{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive PDE discretizations on Cartesian grids\n",
    "## Volume : Algorithmic tools\n",
    "## Part : Domain representation\n",
    "## Chapter : Subsets of $R^d$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to describe a simple subset of $R^d$, and to compute finite differences taking into account a given Dirichlet data on the boundary. It is a prerequisite to the implementation of monotone schemes on non-rectangular domains.\n",
    "\n",
    "*Note:* The library presented in this notebook features some elementary primitives of algorithmic geometry. However, their expressivity is rather limited, and exact predicates are not implemented. Therefore, please consider using a dedicated computational geometry package if you intend to go much beyond the basic examples presented in this series of notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[**Summary**](Summary.ipynb) of volume Algorithmic tools, 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. Domain description](#1.-Domain-description)\n",
    "    * [1.1 Basic shapes, boolean operations, affine transformation.](#1.1-Basic-shapes,-boolean-operations,-affine-transformation.)\n",
    "    * [1.2 Level set function](#1.2-Level-set-function)\n",
    "    * [1.3 Distance to the boundary in a given direction.](#1.3-Distance-to-the-boundary-in-a-given-direction.)\n",
    "  * [2. Boundary-adapted finite differences](#2.-Boundary-adapted-finite-differences)\n",
    "    * [2.1 Interior points](#2.1-Interior-points)\n",
    "    * [2.2 Upwind finite differences](#2.2-Upwind-finite-differences)\n",
    "    * [2.3 Centered finite differences](#2.3-Centered-finite-differences)\n",
    "    * [2.4 Second order finite differences](#2.4-Second-order-finite-differences)\n",
    "  * [3. Mock boundary conditions](#3.-Mock-boundary-conditions)\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. Import the required libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.589949Z",
     "iopub.status.busy": "2024-04-30T08:46:51.589640Z",
     "iopub.status.idle": "2024-04-30T08:46:51.598821Z",
     "shell.execute_reply": "2024-04-30T08:46:51.598356Z"
    }
   },
   "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('SubsetRd','Algo'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.601330Z",
     "iopub.status.busy": "2024-04-30T08:46:51.601144Z",
     "iopub.status.idle": "2024-04-30T08:46:51.654726Z",
     "shell.execute_reply": "2024-04-30T08:46:51.654320Z"
    }
   },
   "outputs": [],
   "source": [
    "from agd import Domain \n",
    "from agd import AutomaticDifferentiation as ad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.656492Z",
     "iopub.status.busy": "2024-04-30T08:46:51.656346Z",
     "iopub.status.idle": "2024-04-30T08:46:51.855652Z",
     "shell.execute_reply": "2024-04-30T08:46:51.855253Z"
    }
   },
   "outputs": [],
   "source": [
    "import scipy.linalg\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.857361Z",
     "iopub.status.busy": "2024-04-30T08:46:51.857231Z",
     "iopub.status.idle": "2024-04-30T08:46:51.859208Z",
     "shell.execute_reply": "2024-04-30T08:46:51.858975Z"
    }
   },
   "outputs": [],
   "source": [
    "def reload_packages():\n",
    "    import importlib\n",
    "    Domain = importlib.reload(sys.modules['agd.Domain'])\n",
    "    ad = importlib.reload(sys.modules['agd.AutomaticDifferentiation'])\n",
    "    ad.reload_submodules()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Domain description\n",
    "\n",
    "The provided library allows to define a family of basic shapes, combine them with boolean operations, and affine transformations. Once the desired shape is constructed, two main functions are available: a level set map, and the distance to the boundary along a given half line."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Basic shapes, boolean operations, affine transformation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a ball and a box domain, here in dimension two, but these primitives are dimension independent.\n",
    "* *Ball* $\\{x\\in R^d;\\, \\|x-x_0\\| \\leq r\\}$ with parameters $(x_0,r)$, the center and the radius (defaults to one).\n",
    "* *Box* $[a_1,b_1] \\times [a_n,b_n]$, a product of intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.860642Z",
     "iopub.status.busy": "2024-04-30T08:46:51.860543Z",
     "iopub.status.idle": "2024-04-30T08:46:51.862307Z",
     "shell.execute_reply": "2024-04-30T08:46:51.862058Z"
    }
   },
   "outputs": [],
   "source": [
    "ball = Domain.Ball([0,0]) # Two dimensional ball centered at the origin with radius one.\n",
    "box = Domain.Box([[0,1],[0,1]]) # Square domain [0,1]x[0,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard boolean operations allow to combine elementary shapes: intersection, union, and relative complement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.863689Z",
     "iopub.status.busy": "2024-04-30T08:46:51.863581Z",
     "iopub.status.idle": "2024-04-30T08:46:51.865263Z",
     "shell.execute_reply": "2024-04-30T08:46:51.865045Z"
    }
   },
   "outputs": [],
   "source": [
    "cap = Domain.Intersection(ball,box)\n",
    "cup = Domain.Union(ball,box)\n",
    "compl = Domain.Complement(ball,box)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bands and Convex polygons are some potentially useful additional shapes:\n",
    "* *Band* $\\{x\\in R^d; b_0 \\leq <x,v> \\leq b_1$, depending on $(v,b)$, where $v$ is called the direction and $b=(b_0,b_1)$ the bounds. \n",
    "* *Convex polygon* $\\mathrm{Hull}(x_1,\\cdots,x_n)$. This primitive is two dimensional only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.866594Z",
     "iopub.status.busy": "2024-04-30T08:46:51.866514Z",
     "iopub.status.idle": "2024-04-30T08:46:51.868691Z",
     "shell.execute_reply": "2024-04-30T08:46:51.868442Z"
    }
   },
   "outputs": [],
   "source": [
    "band = Domain.Band([1.,2.],[-2.,1.]) # Direction, bounds\n",
    "triangle = Domain.ConvexPolygon(np.stack([[1.,0.],[0.,1.],[-1.,-1.]],axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An affine transformation can be applied to the domain, with parameters:\n",
    "* *A* (mult) the matrix of the linear part. (defaults to identity)\n",
    "* $x_0$ (center) the center of the previous linear transformation. (defaults to the origin)\n",
    "* $v$ (shift) a translation to be applied. (defaults to zero)\n",
    "\n",
    "The direct mapping takes the form\n",
    "$$\n",
    "    x \\mapsto A (x-x_0)+x_0 + v\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.870097Z",
     "iopub.status.busy": "2024-04-30T08:46:51.869996Z",
     "iopub.status.idle": "2024-04-30T08:46:51.872233Z",
     "shell.execute_reply": "2024-04-30T08:46:51.872000Z"
    }
   },
   "outputs": [],
   "source": [
    "def rot(t): c,s = np.cos(t),np.sin(t); return np.array(((c,-s),(s,c)))    \n",
    "aff = Domain.AffineTransform(cup,0.7*rot(np.pi/3.),shift=[-0.2,-0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.873558Z",
     "iopub.status.busy": "2024-04-30T08:46:51.873460Z",
     "iopub.status.idle": "2024-04-30T08:46:51.875195Z",
     "shell.execute_reply": "2024-04-30T08:46:51.874960Z"
    }
   },
   "outputs": [],
   "source": [
    "doms = (ball,box,cap,compl,cup,band,triangle,aff)\n",
    "domNames = (\"ball\",\"box\",\"cap\",\"compl\",\"cup\",\"band\",\"triangle\",\"affine\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us display the domains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.876565Z",
     "iopub.status.busy": "2024-04-30T08:46:51.876468Z",
     "iopub.status.idle": "2024-04-30T08:46:51.878357Z",
     "shell.execute_reply": "2024-04-30T08:46:51.878130Z"
    }
   },
   "outputs": [],
   "source": [
    "aX=np.linspace(-1.2,1.2)\n",
    "X = np.array(np.meshgrid(aX,aX,indexing='ij'))\n",
    "h=aX[1]-aX[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:51.879666Z",
     "iopub.status.busy": "2024-04-30T08:46:51.879567Z",
     "iopub.status.idle": "2024-04-30T08:46:52.260817Z",
     "shell.execute_reply": "2024-04-30T08:46:52.260556Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "for i,(dom,name) in enumerate(zip(doms,domNames)):\n",
    "    plt.subplot(2,4,1+i)\n",
    "    plt.contourf(*X,dom.contains(X))\n",
    "    plt.title(name)\n",
    "    plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to select the points around which the domain contains a ball of a given radius $h$, possibly negative. This predicate is only approximate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:52.262364Z",
     "iopub.status.busy": "2024-04-30T08:46:52.262260Z",
     "iopub.status.idle": "2024-04-30T08:46:52.614754Z",
     "shell.execute_reply": "2024-04-30T08:46:52.614486Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "for i,(dom,name) in enumerate(zip(doms,domNames)):\n",
    "    plt.subplot(2,4,1+i)\n",
    "    \n",
    "    interior = dom.contains(X)\n",
    "    erosion = dom.contains_ball(X,2*h)\n",
    "    boundary_layer = np.logical_and(interior,np.logical_not(erosion))\n",
    "    \n",
    "    plt.contourf(*X,boundary_layer)\n",
    "    plt.title(name)\n",
    "    plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Level set function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each domain comes equipped with a level set function, that is negative inside the domain, and positive outside. It is also guaranteed to be $1$-Lipschitz. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:52.616392Z",
     "iopub.status.busy": "2024-04-30T08:46:52.616283Z",
     "iopub.status.idle": "2024-04-30T08:46:52.996386Z",
     "shell.execute_reply": "2024-04-30T08:46:52.996128Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "for i,(dom,name) in enumerate(zip(doms,domNames)):\n",
    "    plt.subplot(2,4,1+i)\n",
    "    plt.contourf(*X,dom.level(X))\n",
    "    plt.title(name)\n",
    "    plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This level set function is in general different from the signed Euclidean distance to the boundary.  \n",
    "If you do need the Euclidean distance function, you may consider solving an eikonal equation, or using an adequate computational geometry package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Distance to the boundary in a given direction.\n",
    "\n",
    "For the design of finite difference schemes, it is important to know the distance from a given point to the domain boundary in a given direction. This is referred to as the \"free way\" from $x$ in the direction $v$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:52.998622Z",
     "iopub.status.busy": "2024-04-30T08:46:52.998512Z",
     "iopub.status.idle": "2024-04-30T08:46:53.000202Z",
     "shell.execute_reply": "2024-04-30T08:46:52.999926Z"
    }
   },
   "outputs": [],
   "source": [
    "#Domain = importlib.reload(Domain)\n",
    "#ball = Domain.Ball(np.array([0,0]))\n",
    "#box = Domain.Box([[0,1],[0,1]])\n",
    "#cap = Domain.Intersection( (ball,box) )\n",
    "#abox = Domain.AbsoluteComplement(box)\n",
    "#aball = Domain.AbsoluteComplement(ball)\n",
    "#compl = Domain.Complement(ball,box)\n",
    "#cup = Domain.Union((ball,box))\n",
    "#acup = Domain.Intersection((aball,abox))\n",
    "#band = Domain.Band([1.,2.],[-2.,1.]) # Direction, bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:53.001643Z",
     "iopub.status.busy": "2024-04-30T08:46:53.001548Z",
     "iopub.status.idle": "2024-04-30T08:46:53.349193Z",
     "shell.execute_reply": "2024-04-30T08:46:53.348890Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v=np.array([1,-0.5])\n",
    "plt.figure(figsize=(16,8))\n",
    "for i,(dom,name) in enumerate(zip(doms,domNames)):\n",
    "    plt.subplot(2,4,i+1)\n",
    "    plt.title(name)\n",
    "    plt.axis('equal')\n",
    "    fw = dom.freeway(X,v)\n",
    "    if np.all(fw==np.inf): continue #Warning triggered otherwise \n",
    "    plt.contourf(*X,fw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:53.350760Z",
     "iopub.status.busy": "2024-04-30T08:46:53.350646Z",
     "iopub.status.idle": "2024-04-30T08:46:53.642436Z",
     "shell.execute_reply": "2024-04-30T08:46:53.642169Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v=np.array([-1,-0.5])\n",
    "plt.figure(figsize=(16,8))\n",
    "for i,(dom,name) in enumerate(zip(doms,domNames)):\n",
    "    plt.subplot(2,4,i+1)\n",
    "    plt.contourf(*X,dom.freeway(X,v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:53.644028Z",
     "iopub.status.busy": "2024-04-30T08:46:53.643919Z",
     "iopub.status.idle": "2024-04-30T08:46:53.974794Z",
     "shell.execute_reply": "2024-04-30T08:46:53.974504Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v=np.array([1,0.])\n",
    "plt.figure(figsize=(16,8))\n",
    "for i,(dom,name) in enumerate(zip(doms,domNames)):\n",
    "    plt.subplot(2,4,i+1)\n",
    "    plt.contourf(*X,dom.freeway(X,v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Boundary-adapted finite differences\n",
    "\n",
    "Only Dirichlet boundary conditions are implemented at present. When a grid point falls outside the domain, the provided boundary data is used instead, as described below.\n",
    "\n",
    "Denote by $\\Omega$ the domain, and $\\Omega_h$ its intersection with the cartesian grid $h Z^d$. Let $x\\in \\Omega_h$ be a point of the domain, and let $e \\in Z^d\\setminus \\{0\\}$ be an offset.\n",
    "\n",
    "* *Upwind finite difference*.  Denote by $h_+>0$ the smallest real such that $x+h_+ e  \\in \\Omega_h \\cup \\partial \\Omega$. The first order upwind finite difference is defined as\n",
    "$$\n",
    "    \\delta^e_h u(x) := \\frac{u(x+h_+e)-u(x)} {h_+}\n",
    "$$\n",
    "* *Centered finite difference*. The standard expression $(u(x+h e)-u(x-he))/(2h)$ is used, unless $x+ h e\\notin \\Omega_h$ or $x-he \\notin \\Omega_h$. In that case, we fall back to the upwind finite difference.\n",
    "* *Second order finite difference*. Let $h_\\pm>0$ denote the smallest real such that $x\\pm h_\\pm e \\in \\Omega_h \\cup \\partial \\Omega$. The second order finite difference is defined as \n",
    "$$\n",
    "    \\Delta^e_h u(x) := \\frac 2 {h_++h_-} \\Big(\\frac{u(x+h_+ e)-u(x)}{h_+} + \\frac{u(x-h_- e)-u(x)}{h_-} \\Big)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the dirichlet data, based on a domain,a function defined on (at least) the boundary, and the cartesian grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:53.976398Z",
     "iopub.status.busy": "2024-04-30T08:46:53.976289Z",
     "iopub.status.idle": "2024-04-30T08:46:53.978588Z",
     "shell.execute_reply": "2024-04-30T08:46:53.978358Z"
    }
   },
   "outputs": [],
   "source": [
    "def bc_value(x): return x[0]+2*x[1]\n",
    "bc_domain = cup\n",
    "bc = Domain.Dirichlet(bc_domain,bc_value,X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Interior points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The gridscale of the domain is automatically extracted. Note that we only support gridscales which are axis independent and position independent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:53.980106Z",
     "iopub.status.busy": "2024-04-30T08:46:53.979998Z",
     "iopub.status.idle": "2024-04-30T08:46:53.982118Z",
     "shell.execute_reply": "2024-04-30T08:46:53.981885Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.048979591836734615"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bc.gridscale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A boolean mask of interior points is constructed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:53.983558Z",
     "iopub.status.busy": "2024-04-30T08:46:53.983454Z",
     "iopub.status.idle": "2024-04-30T08:46:54.039748Z",
     "shell.execute_reply": "2024-04-30T08:46:54.039499Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('domain interior'); plt.axis('equal')\n",
    "plt.contourf(*X,bc.interior);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Actually, this is a very slightly eroded version of the domain, for numerical stability. \n",
    "<!---which does not strictly contain all points of $X$ within it. The purpose of this erosion is to bound below the denominators $h_+$ and $h_-$ in the finite differences at the boundary, for better stability.\n",
    "\n",
    "If necessary, the set of interior points can be explicitly specified at initialization, or even modified afterwards.\n",
    "--->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Upwind finite differences\n",
    "\n",
    "We choose a linear function, in order to confirm that the upwind scheme is exact in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.041259Z",
     "iopub.status.busy": "2024-04-30T08:46:54.041180Z",
     "iopub.status.idle": "2024-04-30T08:46:54.042892Z",
     "shell.execute_reply": "2024-04-30T08:46:54.042647Z"
    }
   },
   "outputs": [],
   "source": [
    "u = bc.value(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.044264Z",
     "iopub.status.busy": "2024-04-30T08:46:54.044187Z",
     "iopub.status.idle": "2024-04-30T08:46:54.046708Z",
     "shell.execute_reply": "2024-04-30T08:46:54.046470Z"
    }
   },
   "outputs": [],
   "source": [
    "du = bc.DiffUpwind(u,(1,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.048070Z",
     "iopub.status.busy": "2024-04-30T08:46:54.047993Z",
     "iopub.status.idle": "2024-04-30T08:46:54.050164Z",
     "shell.execute_reply": "2024-04-30T08:46:54.049942Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0000000000000142, 0.9999999999999833)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "du[bc.interior].max(),du[bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.051571Z",
     "iopub.status.busy": "2024-04-30T08:46:54.051491Z",
     "iopub.status.idle": "2024-04-30T08:46:54.134933Z",
     "shell.execute_reply": "2024-04-30T08:46:54.134648Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Largest and smallest h in finite differences: 0.048979591836734615 0.00047605827449359595\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "du,h = bc.DiffUpwind(u,(1,0),reth=True)\n",
    "print(\"Largest and smallest h in finite differences:\",np.max(h),np.min(h))\n",
    "plt.title(\"Value of h in finite difference\"); plt.axis('equal')\n",
    "plt.contourf(*X,h); plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Differentiating along the horizontal and vertical directions simultaneously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.136457Z",
     "iopub.status.busy": "2024-04-30T08:46:54.136350Z",
     "iopub.status.idle": "2024-04-30T08:46:54.139270Z",
     "shell.execute_reply": "2024-04-30T08:46:54.139026Z"
    }
   },
   "outputs": [],
   "source": [
    "du = bc.DiffUpwind(u,np.eye(2).astype(int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.140733Z",
     "iopub.status.busy": "2024-04-30T08:46:54.140641Z",
     "iopub.status.idle": "2024-04-30T08:46:54.142806Z",
     "shell.execute_reply": "2024-04-30T08:46:54.142558Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0000000000000142, 0.9999999999999833)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "du[0,bc.interior].max(),du[0,bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.144171Z",
     "iopub.status.busy": "2024-04-30T08:46:54.144081Z",
     "iopub.status.idle": "2024-04-30T08:46:54.146171Z",
     "shell.execute_reply": "2024-04-30T08:46:54.145934Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.000000000000028, 1.9999999999999858)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "du[1,bc.interior].max(),du[1,bc.interior].min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Centered finite differences\n",
    "\n",
    "Again, we choose a linear function, in order to confirm that the upwind scheme is exact in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.147544Z",
     "iopub.status.busy": "2024-04-30T08:46:54.147451Z",
     "iopub.status.idle": "2024-04-30T08:46:54.150276Z",
     "shell.execute_reply": "2024-04-30T08:46:54.150024Z"
    }
   },
   "outputs": [],
   "source": [
    "du = bc.DiffCentered(u,(1,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.151596Z",
     "iopub.status.busy": "2024-04-30T08:46:54.151499Z",
     "iopub.status.idle": "2024-04-30T08:46:54.153464Z",
     "shell.execute_reply": "2024-04-30T08:46:54.153238Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.000000000000007, 0.9999999999999833)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "du[bc.interior].max(),du[bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.154774Z",
     "iopub.status.busy": "2024-04-30T08:46:54.154681Z",
     "iopub.status.idle": "2024-04-30T08:46:54.157432Z",
     "shell.execute_reply": "2024-04-30T08:46:54.157200Z"
    }
   },
   "outputs": [],
   "source": [
    "du = bc.DiffCentered(u,np.eye(2).astype(int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.158822Z",
     "iopub.status.busy": "2024-04-30T08:46:54.158725Z",
     "iopub.status.idle": "2024-04-30T08:46:54.160869Z",
     "shell.execute_reply": "2024-04-30T08:46:54.160639Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.000000000000007, 0.9999999999999833)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "du[0,bc.interior].max(),du[0,bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.162235Z",
     "iopub.status.busy": "2024-04-30T08:46:54.162137Z",
     "iopub.status.idle": "2024-04-30T08:46:54.164297Z",
     "shell.execute_reply": "2024-04-30T08:46:54.164074Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.000000000000028, 1.99999999999999)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "du[1,bc.interior].max(),du[1,bc.interior].min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Second order finite differences\n",
    "\n",
    "The second order differences of a linear function identically vanish."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.165699Z",
     "iopub.status.busy": "2024-04-30T08:46:54.165600Z",
     "iopub.status.idle": "2024-04-30T08:46:54.168680Z",
     "shell.execute_reply": "2024-04-30T08:46:54.168443Z"
    }
   },
   "outputs": [],
   "source": [
    "d2u = bc.Diff2(u,(1,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.170012Z",
     "iopub.status.busy": "2024-04-30T08:46:54.169935Z",
     "iopub.status.idle": "2024-04-30T08:46:54.172029Z",
     "shell.execute_reply": "2024-04-30T08:46:54.171763Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1536608264867289e-11, -5.983034965740204e-13)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2u[bc.interior].max(),d2u[bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.173382Z",
     "iopub.status.busy": "2024-04-30T08:46:54.173303Z",
     "iopub.status.idle": "2024-04-30T08:46:54.176618Z",
     "shell.execute_reply": "2024-04-30T08:46:54.176391Z"
    }
   },
   "outputs": [],
   "source": [
    "d2u = bc.Diff2(u,np.eye(2).astype(int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.178011Z",
     "iopub.status.busy": "2024-04-30T08:46:54.177932Z",
     "iopub.status.idle": "2024-04-30T08:46:54.180106Z",
     "shell.execute_reply": "2024-04-30T08:46:54.179880Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1536608264867289e-11, -5.983034965740204e-13)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2u[0,bc.interior].max(),d2u[0,bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.181444Z",
     "iopub.status.busy": "2024-04-30T08:46:54.181368Z",
     "iopub.status.idle": "2024-04-30T08:46:54.183569Z",
     "shell.execute_reply": "2024-04-30T08:46:54.183329Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.9440713794339614e-11, -5.802765675374161e-13)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2u[1,bc.interior].max(),d2u[1,bc.interior].min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to use quadratic polynomials to illustrate consistency in a non-trivial manner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.184874Z",
     "iopub.status.busy": "2024-04-30T08:46:54.184801Z",
     "iopub.status.idle": "2024-04-30T08:46:54.186848Z",
     "shell.execute_reply": "2024-04-30T08:46:54.186609Z"
    }
   },
   "outputs": [],
   "source": [
    "def bc2_value(x): return x[0]**2+x[0]*x[1]\n",
    "bc2 = Domain.Dirichlet(bc_domain,bc2_value,X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.188167Z",
     "iopub.status.busy": "2024-04-30T08:46:54.188094Z",
     "iopub.status.idle": "2024-04-30T08:46:54.189672Z",
     "shell.execute_reply": "2024-04-30T08:46:54.189451Z"
    }
   },
   "outputs": [],
   "source": [
    "u2 = bc2.value(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.190996Z",
     "iopub.status.busy": "2024-04-30T08:46:54.190913Z",
     "iopub.status.idle": "2024-04-30T08:46:54.194607Z",
     "shell.execute_reply": "2024-04-30T08:46:54.194385Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0000000000041758, 1.9999999999877116)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2u = bc2.Diff2(u2,(1,0))\n",
    "d2u[bc.interior].max(),d2u[bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.195950Z",
     "iopub.status.busy": "2024-04-30T08:46:54.195877Z",
     "iopub.status.idle": "2024-04-30T08:46:54.199017Z",
     "shell.execute_reply": "2024-04-30T08:46:54.198792Z"
    }
   },
   "outputs": [],
   "source": [
    "d2u = bc2.Diff2(u2,np.eye(2).astype(int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.200305Z",
     "iopub.status.busy": "2024-04-30T08:46:54.200229Z",
     "iopub.status.idle": "2024-04-30T08:46:54.202494Z",
     "shell.execute_reply": "2024-04-30T08:46:54.202250Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0000000000041758, 1.9999999999877116)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2u[0,bc.interior].max(),d2u[0,bc.interior].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.203784Z",
     "iopub.status.busy": "2024-04-30T08:46:54.203705Z",
     "iopub.status.idle": "2024-04-30T08:46:54.206026Z",
     "shell.execute_reply": "2024-04-30T08:46:54.205801Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.265283626933634e-12, -8.961585388799509e-12)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2u[1,bc.interior].max(),d2u[1,bc.interior].min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Mock boundary conditions\n",
    "\n",
    "There is an alternative way of handling boundary conditions, which is simpler but also much more crude and inaccurate. In that approach, the boundary data is provided in a *neighborhood* of the boundary, and the standard finite difference schemes is used.\n",
    "\n",
    "Be warned that this alternative is both:\n",
    "* Excessively unprecise in applications, because an $O(h)$ error is introduced when extending the boundary conditions.\n",
    "* Excessively precise in synthetic test cases, because the boundary solution is typically the exact analytical solution, which in this way is provided in a substantial narrow band along the boundary.\n",
    "\n",
    "In view of these caveats, we refer to it as mock boundary conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.207460Z",
     "iopub.status.busy": "2024-04-30T08:46:54.207370Z",
     "iopub.status.idle": "2024-04-30T08:46:54.209477Z",
     "shell.execute_reply": "2024-04-30T08:46:54.209252Z"
    }
   },
   "outputs": [],
   "source": [
    "grid_values = bc_value(X) # Boundary conditions are evaluated in the whole domain\n",
    "grid_values[ np.logical_not(bc_domain.contains(X)) ] = np.nan # Define the domain\n",
    "\n",
    "bc_mock = Domain.MockDirichlet(grid_values,h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In that approach, the domain is actually not taken into account when computing the finite differences.\n",
    "\n",
    "However, the provided placeholder values are those of the boundary condition, instead of an arbitrary default. This makes sense in view of the numerical schemes implementation, see e.g. [link](../Notebooks_NonDiv/LinearMonotoneSchemes2D.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.210849Z",
     "iopub.status.busy": "2024-04-30T08:46:54.210768Z",
     "iopub.status.idle": "2024-04-30T08:46:54.212759Z",
     "shell.execute_reply": "2024-04-30T08:46:54.212534Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bc_mock.grid_values is grid_values # Returns the extended boundary conditions "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:54.214100Z",
     "iopub.status.busy": "2024-04-30T08:46:54.214020Z",
     "iopub.status.idle": "2024-04-30T08:46:54.215955Z",
     "shell.execute_reply": "2024-04-30T08:46:54.215737Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bc.grid_values # Arbitrary placeholder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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