxHQ546sLX639YNSEyx9/ucRH+zg+RFAMKjzMhagxDigsxqBDd5KkBhaGEyD6y7u65cuUKkpKSYDAYYDAYkJSUhKtXr1ptX11djTlz5qBHjx5o2bIlwsLC8Oijj+Lnn3+WtBs4cCB0Op3kb+LEiXIuitNofdcPP4SJpLtuuBuH1GDFihWIjIyEr68v4uLicODAAattH3vsMbMxWKfToXv37qY2GRkZFttUVFTY1S9ZKymTJk3C+fPnsWPHDgDAE088gaSkJHz++ecW2//222/4+uuv8fLLL6Nnz564cuUKUlJSMHr0aBw9elTSdtq0aViwYIHptp+fn3wLQkROo/YqCsOGMvEMRcdlZmYiJSUFK1asQN++ffHuu+9i+PDh+P7779GpUyez9kuWLMHrr79uun39+nX07NkT48aNk7QLCAjAqVOnJNN8fX3t6ptsIeXkyZPYsWMHDh06hN69ewMA3nvvPSQkJODUqVPo2rWr2WMMBgNycnIk095++23cfffdKCwslKysFi1aICQkRK7uy4q7feRV2lkPw0+V7u4GKQiDBZF1ixYtwtSpU/H4448DABYvXoydO3di5cqVSE9PN2tfu3ek1pYtW3DlyhVMmTJF0k6n0zV5nJZtd09ubi4MBoMpoABAfHw8DAYDDh48aPN8SktLodPp0Lp1a8n0jz/+GEFBQejevTtmz56NsrIyq/OorKyE0WiU/BGR67miisLdLEQwG/MqKy1/cauqqsKxY8eQmJgomZ6YmGjzWL169WoMHjwY4eHhkunl5eUIDw9Hhw4dMHLkSOTl5dm9HLJVUoqLi9G+fXuz6e3bt0dxcbFN86ioqMDzzz+PSZMmISAgwDR98uTJiIyMREhICL777jvMnTsXx48fN6vC1EpPT8f8+fMdWxAicgq5AwrDCGmB/zkBLx/h8ONrqm4+tmPHjpLp8+bNQ1pamln7S5cuoaamBsHBwZLpwcHBNo3VRUVF2L59O9avXy+ZHhUVhYyMDPTo0QNGoxFLlixB3759cfz4cXTp0sXm5bE7pKSlpTU64B85cgTAzVJPfUIIi9Prq66uxsSJE3Hjxg2sWLFCct+0adNM/0dHR6NLly7o1asXvv76a8TGxprNa+7cuUhNTTXdNhqNZi8gaQt3+XgWBhQiqXPnzkm+3Ov1DX9JqD8u2zpWZ2RkoHXr1hg7dqxkenx8POLj4023+/bti9jYWLz99ttYunSpDUtwk90hZcaMGY2eSRMREYFvvvkGv/zyi9l9Fy9eNEts9VVXV2P8+PEoKCjAF198IVnRlsTGxsLb2xunT5+2GFL0en2jLxARyUftB8uSsvGgWXMBAQGNjp0AEBQUBC8vL7OqSUlJSaNjtRACa9asQVJSEnx8fBps26xZM9x11104ffp0452vw+6QEhQUhKCgoEbbJSQkoLS0FF999RXuvvtuAMDhw4dRWlqKPn36WH1cbUA5ffo09uzZg7Zt2zb6XCdOnEB1dTVCQ0NtXxAicgnu5iFSLh8fH8TFxSEnJwf333+/aXpOTg7GjBnT4GP37duHH3/8EVOnTm30eYQQyM/PR48ePezqn2wHzt5+++0YNmwYpk2bhkOHDuHQoUOYNm0aRo4cKTmzJyoqCps3bwZw8zSmhx56CEePHsXHH3+MmpoaFBcXo7i4GFVVN5PyTz/9hAULFuDo0aM4c+YMsrOzMW7cOMTExKBv375yLY7m6QsbTsFqxG/v2seAQtR0qampeP/997FmzRqcPHkSs2bNQmFhIaZPnw7g5iETjz76qNnjVq9ejd69eyM6Otrsvvnz52Pnzp3473//i/z8fEydOhX5+fmmedpK1uukfPzxx3j22WdNRw2PHj0ay5Ytk7Q5deoUSktLAQDnz5/HZ599BgC48847Je327NmDgQMHwsfHB//617+wZMkSlJeXo2PHjhgxYgTmzZsHLy8vORfHaXj6MXkKBkWSG3f1NN2ECRNw+fJlLFiwAEVFRYiOjkZ2drbpbJ2ioiIUFhZKHlNaWoqsrCwsWbLE4jyvXr2KJ554AsXFxTAYDIiJicH+/ftNe1ZspRNCOH4YsUoZjUYYDAaUlpbatM+u1sB/zXbK8ysxpDizkuJ/VlmbFA+gdQ9XnW5Mns2RkHImeY5d7R0dMxx5jjuT/gYvH/sueFZXTVUF8j98Uda+uhJ/BdnFtB5QiAAGFCJyDoYUIiJSJe7q0T6GFBdSYhXFE/C4CNfi+iYiZ2FI8XCesquHA6drcD2Tq7CK4hkYUlzEk6ooPFaAiIicgSHFBTwpoCgZv+XLi+uXXIVVFM/BkOLBPGVXD8nP1QGF1Toiz8CQIjNWUZSF3/adj+uUXIlVFM/CkOKhPLmKwkHVebguyZUYUDwPQ4qMWEVRLg6uTcd1SERyY0iRiZIDiidXUcg5GFDI1VhF8UwMKeSxONA6huuNXI0BxXMxpMiAVRT14IBrH64vcjUGFM/GkOJkSg4oZBkHXttwPRGRqzGkEIEDcGO4fsgdWEUhhhQnUnoVxZW7etR4sS0OxJYpbb2ocdsi+zGgEMCQQiRR2lmvuEHZnbguyB0YUKgWQ4qTsIqiLZ4+ODOskbswoFBdDClEVnjqIO2py03uVdmpigGFzDR3dwdIfqyiOK52wDb8VOnmnsiP4YTcheGErGElxQmUvquHmk7rA7jWl4+UiwGFGsJKisa5s4pSFq6D/1nhtud3Ni1WVRhOyF0YTsgWDClNxCqK59FCWFFrOOHpx9rAgEK2YkghclDdgV4tgUWt4YS0geGE7MWQomE8YNZ1lFxdYTAhd2M4IUcxpDQBd/VQffUDgbtCC4MJKQHDCTUVQ4pGKaWKorWDZ+3litDCQEJKw3BCzsKQQuRCtgSK+kGGIeQmHjSrbAwmJAeGFCKFYSghtWAwIbkxpDhIycejKGVXTy1P3+VDpCUMJuRKDClERGQVQwm5E0OKxiitikLkDDwexTUYSEhpGFLIJbjLh0g5GEZILRhSHKDk41GIyHMxfJDWMKRoiNJ39bCaQo7w5F09DB3k6ZrJOfMrV64gKSkJBoMBBoMBSUlJuHr1aoOPeeyxx6DT6SR/8fHxkjaVlZV45plnEBQUhJYtW2L06NE4f/68jEtCRCSvyk5VZn9ErrJixQpERkbC19cXcXFxOHDggNW2e/fuNRundTodfvjhB0m7rKwsdOvWDXq9Ht26dcPmzZvt7pesIWXSpEnIz8/Hjh07sGPHDuTn5yMpKanRxw0bNgxFRUWmv+zsbMn9KSkp2Lx5MzZu3Igvv/wS5eXlGDlyJGpqauRaFHIST/5WTFQfAwkpQWZmJlJSUvDiiy8iLy8P/fr1w/Dhw1FYWNjg406dOiUZq7t06WK6Lzc3FxMmTEBSUhKOHz+OpKQkjB8/HocPH7arb7Lt7jl58iR27NiBQ4cOoXfv3gCA9957DwkJCTh16hS6du1q9bF6vR4hISEW7ystLcXq1avx4YcfYvDgwQCAjz76CB07dsTu3bsxdOhQ5y8MEbmFVkMtQwkpyaJFizB16lQ8/vjjAIDFixdj586dWLlyJdLT060+rn379mjdurXF+xYvXowhQ4Zg7ty5AIC5c+di3759WLx4MTZs2GBz32SrpOTm5sJgMJgCCgDEx8fDYDDg4MGDDT527969aN++Pf7whz9g2rRpKCkpMd137NgxVFdXIzEx0TQtLCwM0dHRVudbWVkJo9Eo+XPEmfPtFHvQrNKPR6lLqwMPkS0YUMgV6o95lZWWfzesqqoKx44dk4ypAJCYmNjoWB0TE4PQ0FDce++92LNnj+S+3Nxcs3kOHTq00XnWJ1slpbi4GO3btzeb3r59exQXF1t93PDhwzFu3DiEh4ejoKAAL7/8Mu655x4cO3YMer0excXF8PHxQZs2bSSPCw4Otjrf9PR0zJ8/v2kLRE7Fg2ipMVoMswwo1JiAgko0b+74tn/9+s0w0rFjR8n0efPmIS0tzaz9pUuXUFNTg+DgYMn0hsbU0NBQrFq1CnFxcaisrMSHH36Ie++9F3v37kX//v0B3MwA9szTGrtDSlpaWqMD/pEjRwAAOp35ihZCWJxea8KECab/o6Oj0atXL4SHh2Pbtm144IEHrD6uofnOnTsXqamppttGo9HsBSQikhMDCrnSuXPnEBAQYLqt1zf8m2D1x8+GxtSuXbtKDtlISEjAuXPn8Oabb5pCir3ztMbukDJjxgxMnDixwTYRERH45ptv8Msvv5jdd/HiRbN01ZDQ0FCEh4fj9OnTAICQkBBUVVXhypUrkmpKSUkJ+vTpY3Eeer2+0RdIzdS0q6cuVlPIUzCgkKsFBARIQoo1QUFB8PLyMqtwlJSU2DVWx8fH46OPPjLdDgkJafI8AQeOSQkKCkJUVFSDf76+vkhISEBpaSm++uor02MPHz6M0tJSq2HCksuXL+PcuXMIDQ0FAMTFxcHb2xs5OTmmNkVFRfjuu+/smi8pgxZL+tR03C5ILhEdLrq7C4ri4+ODuLg4yZgKADk5OXaNqXl5eaZxGrhZXak/z127dtk9Tst2TMrtt9+OYcOGYdq0aXj33XcBAE888QRGjhwpKRNFRUUhPT0d999/P8rLy5GWloYHH3wQoaGhOHPmDF544QUEBQXh/vvvBwAYDAZMnToVzz33HNq2bYvAwEDMnj0bPXr0MJ3tQ+rCigrVpbWAwiqKcjCgWJaamoqkpCT06tULCQkJWLVqFQoLCzF9+nQANw+ZuHDhAtatWwfg5pk7ERER6N69O6qqqvDRRx8hKysLWVlZpnnOnDkT/fv3x8KFCzFmzBhs3boVu3fvxpdffmlX32S94uzHH3+MZ5991nSE7+jRo7Fs2TJJm1OnTqG0tBQA4OXlhW+//Rbr1q3D1atXERoaikGDBiEzMxP+/v6mx/zjH/9A8+bNMX78ePz++++49957kZGRAS8vLzkXh2TEoEJE5B4TJkzA5cuXsWDBAhQVFSE6OhrZ2dkIDw8HcHNvRd1rplRVVWH27Nm4cOEC/Pz80L17d2zbtg333XefqU2fPn2wceNGvPTSS3j55ZfRuXNnZGZmSs74tYVOCOFxI4PRaITBYEBpaalN++xqRXywUMZeOU6tx6RYwqDi2bRWRQFYSVGKulWUvfe+addjHR0zHHmO/n98Bc2b+zo8n+vXK7D/ywWy9tWVZL3iLMlPSwEF0OYgRZ6LAYWoaRhSSHEYVDwTX3eSC49FUS+GFFKksnAdBy0PwteaiCxhSCFF4+BFRE3BKoq6MaSQ4rGqom18bUkuDCjqx5BCqsGwoj18PUkuDCjawJBCqsOwog1afw15Zo/7MKBoh6wXcyOSU91BjtdXURetBxRyHwYUbWFIIU1gYFEPBhSSA8OJNjGkkObUHwQZWpSDAYWcjeFE2xhSSPMsDYwMLq7HgELOxHDiGRhSyCPZOmAyzDgHAwo5C8OJZ2FIIWpAUwZXBhyGE3IOBhPPxZBCJBNPr9Z4ckDh6cdNw1BCtRhSiNysocFcjQHGk8MJ2Y+BhBrCkEKkYNYGfKWFFwYTagiDCDmKIYVIhZQQXhhMqBZDCMmFIYVIQ+TcdcRQQgwj5GoMKUQegiGD7MFAQkrAkKJylZ2qoC/0cXc3iEgDGExIaRhSiIicSG2nHzOYkJI1c3cHiIjIPRhQSOlYSSEi8jAMJ6QWrKRogNrKy0TkPgwopCYMKUREHoIBhdSGIYWIyAMwoJAaMaRoBHf5ELkf34dEzsWQQkSkcayikFoxpGgIv8URUX0MKKRmDClERESkSLxOisbwMvnuZWs1i6+R9rCSSeR8DClETeDowFT3cQwsJBfu6iG1Y0jRIFZT5OXsb8y18+NrRkQkxZBCZANXlPIZVojkNSTkB3d3gezEA2c1ivvHnaOyU5XL1yVfO/VR4mvGXT2kBbKGlCtXriApKQkGgwEGgwFJSUm4evVqg4/R6XQW/9544w1Tm4EDB5rdP3HiRDkXRZWU+MGpFu4IJ/Wfn4ich1WUhq1YsQKRkZHw9fVFXFwcDhw4YLXtpk2bMGTIELRr1w4BAQFISEjAzp07JW0yMjIsjuUVFRV29UvWkDJp0iTk5+djx44d2LFjB/Lz85GUlNTgY4qKiiR/a9asgU6nw4MPPihpN23aNEm7d999V85FUS0OdrarDSZKWWdK6guRmjGgNCwzMxMpKSl48cUXkZeXh379+mH48OEoLCy02H7//v0YMmQIsrOzcezYMQwaNAijRo1CXl6epF1AQIDZmO7r62tX32Q7JuXkyZPYsWMHDh06hN69ewMA3nvvPSQkJODUqVPo2rWrxceFhIRIbm/duhWDBg3CrbfeKpneokULs7ZkGQ+kbZjSgwBfP2VT+vbj6RhQGrdo0SJMnToVjz/+OABg8eLF2LlzJ1auXIn09HSz9osXL5bcfu2117B161Z8/vnniImJMU3X6XRNHqdlq6Tk5ubCYDCYAgoAxMfHw2Aw4ODBgzbN45dffsG2bdswdepUs/s+/vhjBAUFoXv37pg9ezbKysqszqeyshJGo1Hy52n4QWpOTZUKtfSTlIHHo9wMJ54cUOqPeZWVlRbbVVVV4dixY0hMTJRMT0xMtHmsvnHjBsrKyhAYGCiZXl5ejvDwcHTo0AEjR440q7TYQrZKSnFxMdq3b282vX379iguLrZpHh988AH8/f3xwAMPSKZPnjwZkZGRCAkJwXfffYe5c+fi+PHjyMnJsTif9PR0zJ8/3/6F0Bh+I79JrQM+Xz8i26g5nPj852c0b+b4+7zZjZufbx07dpRMnzdvHtLS0szaX7p0CTU1NQgODpZMDw4Otnmsfuutt3Dt2jWMHz/eNC0qKgoZGRno0aMHjEYjlixZgr59++L48ePo0qWLzctjd0hJS0trdMA/cuQIgJulnvqEEBanW7JmzRpMnjzZbB/WtGnTTP9HR0ejS5cu6NWrF77++mvExsaazWfu3LlITU013TYajWYvoKfw1IFOrcGkPk99/ZRKK9uVFqg5mMjh3LlzCAgIMN3W6/UNtq8/Lts6Vm/YsAFpaWnYunWrpDARHx+P+Ph40+2+ffsiNjYWb7/9NpYuXWrrYtgfUmbMmNHomTQRERH45ptv8Msvv5jdd/HiRbPEZsmBAwdw6tQpZGZmNto2NjYW3t7eOH36tMWQotfrG32BPIknDXRaHEQ86fUjsoahpGEBAQGSkGJNUFAQvLy8zKomJSUljY7VmZmZmDp1Kj755BMMHjy4wbbNmjXDXXfdhdOnTzfe+TrsDilBQUEICgpqtF1CQgJKS0vx1Vdf4e677wYAHD58GKWlpejTp0+jj1+9ejXi4uLQs2fPRtueOHEC1dXVCA0NbXwBCID2BzothpO6tP76qYHWtzF7MTSok4+PD+Li4pCTk4P777/fND0nJwdjxoyx+rgNGzbgT3/6EzZs2IARI0Y0+jxCCOTn56NHjx529U+2A2dvv/12DBs2DNOmTcOhQ4dw6NAhTJs2DSNHjpSc2RMVFYXNmzdLHms0GvHJJ5+YjjSu66effsKCBQtw9OhRnDlzBtnZ2Rg3bhxiYmLQt29fuRZHk9R04KgtlHYKsdw8ZTlJ+RhQ1C01NRXvv/8+1qxZg5MnT2LWrFkoLCzE9OnTAdw8ZOLRRx81td+wYQMeffRRvPXWW4iPj0dxcTGKi4tRWlpqajN//nzs3LkT//3vf5Gfn4+pU6ciPz/fNE9byXpZ/I8//hjPPvus6ajh0aNHY9myZZI2p06dkiwYAGzcuBFCCDz88MNm8/Tx8cG//vUvLFmyBOXl5ejYsSNGjBiBefPmwcvLS76F0TC1fyv35MFa7a+dWil5m3P1mT0MKOo3YcIEXL58GQsWLEBRURGio6ORnZ2N8PBwADevX1b3minvvvsurl+/jqeffhpPP/20aXpycjIyMjIAAFevXsUTTzyB4uJiGAwGxMTEYP/+/aY9K7bSCSFE0xdRXYxGIwwGA0pLS23aZ1cr4oOFMvZKGdQy4Cl5kHAHtbxuWqHk7c+VIUWtAeXF7v+0q72jY4YjzzG4/eNNOrvn+o0q7C55X9a+uhJ/YJAk6n74KmngU/KgoASsqLgOt0Ui12FIIavc/au8HAzsw6BCrqTWKgqpC0MKNap+WJBjIGQgITXgdkrkWgwpZLfGPqgthRh+uLsGqylEpCUMKeR0DCTuxaAiDzVs1/zNHtIa2a6TQkTuo4YBVU24PoncgyHFDvyWQmrCgZWI1I4hxU4MKqQmnnQFXrlw/RG5D0MKkQfgQOsYrjci92JIIfIQHHDtw/VF5H4MKUQehAOvbdS4nrgrmrSIIcUB/DAgNVPjAOxKXD9EysGQQuSBOBBbxvVCpCwMKUQeimf+SHFdECkPQwqRh+PgrP51wF3QpFUMKUTk0VUVT11uIjVgSHEQv7mQFnnagO1py0ukNvyBQSKSqB24tfwjhVoKJ/zCRFrGkEJEFmkxrGgpnJBjHgr42t1dIDtwd08T8BsMeQKtHK+ihWWgpmFAUR9WUojIJmqtrGg5nPCLEmkdQwpREzU0UJw5386FPXENNYQVLQcTcgyrKOrEkNJEER0uanIgosbZ8i22to0Wt5G6QUApgYXhhCxhQFEvhhQiOzlSYtd6mHVXYPHkUOLOXT1DQn5w23OTZ2FIcQKtD0D0P00ZGDxlO7EUHJwVXDw5lJBjWEVRN4YUJ/GUAchTOetbq6duJwwXzsUDZm3DgKJ+PAWZqBHOHhA4wBDJjwFFGxhSnIiDj7ZEdLgo22vKbYUcxW2ncQwo2sGQ4mT8AFE/OcNJ/echsocSthmlHzTLgKItDCkyUMIHCTnG1a8dtxUi52FA0R4eOCsTTz1AUq3cGRa4rZAtGGitYzjRLlZSZMQPFeVz1a4dW/pBZI1Stg8l7uphQNE2hhSZKeXDhaSUEk7qUlp/SBmUsl0woJA7cHePC2j50uhqo5QPfGu464fqUvr26i4MJ56DIcWFGFbcR00f9txOCFDWNqukKgoDimeRdXfP3/72N/Tp0wctWrRA69atbXqMEAJpaWkICwuDn58fBg4ciBMnTkjaVFZW4plnnkFQUBBatmyJ0aNH4/z58zIsgTyUuKtBi2rXs1rXtVr7TU2jtG1WKQHloYCvGVBktGLFCkRGRsLX1xdxcXE4cOBAg+337duHuLg4+Pr64tZbb8U777xj1iYrKwvdunWDXq9Ht27dsHnzZrv7JWtIqaqqwrhx4/DUU0/Z/Ji///3vWLRoEZYtW4YjR44gJCQEQ4YMQVlZmalNSkoKNm/ejI0bN+LLL79EeXk5Ro4ciZqaGjkWQzZ1B1ElfSiplRbXp5aWhRqmxNdaCQGF4UR+mZmZSElJwYsvvoi8vDz069cPw4cPR2FhocX2BQUFuO+++9CvXz/k5eXhhRdewLPPPousrCxTm9zcXEyYMAFJSUk4fvw4kpKSMH78eBw+fNiuvumEEKJJS2eDjIwMpKSk4OrVqw22E0IgLCwMKSkpmDNnDoCbVZPg4GAsXLgQTz75JEpLS9GuXTt8+OGHmDBhAgDg559/RseOHZGdnY2hQ4c22h+j0QiDwYDS0lIEBATYvBwD/zXb5rbOwHJ/w5T2ge4K3Ca0R6nbsVICihy6dvzZrvaOjhmOPMfg9o+jeTPHf5Dz+o0q7C55366+9u7dG7GxsVi5cqVp2u23346xY8ciPT3drP2cOXPw2Wef4eTJk6Zp06dPx/Hjx5GbmwsAmDBhAoxGI7Zv325qM2zYMLRp0wYbNmyweXkUdUxKQUEBiouLkZiYaJqm1+sxYMAAHDx4EE8++SSOHTuG6upqSZuwsDBER0fj4MGDFkNKZWUlKisrTbdLS0sB3Nwo7HH9WmXjjZyoQxvzXViFPwe5tA9K0Snsktm069fc0BE3q7tNeOq2oAV1t2elbceDgv8DAKgod18fxvofBwCUlzXS0EH2fvbXtnfBd3pcF1XAjSY+HubLqNfrodfrzdpXVVXh2LFjeP755yXTExMTcfDgQYvPkZubKxmDAWDo0KFYvXo1qqur4e3tjdzcXMyaNcuszeLFi+1aHkWFlOLiYgBAcHCwZHpwcDDOnj1rauPj44M2bdqYtal9fH3p6emYP3++2fSOHTs6o9vkAufc3QEiJ1Ly9vxvd3cAwKuyP4PBoUeVlZXBYHDssY3x8fFBSEgI9hava/K8WrVqZTa+zZs3D2lpaWZtL126hJqaGovjrrUxtbi42GL769ev49KlSwgNDbXaxto8rbE7pKSlpVkc8Os6cuQIevXqZe+sTXQ6neS2EMJsWn0NtZk7dy5SU1NNt2/cuIFff/0Vbdu2bXS+dRmNRnTs2BHnzp2TreQnB/bb9dTad/bbtdhv13Ok70IIlJWVISwsTLZ++fr6oqCgAFVVVU2el6Xx0FIVpS57x11L7etPd2Qsr8/ukDJjxgxMnDixwTYRERH2zhYAEBISAuBmSgsNDTVNLykpMSWykJAQVFVV4cqVK5JqSklJCfr06WNxvpbKXLaebWRJQECA6t6YAPvtDmrtO/vtWuy369nbd7kqKHX5+vrC19dX9uepKygoCF5eXmYVjrrjbn0hISEW2zdv3hxt27ZtsI21eVpj99k9QUFBiIqKavDP0ZUcGRmJkJAQ5OTkmKZVVVVh3759pgASFxcHb29vSZuioiJ89913VkMKERERmfPx8UFcXJxkTAWAnJwcq2NqQkKCWftdu3ahV69e8Pb2brCNveO0rMekFBYW4tdff0VhYSFqamqQn58PALjtttvQqlUrAEBUVBTS09Nx//33Q6fTISUlBa+99hq6dOmCLl264LXXXkOLFi0wadIkADfT7NSpU/Hcc8+hbdu2CAwMxOzZs9GjRw8MHjxYzsUhIiLSnNTUVCQlJaFXr15ISEjAqlWrUFhYiOnTpwO4ecjEhQsXsG7dzeNlpk+fjmXLliE1NRXTpk1Dbm4uVq9eLTlrZ+bMmejfvz8WLlyIMWPGYOvWrdi9eze+/PJL+zonZJScnCwAmP3t2bPH1AaAWLt2ren2jRs3xLx580RISIjQ6/Wif//+4ttvv5XM9/fffxczZswQgYGBws/PT4wcOVIUFhbKuShCCCEqKirEvHnzREVFhezP5Uzst+upte/st2ux366n5r7Lafny5SI8PFz4+PiI2NhYsW/fPtN9ycnJYsCAAZL2e/fuFTExMcLHx0dERESIlStXms3zk08+EV27dhXe3t4iKipKZGVl2d0vl1wnhYiIiMhe/BVkIiIiUiSGFCIiIlIkhhQiIiJSJIYUIiIiUiSGFCIiIlIkhpQ6/va3v6FPnz5o0aKFzVekFUIgLS0NYWFh8PPzw8CBA3HixAlJm8rKSjzzzDMICgpCy5YtMXr0aJw/b/7jgY66cuUKkpKSYDAYYDAYkJSU1OgvTut0Oot/b7zxhqnNwIEDze5v7GrDruj7Y489Ztav+Ph4SRulrfPq6mrMmTMHPXr0QMuWLREWFoZHH30UP/8s/TVWZ6/zFStWIDIyEr6+voiLi8OBAwcabL9v3z7ExcXB19cXt956K9555x2zNllZWejWrRv0ej26deuGzZs3O9w/Z/R706ZNGDJkCNq1a4eAgAAkJCRg586dkjYZGRkWt/eKigq39n3v3r0W+/XDD9JfIFbaOrf0HtTpdOjevbupjSvW+f79+zFq1CiEhYVBp9Nhy5YtjT5GKds42cjuk5Y17JVXXhGLFi0SqampwmAw2PSY119/Xfj7+4usrCzx7bffigkTJojQ0FBhNBpNbaZPny5uueUWkZOTI77++msxaNAg0bNnT3H9+nWn9HvYsGEiOjpaHDx4UBw8eFBER0eLkSNHNviYoqIiyd+aNWuETqcTP/30k6nNgAEDxLRp0yTtrl696pQ+N6XvycnJYtiwYZJ+Xb58WdJGaev86tWrYvDgwSIzM1P88MMPIjc3V/Tu3VvExcVJ2jlznW/cuFF4e3uL9957T3z//fdi5syZomXLluLs2bMW2//3v/8VLVq0EDNnzhTff/+9eO+994S3t7f49NNPTW0OHjwovLy8xGuvvSZOnjwpXnvtNdG8eXNx6NAhh/rojH7PnDlTLFy4UHz11VfiP//5j5g7d67w9vYWX3/9tanN2rVrRUBAgNl272z29n3Pnj0CgDh16pSkX3W3UyWu86tXr0r6e+7cOREYGCjmzZtnauOKdZ6dnS1efPFFkZWVJQCIzZs3N9heKds42Y4hxYK1a9faFFJu3LghQkJCxOuvv26aVlFRIQwGg3jnnXeEEDffzN7e3mLjxo2mNhcuXBDNmjUTO3bsaHJfv//+ewFA8gbKzc0VAMQPP/xg83zGjBkj7rnnHsm0AQMGiJkzZza5j9Y42vfk5GQxZswYq/erZZ1/9dVXAoBkIHDmOr/77rvF9OnTJdOioqLE888/b7H9X/7yFxEVFSWZ9uSTT4r4+HjT7fHjx4thw4ZJ2gwdOlRMnDjRKX0Wwv5+W9KtWzcxf/58021b39NNZW/fa0PKlStXrM5TDet88+bNQqfTiTNnzpimuWqd17IlpChlGyfbcXdPExQUFKC4uBiJiYmmaXq9HgMGDMDBgwcBAMeOHUN1dbWkTVhYGKKjo01tmiI3NxcGgwG9e/c2TYuPj4fBYLB5/r/88gu2bduGqVOnmt338ccfIygoCN27d8fs2bNRVlbW5D47o+979+5F+/bt8Yc//AHTpk1DSUmJ6T41rHMAKC0thU6nM9u16Ix1XlVVhWPHjknWAQAkJiZa7WNubq5Z+6FDh+Lo0aOorq5usI0z1quj/a7vxo0bKCsrQ2BgoGR6eXk5wsPD0aFDB4wcORJ5eXlO6XOtpvQ9JiYGoaGhuPfee7Fnzx7JfWpY56tXr8bgwYMRHh4umS73OreXErZxso+sv92jdbW/8Fj/Vx2Dg4Nx9uxZUxsfHx/JLzbXtqn/C5GO9qF9+/Zm09u3b2/z/D/44AP4+/vjgQcekEyfPHmy6Ucfv/vuO8ydOxfHjx83+9EoV/d9+PDhGDduHMLDw1FQUICXX34Z99xzD44dOwa9Xq+KdV5RUYHnn38ekyZNkvwSq7PW+aVLl1BTU2Nx27TWx+LiYovtr1+/jkuXLiE0NNRqG2esV0f7Xd9bb72Fa9euYfz48aZpUVFRyMjIQI8ePWA0GrFkyRL07dsXx48fR5cuXdzW99DQUKxatQpxcXGorKzEhx9+iHvvvRd79+5F//79AVh/XZSyzouKirB9+3asX79eMt0V69xeStjGyT6aDylpaWmYP39+g22OHDmCXr16OfwcOp1OclsIYTatvsba2NpvS89vax9qrVmzBpMnTzb79epp06aZ/o+OjkaXLl3Qq1cvfP3114iNjXVb3ydMmCDpV69evRAeHo5t27aZBS175uuqdV5dXY2JEyfixo0bWLFiheQ+R9e5NfZum5ba15/uyPZuL0efY8OGDUhLS8PWrVslQTI+Pl5ycHXfvn0RGxuLt99+G0uXLnVex2Ff37t27YquXbuabickJODcuXN48803TSHF3nk6ytHnyMjIQOvWrTF27FjJdFeuc3soZRsn22g+pMyYMaPRsyMiIiIcmndISAiAm+k8NDTUNL2kpMSUxENCQlBVVYUrV65IvtmXlJQ0+JPVtvb7m2++wS+//GJ238WLF82+DVhy4MABnDp1CpmZmY22jY2Nhbe3N06fPt3ggOmqvtcKDQ1FeHg4Tp8+DUDZ67y6uhrjx49HQUEBvvjiC0kVxRJb13l9QUFB8PLyMvv2V3fbrC8kJMRi++bNm6Nt27YNtrHn9XJ2v2tlZmZi6tSp+OSTTxr9RfRmzZrhrrvuMm0zztCUvtcVHx+Pjz76yHRbyetcCIE1a9YgKSkJPj4+DbaVY53bSwnbONnJ9YfBKJ+9B84uXLjQNK2ystLigbOZmZmmNj///LPTD+I8fPiwadqhQ4dsPogzOTnZ7AwTa7799lsBQPLrmE3R1L7XunTpktDr9eKDDz4QQih3nVdVVYmxY8eK7t27i5KSEpueqynr/O677xZPPfWUZNrtt9/e4IGzt99+u2Ta9OnTzQ4qHD58uKTNsGHDnH4Qpz39FkKI9evXC19f30YPnKx148YN0atXLzFlypSmdNWMI32v78EHHxSDBg0y3VbqOhfifwf+1v+lekvkWue1YOOBs0rYxsl2DCl1nD17VuTl5Yn58+eLVq1aiby8PJGXlyfKyspMbbp27So2bdpkuv36668Lg8EgNm3aJL799lvx8MMPWzwFuUOHDmL37t3i66+/Fvfcc4/TT4e94447RG5ursjNzRU9evQwOx22fr+FEKK0tFS0aNHC4k9s//jjj2L+/PniyJEjoqCgQGzbtk1ERUWJmJgYp/Xbkb6XlZWJ5557Thw8eFAUFBSIPXv2iISEBHHLLbcoep1XV1eL0aNHiw4dOoj8/HzJKZmVlZVCCOev89rTSlevXi2+//57kZKSIlq2bGk6A+P5558XSUlJpva1p2fOmjVLfP/992L16tVmp2f++9//Fl5eXuL1118XJ0+eFK+//rpsp8Pa2u/169eL5s2bi+XLl1s9dTstLU3s2LFD/PTTTyIvL09MmTJFNG/eXBI03dH3f/zjH2Lz5s3iP//5j/juu+/E888/LwBIftJeieu81iOPPCJ69+5tcZ6uWOdlZWWmz2kAYtGiRSIvL890xpxSt3GyHUNKHcnJyQKA2d+ePXtMbQCItWvXmm7fuHFDzJs3T4SEhAi9Xi/69+9v9q3i999/FzNmzBCBgYHCz89PjBw5UhQWFjqt35cvXxaTJ08W/v7+wt/fX0yePNnslMb6/RZCiHfffVf4+flZvA5HYWGh6N+/vwgMDBQ+Pj6ic+fO4tlnnzW7Homr+/7bb7+JxMRE0a5dO+Ht7S06deokkpOTzdan0tZ5QUGBxW2r7vYlxzpfvny5CA8PFz4+PiI2NlZSkUlOThYDBgyQtN+7d6+IiYkRPj4+IiIiwmKA/eSTT0TXrl2Ft7e3iIqKkgyozmJPvwcMGGBxvSYnJ5vapKSkiE6dOgkfHx/Rrl07kZiYKA4ePOj0ftvb94ULF4rOnTsLX19f0aZNG/HHP/5RbNu2zWyeSlvnQtysWPr5+YlVq1ZZnJ8r1nltJcfaa6/kbZxsoxPi/44aIiIiIlIQXieFiIiIFIkhhYiIiBSJIYWIiIgUiSGFiIiIFIkhhYiIiBSJIYWIiIgUiSGFiIiIFIkhhYiIiBSJIYWIiIgUiSGFiIiIFIkhhYiIiBTp/wefcBYQ7LkW4gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "distance = -epsilon*np.log(solution)\n", "plt.axis('equal'); plt.title(\"Arrival times for Zermelo's navigation problem\")\n", "plt.contourf(*X,distance); plt.colorbar();" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.654815Z", "iopub.status.busy": "2024-04-30T08:47:04.654706Z", "iopub.status.idle": "2024-04-30T08:47:04.657895Z", "shell.execute_reply": "2024-04-30T08:47:04.657571Z" } }, "outputs": [], "source": [ "grad = np.array(np.gradient(distance,bc.gridscale))\n", "flow = lp.solve_AV(bc.as_field(metric),grad)\n", "flow = flow/np.sqrt(lp.dot_VV(flow,grad)) + bc.as_field(drift)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.659395Z", "iopub.status.busy": "2024-04-30T08:47:04.659315Z", "iopub.status.idle": "2024-04-30T08:47:04.989662Z", "shell.execute_reply": "2024-04-30T08:47:04.989393Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title(\"Minimal paths for Zermelo's navigation problem\")\n", "streamplot_ij(*X,*flow);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Second-order scheme with upwind first order differences\n", "\n", "For completeness, we present a non-centered scheme for second order linear equations.\n", "In comparison with the centered scheme presented in the previous section, this one is:\n", "* More diffusive, and only first order accurate.\n", "* Unconditionally stable, independently of the grid scale.\n", "\n", "In practice, we recommend using the centered scheme, unless the second order coefficients are degenerate or excessively small." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.991577Z", "iopub.status.busy": "2024-04-30T08:47:04.991466Z", "iopub.status.idle": "2024-04-30T08:47:04.994185Z", "shell.execute_reply": "2024-04-30T08:47:04.993952Z" }, "tags": [ "ExportCode" ] }, "outputs": [], "source": [ "def SchemeUpwind(u,cst,mult,omega,diff,bc):\n", " \"\"\"Discretization of a linear non-divergence form second order PDE\n", " cst + mult u + - tr(diff hess(u)) = 0\n", " First order accurate, upwind finite differences are used for \n", " - bc : boundary conditions. \n", " \"\"\"\n", " # Decompose the tensor field\n", " coefs2,offsets2 = Selling.Decomposition(diff)\n", " omega,coefs2 = (bc.as_field(e) for e in (omega,coefs2)) \n", "\n", " # Decompose the vector field\n", " coefs1 = -np.abs(omega)\n", " basis = bc.as_field(np.eye(len(omega)))\n", " offsets1 = -np.sign(omega)*basis\n", " \n", " # Compute the first and second order finite differences \n", " du = bc.DiffUpwind(u,offsets1.astype(int))\n", " d2u = bc.Diff2(u,offsets2)\n", " \n", " # In interior : cst + mult u + - tr(diff hess(u)) = 0\n", " residue = cst + mult*u +lp.dot_VV(coefs1,du) - lp.dot_VV(coefs2,d2u)\n", " \n", " # On boundary : u-bc = 0\n", " return np.where(bc.interior,residue,u-bc.grid_values)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:04.995558Z", "iopub.status.busy": "2024-04-30T08:47:04.995461Z", "iopub.status.idle": "2024-04-30T08:47:05.109603Z", "shell.execute_reply": "2024-04-30T08:47:05.109184Z" } }, "outputs": [], "source": [ "u_ad = ad.Sparse.identity(bc.shape)\n", "solutionUpwind = SchemeUpwind(u_ad,cst,mult,omega,diff,bc).solve()\n", "solutionCentered = SchemeCentered(u_ad,cst,mult,omega,diff,bc).solve()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:05.111344Z", "iopub.status.busy": "2024-04-30T08:47:05.111238Z", "iopub.status.idle": "2024-04-30T08:47:05.175801Z", "shell.execute_reply": "2024-04-30T08:47:05.175518Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "distanceUpwind = -epsilon*np.log(solutionUpwind)\n", "plt.axis('equal'); plt.title(\"Arrival times for Zermelo's navigation problem\")\n", "plt.contourf(*X,distanceUpwind);" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:05.177313Z", "iopub.status.busy": "2024-04-30T08:47:05.177199Z", "iopub.status.idle": "2024-04-30T08:47:05.274055Z", "shell.execute_reply": "2024-04-30T08:47:05.273767Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "distanceCentered = -epsilon*np.log(solutionCentered)\n", "plt.title('Difference between the upwind and centered schemes')\n", "plt.contourf(*X,distanceUpwind-distanceCentered); \n", "plt.colorbar(); plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }