Poisson_Colab.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Poisson_Colab.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [
        "vS_YdSbqFOln",
        "9SJXe6I5JUwF",
        "r6GW2fwLE042"
      ],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/van-dang/FEniCS-Colab/blob/master/Poisson_Colab.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "vS_YdSbqFOln",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Kiến thức nền tảng"
      ]
    },
    {
      "metadata": {
        "id": "CiQ9r51xKgWh",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# This demo adapts an existing code to solve the Poisson equation\n",
        "# The orignal code is available here: https://fenicsproject.org/tutorial/\n",
        "\n",
        "\"\"\"\n",
        "FEniCS tutorial demo program: Poisson equation with Dirichlet conditions.\n",
        "Test problem is chosen to give an exact solution at all nodes of the mesh.\n",
        "\n",
        "  -Laplace(u) = f    in the unit square\n",
        "            u = u_D  on the boundary\n",
        "\n",
        "  u_D = 1 + x^2 + 2y^2\n",
        "    f = -6\n",
        "\"\"\"\n",
        "\n",
        "# Original code is available at https://fenicsproject.org/tutorial/\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "HJPROjgip-Vb",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Phương trình Poisson được định nghĩa trên một miền tính toán $\\Omega$ có dạng như sau:\n",
        "\n",
        "$$-\\Delta u=f$$\n",
        "\n",
        "Phương trình cần được bổ sung với một hoặc vài điều kiện trên biên $\\partial \\Omega$. Ở đây giả sử điều kiện Dirichlet được sử dụng\n",
        "\n",
        "$$u = u_D \\text{ on } \\partial \\Omega$$\n",
        "\n",
        "Để kiểm tra tính chính xác của việc cài đặt thuật toán, người ta thường giả sử nghiệm đã biết trước là hàm $u_e$ nào đó. Giả sử $u_e=1 + x^2 + 2\\,y^2$, ta có thể tính được nguồn $f=-\\Delta u_e=-6$ và trên biên thì $u_D=u_e$.\n",
        "\n",
        "Để giải phương trình, người ta cần biết sẽ tìm nghiệm ở đâu. Vì vậy, không gian hàm cần được định nghĩa. Trước hết mình chọn không gian hàm cho nghiệm cần tìm (trial function space) \n",
        "\n",
        "$$V=\\Biggl\\{u:\\Omega\\to\\mathbb{R}\\,\\Biggl| \\,\\int\\limits_\\Omega u^2 + |\\nabla u|^2\\,d\\Omega<\\infty, u=u_D\\text{ on }\\partial \\Omega\\Biggl\\}$$\n",
        "\n",
        "Nghiệm của PPPTHH là nghiệm yếu (weak solution), vì vậy người ta cần chọn thêm không gian hàm kiểm tra (test function space)\n",
        "\n",
        "$$\\hat{V}=\\Biggl\\{v:\\Omega\\to\\mathbb{R}\\,\\Biggl| \\,\\int\\limits_\\Omega v^2 + |\\nabla v|^2\\,d\\Omega<\\infty, v=0\\text{ on }\\partial \\Omega\\Biggl\\}$$\n",
        "\n",
        "Muốn tìm nghiệm $u$ trong trial function space $V$, đầu tiên, người ta nhân 2 vế của phương trình Poisson với một test function $v\\in \\hat{V}$ và lấy tích phân trên $\\Omega$\n",
        "\n",
        "$$\\displaystyle -\\int\\limits_{\\Omega} \\Delta u\\, v\\, d\\Omega= \\int\\limits_{\\Omega} f\\, v\\, d\\Omega.$$\n",
        "\n",
        "Áp dụng công thức Green thứ nhất, i. e.\n",
        "\n",
        "$$\\displaystyle \\int\\limits_{\\Omega} \\Delta u\\, v\\, d\\Omega=\\int\\limits_{\\partial\\Omega} \\nabla u\\cdot \\mathbf{n}\\, v\\, ds - \\int\\limits_{\\Omega} \\nabla u \\cdot\\nabla v\\, d\\Omega,$$\n",
        "\n",
        "Do định nghĩa của $\\hat{V}$, cụm liên quan đến biên bị triệt tiêu\n",
        "\n",
        "$$\\displaystyle \\int\\limits_{\\Omega} \\nabla u \\cdot\\nabla v\\, d\\Omega=\\int\\limits_{\\Omega} f\\, v\\, d\\Omega$$.\n",
        "\n",
        "\n",
        "PPPTHH được diễn đạt như sau: Tìm $u\\in V$ sao cho\n",
        "\n",
        "$$a(u,v)=L(v)$$ cho tất cả $v\\in \\hat{V}$. Ở đây \n",
        "\n",
        "$\\displaystyle a(u,v)=\\int\\limits_{\\Omega} \\nabla u \\cdot\\nabla v\\, d\\Omega$ được gọi là bilinear form.\n",
        "\n",
        "\n",
        "$\\displaystyle L(v)=\\int\\limits_{\\Omega} f\\, v\\, d\\Omega$ được gọi là linear form.\n",
        "\n",
        "Chú ý không gian hàm trên đây là liên tục và vô hạn chiều. Người ta muốn tìm nghiệm xấp xỉ trên không gian hữu hạn chiều."
      ]
    },
    {
      "metadata": {
        "id": "9SJXe6I5JUwF",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Setting a working environment with FEniCS"
      ]
    },
    {
      "metadata": {
        "id": "4jWzVxURFVLj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 15456
        },
        "outputId": "489d224f-5135-4ee0-a8a6-2a7afa761fce"
      },
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "\n",
        "import platform, sys\n",
        "python_version=platform.python_version()\n",
        "from distutils.version import LooseVersion, StrictVersion\n",
        "\n",
        "if ( LooseVersion(python_version) < LooseVersion(\"3.0.0\")):\n",
        "    print(\"Python3 is needed!\");\n",
        "    print(\"How to fix: Runtime/Change_runtime_type/Python 3\");\n",
        "    sys.exit()\n",
        "    \n",
        "try:\n",
        "    from dolfin import *; from mshr import *\n",
        "except ImportError as e:\n",
        "    !apt-get install -y -qq software-properties-common python-software-properties module-init-tools\n",
        "    !add-apt-repository -y ppa:fenics-packages/fenics\n",
        "    !apt-get update -qq\n",
        "    !apt install -y --no-install-recommends fenics\n",
        "    from dolfin import *; from mshr import *\n",
        "    \n",
        "import matplotlib.pyplot as plt;\n",
        "from IPython.display import clear_output, display; import time; import dolfin.common.plotting as fenicsplot \n",
        "import time\n",
        "\n",
        "import os, sys, shutil\n",
        "\n",
        "dolfin_version = dolfin.__version__\n",
        "print ('dolfin version:', dolfin_version)\n",
        "\n",
        "!rm -rf * # clean up all files\n",
        "# Useful commands\n",
        "# Remove an empty folder      : os.rmdir(\"my_results\")\n",
        "# Remove a folder with files  : shutil.rmtree(\"results\")\n",
        "# Make a folder               : os.mkdir(\"my_results\")\n",
        "# Runtime/Change_runtime_type/Python3"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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            "Reading package lists... Done\n",
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
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            "The following additional packages will be installed:\n",
            "  cmake cmake-data dolfin-bin dolfin-doc ibverbs-providers libamd2\n",
            "  libarchive13 libarpack2 libarpack2-dev libblas-dev libblas3\n",
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            "  libjsoncpp1 libklu1 libldl2 libltdl-dev libltdl7 liblzo2-2 libmetis5\n",
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            "  libproj-dev libproj12 libpsm-infinipath1 libptscotch-6.0 libptscotch-dev\n",
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            "  libscalapack-openmpi2.0 libscotch-6.0 libscotch-dev libslepc3.7.4\n",
            "  libslepc3.7.4-dev libspooles-dev libspooles2.2 libspqr2 libssl-dev\n",
            "  libsuitesparse-dev libsuitesparseconfig5 libsuperlu-dev libsuperlu-dist5\n",
            "  libsuperlu5 libtet1.5 libumfpack5 libuv1 mpi-default-bin mpi-default-dev\n",
            "  ocl-icd-libopencl1 openmpi-bin openmpi-common proj-data pybind11-dev\n",
            "  python-ufl-doc python3-dijitso python3-dolfin python3-ffc python3-fiat\n",
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            "  python3-pkg-resources python3-pkgconfig python3-ply python3-pybind11\n",
            "  python3-slepc4py python3-sympy python3-ufl\n",
            "Suggested packages:\n",
            "  cmake-doc ninja-build lrzip liblapack-doc libboost-doc\n",
            "  libboost-graph1.65-dev libboost1.65-doc libboost-container1.65-dev\n",
            "  libboost-context1.65-dev libboost-coroutine1.65-dev\n",
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            "  libboost-random1.65-dev libboost-signals1.65-dev libboost-stacktrace1.65-dev\n",
            "  libboost-test1.65-dev libboost-type-erasure1.65-dev libboost-wave1.65-dev\n",
            "  libboost1.65-tools-dev libmpfrc++-dev libntl-dev libeigen3-doc libmrpt-dev\n",
            "  libfftw3-doc libhdf5-doc libhwloc-contrib-plugins libtool-doc openmpi-doc\n",
            "  pciutils petsc-dev libpetsc3.7.7-dbg petsc3.7.7-doc libluminate-dev proj-bin\n",
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            "  python-dijitso-doc python3-gmpy2 python3-matplotlib python-mpmath-doc\n",
            "  python-numpy-doc python3-nose python3-numpy-dbg python3-setuptools\n",
            "  python-ply-doc texlive-fonts-extra dvipng python-sympy-doc\n",
            "Recommended packages:\n",
            "  libtool tcsh | csh | c-shell ksh | mksh | pdksh | zsh libssl-doc\n",
            "  python-petsc4py-docs python-slepc4py-docs python3-pil ipython3\n",
            "The following NEW packages will be installed:\n",
            "  cmake cmake-data dolfin-bin dolfin-doc fenics ibverbs-providers libamd2\n",
            "  libarchive13 libarpack2 libarpack2-dev libblas-dev libblas3\n",
            "  libboost-atomic1.65-dev libboost-atomic1.65.1 libboost-chrono-dev\n",
            "  libboost-chrono1.65-dev libboost-chrono1.65.1 libboost-date-time1.65-dev\n",
            "  libboost-date-time1.65.1 libboost-dev libboost-filesystem-dev\n",
            "  libboost-filesystem1.65-dev libboost-filesystem1.65.1 libboost-iostreams-dev\n",
            "  libboost-iostreams1.65-dev libboost-iostreams1.65.1 libboost-math-dev\n",
            "  libboost-math1.65-dev libboost-math1.65.1 libboost-mpi-dev\n",
            "  libboost-mpi1.65-dev libboost-mpi1.65.1 libboost-program-options-dev\n",
            "  libboost-program-options1.65-dev libboost-program-options1.65.1\n",
            "  libboost-regex1.65-dev libboost-regex1.65.1 libboost-serialization-dev\n",
            "  libboost-serialization1.65-dev libboost-serialization1.65.1\n",
            "  libboost-system1.65-dev libboost-system1.65.1 libboost-thread-dev\n",
            "  libboost-thread1.65-dev libboost-thread1.65.1 libboost-timer-dev\n",
            "  libboost-timer1.65-dev libboost-timer1.65.1 libboost1.65-dev libbtf1\n",
            "  libcamd2 libccolamd2 libcholmod3 libcolamd2 libcxsparse3 libdolfin-dev\n",
            "  libdolfin2018.1 libeigen3-dev libfabric1 libfftw3-bin libfftw3-dev\n",
            "  libfftw3-double3 libfftw3-long3 libfftw3-mpi-dev libfftw3-mpi3\n",
            "  libfftw3-quad3 libfftw3-single3 libgraphblas1 libhdf5-mpi-dev\n",
            "  libhdf5-openmpi-100 libhdf5-openmpi-dev libhwloc-dev libhwloc-plugins\n",
            "  libhwloc5 libhypre-2.13.0 libhypre-dev libibverbs-dev libibverbs1\n",
            "  libjsoncpp1 libklu1 libldl2 libltdl-dev libltdl7 liblzo2-2 libmetis5\n",
            "  libmshr-dev libmshr2018.1 libmumps-5.1.2 libmumps-dev libnl-3-200\n",
            "  libnl-route-3-200 libnuma-dev libnuma1 libopenmpi-dev libopenmpi2\n",
            "  libparpack2 libparpack2-dev libpciaccess0 libpetsc3.7.7 libpetsc3.7.7-dev\n",
            "  libproj-dev libproj12 libpsm-infinipath1 libptscotch-6.0 libptscotch-dev\n",
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            "  libslepc3.7.4-dev libspooles-dev libspooles2.2 libspqr2 libssl-dev\n",
            "  libsuitesparse-dev libsuitesparseconfig5 libsuperlu-dev libsuperlu-dist5\n",
            "  libsuperlu5 libtet1.5 libumfpack5 libuv1 mpi-default-bin mpi-default-dev\n",
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            "  python-ufl-doc python3-dijitso python3-dolfin python3-ffc python3-fiat\n",
            "  python3-mpi4py python3-mpmath python3-mshr python3-numpy python3-petsc4py\n",
            "  python3-pkg-resources python3-pkgconfig python3-ply python3-pybind11\n",
            "  python3-slepc4py python3-sympy python3-ufl\n",
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            "Get:24 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-iostreams1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [37.0 kB]\n",
            "Get:25 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-iostreams-dev amd64 1.65.1.0ubuntu1 [2,916 B]\n",
            "Get:26 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-math1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [311 kB]\n",
            "Get:27 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-math1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [560 kB]\n",
            "Get:28 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-math-dev amd64 1.65.1.0ubuntu1 [3,112 B]\n",
            "Get:29 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-serialization1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [99.3 kB]\n",
            "Get:30 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-serialization1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [137 kB]\n",
            "Get:31 http://archive.ubuntu.com/ubuntu bionic/main amd64 libnl-3-200 amd64 3.2.29-0ubuntu3 [52.8 kB]\n",
            "Get:32 http://archive.ubuntu.com/ubuntu bionic/main amd64 libnl-route-3-200 amd64 3.2.29-0ubuntu3 [146 kB]\n",
            "Get:33 http://archive.ubuntu.com/ubuntu bionic/main amd64 libibverbs1 amd64 17.1-1 [44.4 kB]\n",
            "Get:34 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libpsm-infinipath1 amd64 3.3+20.604758e7-5 [174 kB]\n",
            "Get:35 http://archive.ubuntu.com/ubuntu bionic/main amd64 librdmacm1 amd64 17.1-1 [56.1 kB]\n",
            "Get:36 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libfabric1 amd64 1.5.3-1 [302 kB]\n",
            "Get:37 http://archive.ubuntu.com/ubuntu bionic/main amd64 libltdl7 amd64 2.4.6-2 [38.8 kB]\n",
            "Get:38 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhwloc5 amd64 1.11.9-1 [105 kB]\n",
            "Get:39 http://archive.ubuntu.com/ubuntu bionic/main amd64 libpciaccess0 amd64 0.14-1 [17.9 kB]\n",
            "Get:40 http://archive.ubuntu.com/ubuntu bionic/main amd64 ocl-icd-libopencl1 amd64 2.2.11-1ubuntu1 [30.3 kB]\n",
            "Get:41 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhwloc-plugins amd64 1.11.9-1 [12.5 kB]\n",
            "Get:42 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libopenmpi2 amd64 2.1.1-8 [2,056 kB]\n",
            "Get:43 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-mpi1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [47.0 kB]\n",
            "Get:44 http://archive.ubuntu.com/ubuntu bionic/universe amd64 openmpi-common all 2.1.1-8 [140 kB]\n",
            "Get:45 http://archive.ubuntu.com/ubuntu bionic/main amd64 ibverbs-providers amd64 17.1-1 [160 kB]\n",
            "Get:46 http://archive.ubuntu.com/ubuntu bionic/main amd64 libibverbs-dev amd64 17.1-1 [103 kB]\n",
            "Get:47 http://archive.ubuntu.com/ubuntu bionic/main amd64 libnuma-dev amd64 2.0.11-2.1 [32.2 kB]\n",
            "Get:48 http://archive.ubuntu.com/ubuntu bionic/main amd64 libltdl-dev amd64 2.4.6-2 [162 kB]\n",
            "Get:49 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhwloc-dev amd64 1.11.9-1 [167 kB]\n",
            "Get:50 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libopenmpi-dev amd64 2.1.1-8 [925 kB]\n",
            "Get:51 http://archive.ubuntu.com/ubuntu bionic/universe amd64 mpi-default-dev amd64 1.10 [3,888 B]\n",
            "Get:52 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-mpi1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [137 kB]\n",
            "Get:53 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-mpi-dev amd64 1.65.1.0ubuntu1 [3,004 B]\n",
            "Get:54 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-program-options1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [137 kB]\n",
            "Get:55 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-program-options1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [163 kB]\n",
            "Get:56 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python3-ufl all 2018.1.0-4~ppa1~bionic1 [155 kB]\n",
            "Get:57 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-program-options-dev amd64 1.65.1.0ubuntu1 [2,940 B]\n",
            "Get:58 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-serialization-dev amd64 1.65.1.0ubuntu1 [3,144 B]\n",
            "Get:59 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-atomic1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [7,268 B]\n",
            "Get:60 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-atomic1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [5,160 B]\n",
            "Get:61 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-date-time1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [20.5 kB]\n",
            "Get:62 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-date-time1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [26.7 kB]\n",
            "Get:63 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-thread1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [43.2 kB]\n",
            "Get:64 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-thread1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [49.0 kB]\n",
            "Get:65 http://archive.ubuntu.com/ubuntu bionic/main amd64 libboost-thread-dev amd64 1.65.1.0ubuntu1 [2,948 B]\n",
            "Get:66 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-timer1.65.1 amd64 1.65.1+dfsg-0ubuntu5 [11.9 kB]\n",
            "Get:67 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-timer1.65-dev amd64 1.65.1+dfsg-0ubuntu5 [11.8 kB]\n",
            "Get:68 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libboost-timer-dev amd64 1.65.1.0ubuntu1 [3,044 B]\n",
            "Get:69 http://archive.ubuntu.com/ubuntu bionic/main amd64 libsuitesparseconfig5 amd64 1:5.1.2-2 [9,044 B]\n",
            "Get:70 http://archive.ubuntu.com/ubuntu bionic/main amd64 libamd2 amd64 1:5.1.2-2 [19.5 kB]\n",
            "Get:71 http://archive.ubuntu.com/ubuntu bionic/main amd64 libblas3 amd64 3.7.1-4ubuntu1 [140 kB]\n",
            "Get:72 http://archive.ubuntu.com/ubuntu bionic/main amd64 libcamd2 amd64 1:5.1.2-2 [20.9 kB]\n",
            "Get:73 http://archive.ubuntu.com/ubuntu bionic/main amd64 libccolamd2 amd64 1:5.1.2-2 [21.7 kB]\n",
            "Get:74 http://archive.ubuntu.com/ubuntu bionic/main amd64 libcolamd2 amd64 1:5.1.2-2 [16.2 kB]\n",
            "Get:75 http://archive.ubuntu.com/ubuntu bionic/main amd64 libmetis5 amd64 5.1.0.dfsg-5 [169 kB]\n",
            "Get:76 http://archive.ubuntu.com/ubuntu bionic/main amd64 libcholmod3 amd64 1:5.1.2-2 [300 kB]\n",
            "Get:77 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhdf5-openmpi-100 amd64 1.10.0-patch1+docs-4 [1,289 kB]\n",
            "Get:78 http://archive.ubuntu.com/ubuntu bionic/main amd64 libfftw3-double3 amd64 3.3.7-1 [735 kB]\n",
            "Get:79 http://archive.ubuntu.com/ubuntu bionic/main amd64 libfftw3-long3 amd64 3.3.7-1 [308 kB]\n",
            "Get:80 http://archive.ubuntu.com/ubuntu bionic/main amd64 libfftw3-single3 amd64 3.3.7-1 [764 kB]\n",
            "Get:81 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python3-dijitso all 2018.1.0-5~ppa2~bionic1 [24.1 kB]\n",
            "Get:82 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libfftw3-mpi3 amd64 3.3.7-1 [47.5 kB]\n",
            "Get:83 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libscotch-6.0 amd64 6.0.4.dfsg1-8 [403 kB]\n",
            "Get:84 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libptscotch-6.0 amd64 6.0.4.dfsg1-8 [654 kB]\n",
            "Get:85 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libsuperlu-dist5 amd64 5.3.0+dfsg1-1 [213 kB]\n",
            "Get:86 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libsuperlu5 amd64 5.2.1+dfsg1-3 [161 kB]\n",
            "Get:87 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhypre-2.13.0 amd64 2.13.0-2 [1,718 kB]\n",
            "Get:88 http://archive.ubuntu.com/ubuntu bionic/main amd64 libbtf1 amd64 1:5.1.2-2 [10.6 kB]\n",
            "Get:89 http://archive.ubuntu.com/ubuntu bionic/main amd64 libklu1 amd64 1:5.1.2-2 [69.3 kB]\n",
            "Get:90 http://archive.ubuntu.com/ubuntu bionic/universe amd64 openmpi-bin amd64 2.1.1-8 [88.2 kB]\n",
            "Get:91 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python3-ffc all 2018.1.0-5~ppa1~bionic1 [224 kB]\n",
            "Get:92 http://archive.ubuntu.com/ubuntu bionic/universe amd64 mpi-default-bin amd64 1.10 [3,108 B]\n",
            "Get:93 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libscalapack-openmpi2.0 amd64 2.0.2-4 [1,473 kB]\n",
            "Get:94 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libmumps-5.1.2 amd64 5.1.2-4 [1,103 kB]\n",
            "Get:95 http://archive.ubuntu.com/ubuntu bionic/main amd64 libumfpack5 amd64 1:5.1.2-2 [229 kB]\n",
            "Get:96 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libpetsc3.7.7 amd64 3.7.7+dfsg1-2build5 [3,935 kB]\n",
            "Get:97 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 libdolfin-dev amd64 2018.1.0.post1-8~ppa1~bionic2 [200 kB]\n",
            "Get:98 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libarpack2 amd64 3.5.0+real-2 [89.7 kB]\n",
            "Get:99 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libparpack2 amd64 3.5.0+real-2 [84.5 kB]\n",
            "Get:100 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libslepc3.7.4 amd64 3.7.4+dfsg1-2build8 [743 kB]\n",
            "Get:101 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libeigen3-dev all 3.3.4-4 [810 kB]\n",
            "Get:102 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhdf5-openmpi-dev amd64 1.10.0-patch1+docs-4 [2,392 kB]\n",
            "Get:103 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhdf5-mpi-dev amd64 1.10.0-patch1+docs-4 [3,074 B]\n",
            "Get:104 http://archive.ubuntu.com/ubuntu bionic/main amd64 libcxsparse3 amd64 1:5.1.2-2 [63.9 kB]\n",
            "Get:105 http://archive.ubuntu.com/ubuntu bionic/main amd64 libgraphblas1 amd64 1:5.1.2-2 [384 kB]\n",
            "Get:106 http://archive.ubuntu.com/ubuntu bionic/main amd64 libldl2 amd64 1:5.1.2-2 [10.3 kB]\n",
            "Get:107 http://archive.ubuntu.com/ubuntu bionic/main amd64 librbio2 amd64 1:5.1.2-2 [24.0 kB]\n",
            "Get:108 http://archive.ubuntu.com/ubuntu bionic/main amd64 libspqr2 amd64 1:5.1.2-2 [64.2 kB]\n",
            "Get:109 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 pybind11-dev all 2.2.3-1fenics1bionic1 [129 kB]\n",
            "Get:110 http://archive.ubuntu.com/ubuntu bionic/main amd64 libblas-dev amd64 3.7.1-4ubuntu1 [143 kB]\n",
            "Get:111 http://archive.ubuntu.com/ubuntu bionic/main amd64 libsuitesparse-dev amd64 1:5.1.2-2 [1,235 kB]\n",
            "Get:112 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python3-pybind11 all 2.2.3-1fenics1bionic1 [21.5 kB]\n",
            "Get:113 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libscotch-dev amd64 6.0.4.dfsg1-8 [1,791 kB]\n",
            "Get:114 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python3-dolfin amd64 2018.1.0.post1-8~ppa1~bionic2 [699 kB]\n",
            "Get:115 http://archive.ubuntu.com/ubuntu bionic/main amd64 python3-numpy amd64 1:1.13.3-2ubuntu1 [1,943 kB]\n",
            "Get:116 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python3-mpmath all 1.0.0-1 [400 kB]\n",
            "Get:117 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python3-sympy all 1.1.1-5 [2,569 kB]\n",
            "Get:118 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 dolfin-bin all 2018.1.0.post1-8~ppa1~bionic2 [21.0 kB]\n",
            "Get:119 http://archive.ubuntu.com/ubuntu bionic/main amd64 python3-pkg-resources all 39.0.1-2 [98.8 kB]\n",
            "Get:120 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python3-mpi4py amd64 2.0.0-3 [420 kB]\n",
            "Get:121 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libspooles2.2 amd64 2.2-12build1 [458 kB]\n",
            "Get:122 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libspooles-dev amd64 2.2-12build1 [587 kB]\n",
            "Get:123 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 dolfin-doc all 2018.1.0.post1-8~ppa1~bionic2 [4,106 kB]\n",
            "Get:124 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libsuperlu-dev amd64 5.2.1+dfsg1-3 [16.3 kB]\n",
            "Get:125 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libhypre-dev amd64 2.13.0-2 [134 kB]\n",
            "Get:126 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libptscotch-dev amd64 6.0.4.dfsg1-8 [5,416 kB]\n",
            "Get:127 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libscalapack-openmpi-dev amd64 2.0.2-4 [6,068 B]\n",
            "Get:128 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libscalapack-mpi-dev amd64 2.0.2-4 [2,108 B]\n",
            "Get:129 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libmumps-dev amd64 5.1.2-4 [984 kB]\n",
            "Get:130 http://archive.ubuntu.com/ubuntu bionic/main amd64 libfftw3-quad3 amd64 3.3.7-1 [552 kB]\n",
            "Get:131 http://archive.ubuntu.com/ubuntu bionic/main amd64 libfftw3-bin amd64 3.3.7-1 [32.7 kB]\n",
            "Get:132 http://archive.ubuntu.com/ubuntu bionic/main amd64 libfftw3-dev amd64 3.3.7-1 [2,108 kB]\n",
            "Get:133 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libfftw3-mpi-dev amd64 3.3.7-1 [47.6 kB]\n",
            "Get:134 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python-ufl-doc all 2018.1.0-4~ppa1~bionic1 [13.3 kB]\n",
            "Get:135 http://archive.ubuntu.com/ubuntu bionic-updates/main amd64 libssl-dev amd64 1.1.0g-2ubuntu4.1 [1,372 kB]\n",
            "Get:136 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libpetsc3.7.7-dev amd64 3.7.7+dfsg1-2build5 [3,495 kB]\n",
            "Get:137 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libarpack2-dev amd64 3.5.0+real-2 [97.3 kB]\n",
            "Get:138 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 libmshr2018.1 amd64 2018.1.0+full1-3~ppa1~bionic2 [1,463 kB]\n",
            "Get:139 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libparpack2-dev amd64 3.5.0+real-2 [92.0 kB]\n",
            "Get:140 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libslepc3.7.4-dev amd64 3.7.4+dfsg1-2build8 [1,701 kB]\n",
            "Get:141 http://archive.ubuntu.com/ubuntu bionic/main amd64 python3-ply all 3.11-1 [46.6 kB]\n",
            "Get:142 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python3-petsc4py amd64 3.7.0-3build2 [719 kB]\n",
            "Get:143 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python3-slepc4py amd64 3.7.0-3build1 [155 kB]\n",
            "Get:144 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python3-pkgconfig all 1.3.1-1 [6,328 B]\n",
            "Get:145 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libtet1.5 amd64 1.5.0-4 [235 kB]\n",
            "Get:146 http://archive.ubuntu.com/ubuntu bionic/universe amd64 proj-data all 4.9.3-2 [4,020 kB]\n",
            "Get:147 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 libmshr-dev amd64 2018.1.0+full1-3~ppa1~bionic2 [60.7 kB]\n",
            "Get:148 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libproj12 amd64 4.9.3-2 [159 kB]\n",
            "Get:149 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 python3-mshr amd64 2018.1.0+full1-3~ppa1~bionic2 [86.2 kB]\n",
            "Get:150 http://archive.ubuntu.com/ubuntu bionic/universe amd64 libproj-dev amd64 4.9.3-2 [199 kB]\n",
            "Get:151 http://ppa.launchpad.net/fenics-packages/fenics/ubuntu bionic/main amd64 fenics all 1:2018.1.0.2~ppa1~bionic1 [3,912 B]\n",
            "Fetched 78.3 MB in 2s (43.0 MB/s)\n",
            "Extracting templates from packages: 100%\n",
            "Selecting previously unselected package liblzo2-2:amd64.\n",
            "(Reading database ... 22278 files and directories currently installed.)\n",
            "Preparing to unpack .../000-liblzo2-2_2.08-1.2_amd64.deb ...\n",
            "Unpacking liblzo2-2:amd64 (2.08-1.2) ...\n",
            "Selecting previously unselected package libnuma1:amd64.\n",
            "Preparing to unpack .../001-libnuma1_2.0.11-2.1_amd64.deb ...\n",
            "Unpacking libnuma1:amd64 (2.0.11-2.1) ...\n",
            "Selecting previously unselected package cmake-data.\n",
            "Preparing to unpack .../002-cmake-data_3.10.2-1ubuntu2_all.deb ...\n",
            "Unpacking cmake-data (3.10.2-1ubuntu2) ...\n",
            "Selecting previously unselected package libarchive13:amd64.\n",
            "Preparing to unpack .../003-libarchive13_3.2.2-3.1ubuntu0.1_amd64.deb ...\n",
            "Unpacking libarchive13:amd64 (3.2.2-3.1ubuntu0.1) ...\n",
            "Selecting previously unselected package libjsoncpp1:amd64.\n",
            "Preparing to unpack .../004-libjsoncpp1_1.7.4-3_amd64.deb ...\n",
            "Unpacking libjsoncpp1:amd64 (1.7.4-3) ...\n",
            "Selecting previously unselected package librhash0:amd64.\n",
            "Preparing to unpack .../005-librhash0_1.3.6-2_amd64.deb ...\n",
            "Unpacking librhash0:amd64 (1.3.6-2) ...\n",
            "Selecting previously unselected package libuv1:amd64.\n",
            "Preparing to unpack .../006-libuv1_1.18.0-3_amd64.deb ...\n",
            "Unpacking libuv1:amd64 (1.18.0-3) ...\n",
            "Selecting previously unselected package cmake.\n",
            "Preparing to unpack .../007-cmake_3.10.2-1ubuntu2_amd64.deb ...\n",
            "Unpacking cmake (3.10.2-1ubuntu2) ...\n",
            "Selecting previously unselected package libboost1.65-dev:amd64.\n",
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            "Unpacking libboost1.65-dev:amd64 (1.65.1+dfsg-0ubuntu5) ...\n",
            "Selecting previously unselected package libboost-system1.65.1:amd64.\n",
            "Preparing to unpack .../009-libboost-system1.65.1_1.65.1+dfsg-0ubuntu5_amd64.deb ...\n",
            "Unpacking libboost-system1.65.1:amd64 (1.65.1+dfsg-0ubuntu5) ...\n",
            "Selecting previously unselected package libboost-chrono1.65.1:amd64.\n",
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            "Unpacking libboost-chrono1.65.1:amd64 (1.65.1+dfsg-0ubuntu5) ...\n",
            "Selecting previously unselected package libboost-chrono1.65-dev:amd64.\n",
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            "Unpacking libboost-chrono1.65-dev:amd64 (1.65.1+dfsg-0ubuntu5) ...\n",
            "Selecting previously unselected package libboost-chrono-dev:amd64.\n",
            "Preparing to unpack .../012-libboost-chrono-dev_1.65.1.0ubuntu1_amd64.deb ...\n",
            "Unpacking libboost-chrono-dev:amd64 (1.65.1.0ubuntu1) ...\n",
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            "Unpacking libboost-dev:amd64 (1.65.1.0ubuntu1) ...\n",
            "Selecting previously unselected package libboost-filesystem1.65.1:amd64.\n",
            "Preparing to unpack .../014-libboost-filesystem1.65.1_1.65.1+dfsg-0ubuntu5_amd64.deb ...\n",
            "Unpacking libboost-filesystem1.65.1:amd64 (1.65.1+dfsg-0ubuntu5) ...\n",
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            "Unpacking libboost-system1.65-dev:amd64 (1.65.1+dfsg-0ubuntu5) ...\n",
            "Selecting previously unselected package libboost-filesystem1.65-dev:amd64.\n",
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            "update-alternatives: warning: skip creation of /usr/share/man/man1/mpifort.1.gz because associated file /usr/share/man/man1/mpifort.openmpi.1.gz (of link group mpi) doesn't exist\n",
            "Setting up libptscotch-6.0 (6.0.4.dfsg1-8) ...\n",
            "Setting up libfftw3-mpi3:amd64 (3.3.7-1) ...\n",
            "Setting up libspooles2.2:amd64 (2.2-12build1) ...\n",
            "Setting up openmpi-bin (2.1.1-8) ...\n",
            "update-alternatives: using /usr/bin/mpirun.openmpi to provide /usr/bin/mpirun (mpirun) in auto mode\n",
            "update-alternatives: warning: skip creation of /usr/share/man/man1/mpirun.1.gz because associated file /usr/share/man/man1/mpirun.openmpi.1.gz (of link group mpirun) doesn't exist\n",
            "update-alternatives: warning: skip creation of /usr/share/man/man1/mpiexec.1.gz because associated file /usr/share/man/man1/mpiexec.openmpi.1.gz (of link group mpirun) doesn't exist\n",
            "Setting up mpi-default-dev (1.10) ...\n",
            "Setting up libhdf5-openmpi-dev (1.10.0-patch1+docs-4) ...\n",
            "update-alternatives: using /usr/bin/h5pcc.openmpi to provide /usr/bin/h5pcc (h5pcc) in auto mode\n",
            "update-alternatives: warning: skip creation of /usr/share/man/man1/h5pcc.1.gz because associated file /usr/share/man/man1/h5pcc.openmpi.1.gz (of link group h5pcc) doesn't exist\n",
            "update-alternatives: warning: skip creation of /usr/share/man/man1/h5pfc.1.gz because associated file /usr/share/man/man1/h5pfc.openmpi.1.gz (of link group h5pcc) doesn't exist\n",
            "Setting up libscotch-dev (6.0.4.dfsg1-8) ...\n",
            "Setting up libsuperlu-dist5 (5.3.0+dfsg1-1) ...\n",
            "Setting up python3-mpi4py (2.0.0-3) ...\n",
            "Setting up libspooles-dev:amd64 (2.2-12build1) ...\n",
            "Setting up libboost-mpi1.65-dev (1.65.1+dfsg-0ubuntu5) ...\n",
            "Setting up mpi-default-bin (1.10) ...\n",
            "Setting up libfftw3-mpi-dev:amd64 (3.3.7-1) ...\n",
            "Setting up libparpack2-dev:amd64 (3.5.0+real-2) ...\n",
            "Setting up libptscotch-dev (6.0.4.dfsg1-8) ...\n",
            "Setting up libscalapack-openmpi2.0 (2.0.2-4) ...\n",
            "Setting up libhypre-2.13.0:amd64 (2.13.0-2) ...\n",
            "Setting up python3-dijitso (2018.1.0-5~ppa2~bionic1) ...\n",
            "Setting up libhdf5-mpi-dev (1.10.0-patch1+docs-4) ...\n",
            "Setting up libscalapack-openmpi-dev (2.0.2-4) ...\n",
            "Setting up libboost-mpi-dev (1.65.1.0ubuntu1) ...\n",
            "Setting up python3-ffc (2018.1.0-5~ppa1~bionic1) ...\n",
            "update-alternatives: using /usr/lib/python3/dist-packages/ffc/backends/ufc/ufc.h to provide /usr/include/ufc.h (ufc.h) in auto mode\n",
            "Setting up libmumps-5.1.2:amd64 (5.1.2-4) ...\n",
            "Setting up libhypre-dev:amd64 (2.13.0-2) ...\n",
            "Setting up libscalapack-mpi-dev (2.0.2-4) ...\n",
            "Setting up libmumps-dev:amd64 (5.1.2-4) ...\n",
            "Setting up libpetsc3.7.7:amd64 (3.7.7+dfsg1-2build5) ...\n",
            "update-alternatives: using /usr/lib/x86_64-linux-gnu/libpetsc_real.so.3.7.7 to provide /usr/lib/x86_64-linux-gnu/libpetsc.so.3.7 (libpetsc.so.3.7) in auto mode\n",
            "update-alternatives: using /usr/lib/x86_64-linux-gnu/libpetsc_real.so.3.7.7 to provide /usr/lib/x86_64-linux-gnu/libpetsc_real.so.3.7 (libpetsc_real.so.3.7) in auto mode\n",
            "Setting up python3-petsc4py (3.7.0-3build2) ...\n",
            "Setting up libpetsc3.7.7-dev:amd64 (3.7.7+dfsg1-2build5) ...\n",
            "update-alternatives: error: no alternatives for petsc\n",
            "update-alternatives: using /usr/lib/petscdir/3.7.7/x86_64-linux-gnu-real to provide /usr/lib/petsc (petsc) in auto mode\n",
            "update-alternatives: using /usr/lib/x86_64-linux-gnu/libpetsc_real.so.3.7.7 to provide /usr/lib/x86_64-linux-gnu/libpetsc_real.so (libpetsc_real.so) in auto mode\n",
            "update-alternatives: using /usr/lib/petscdir/3.7.7/x86_64-linux-gnu-real to provide /usr/lib/petscdir/3.7 (petsc3.7) in auto mode\n",
            "update-alternatives: using /usr/lib/petscdir/3.7.7/x86_64-linux-gnu-real to provide /usr/lib/petscdir/3.7-real (petsc3.7-real) in auto mode\n",
            "Setting up libslepc3.7.4 (3.7.4+dfsg1-2build8) ...\n",
            "update-alternatives: using /usr/lib/x86_64-linux-gnu/libslepc_real.so.3.7.4 to provide /usr/lib/x86_64-linux-gnu/libslepc.so.3.7 (libslepc.so.3.7) in auto mode\n",
            "update-alternatives: using /usr/lib/x86_64-linux-gnu/libslepc_real.so.3.7.4 to provide /usr/lib/x86_64-linux-gnu/libslepc_real.so.3.7 (libslepc_real.so.3.7) in auto mode\n",
            "Setting up python3-slepc4py (3.7.0-3build1) ...\n",
            "Setting up libdolfin2018.1 (2018.1.0.post1-8~ppa1~bionic2) ...\n",
            "Setting up libslepc3.7.4-dev (3.7.4+dfsg1-2build8) ...\n",
            "update-alternatives: error: no alternatives for slepc\n",
            "update-alternatives: using /usr/lib/slepcdir/3.7.4/x86_64-linux-gnu-real to provide /usr/lib/slepc (slepc) in auto mode\n",
            "update-alternatives: using /usr/lib/x86_64-linux-gnu/libslepc_real.so.3.7.4 to provide /usr/lib/x86_64-linux-gnu/libslepc_real.so (libslepc_real.so) in auto mode\n",
            "update-alternatives: using /usr/lib/slepcdir/3.7.4/x86_64-linux-gnu-real to provide /usr/lib/slepcdir/3.7 (slepc3.7) in auto mode\n",
            "update-alternatives: using /usr/lib/slepcdir/3.7.4/x86_64-linux-gnu-real to provide /usr/lib/slepcdir/3.7-real (slepc3.7-real) in auto mode\n",
            "Setting up libmshr2018.1 (2018.1.0+full1-3~ppa1~bionic2) ...\n",
            "Setting up libdolfin-dev (2018.1.0.post1-8~ppa1~bionic2) ...\n",
            "Setting up libmshr-dev (2018.1.0+full1-3~ppa1~bionic2) ...\n",
            "Setting up python3-dolfin (2018.1.0.post1-8~ppa1~bionic2) ...\n",
            "Setting up dolfin-doc (2018.1.0.post1-8~ppa1~bionic2) ...\n",
            "Setting up dolfin-bin (2018.1.0.post1-8~ppa1~bionic2) ...\n",
            "Setting up python3-mshr (2018.1.0+full1-3~ppa1~bionic2) ...\n",
            "Setting up fenics (1:2018.1.0.2~ppa1~bionic1) ...\n",
            "Processing triggers for libc-bin (2.27-3ubuntu1) ...\n",
            "dolfin version: 2018.1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "aiUvz-WE70WC",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# The Poisson solver"
      ]
    },
    {
      "metadata": {
        "id": "EYZW_n-P69-j",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 385
        },
        "outputId": "9e1bd7bd-1d7b-4536-fa7e-6b3fb82d045d"
      },
      "cell_type": "code",
      "source": [
        "from __future__ import print_function\n",
        "from fenics import *\n",
        "\n",
        "# Create mesh and define function space\n",
        "mesh = UnitSquareMesh(10, 10)\n",
        "V = FunctionSpace(mesh, 'CG', 1)\n",
        "\n",
        "# Define boundary condition\n",
        "u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2)\n",
        "\n",
        "def boundary(x, on_boundary):\n",
        "    return on_boundary\n",
        "\n",
        "bc = DirichletBC(V, u_D, boundary)\n",
        "\n",
        "# Define variational problem\n",
        "u = TrialFunction(V)\n",
        "v = TestFunction(V)\n",
        "f = Constant(-6.0)\n",
        "a = dot(grad(u), grad(v))*dx\n",
        "L = f*v*dx\n",
        "\n",
        "# Compute solution\n",
        "u = Function(V)\n",
        "solve(a == L, u, bc)\n",
        "\n",
        "# Plot solution and mesh\n",
        "plot(u,cmap=\"coolwarm\")\n",
        "plot(mesh)\n",
        "\n",
        "# Save solution to file in VTK format\n",
        "vtkfile = File('solution.pvd')\n",
        "vtkfile << u\n",
        "\n",
        "# Compute error in L2 norm\n",
        "error_L2 = errornorm(u_D, u, 'L2')\n",
        "\n",
        "# Compute maximum error at vertices\n",
        "vertex_values_u_D = u_D.compute_vertex_values(mesh)\n",
        "vertex_values_u = u.compute_vertex_values(mesh)\n",
        "import numpy as np\n",
        "error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u))\n",
        "\n",
        "# Print errors\n",
        "print('error_L2  =', error_L2)\n",
        "print('error_max =', error_max)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "error_L2  = 0.005270462766948929\n",
            "error_max = 3.3306690738754696e-15\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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C8IusYVpAEWrPpFB399+CpzTbl9uTCKyYdVKdCaECyAr1WDtGYklsaq7D462NlhGqZcQ8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\nDwuZo/tabFeuaUHC/utD6I3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pvatezjWd4fHnQ8fzfta2vBENC2ryfkY7gcAo3xpLZfCH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T5DPZO7Axk1mM6wsIWqia2BCRWASajSsseZhUo1AWBGqPnR+hYq4GKVqg8++ACnTp3C1q1bcezY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\nrE9NPuz7biwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f151eccbcc0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}