tutorials/09_Assemble stiffness matrix and solve.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assembling Stiffness matrix; Impose Boundary conditions; Solve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This workflow can be extended to any geometry.\n",
    "\n",
    "Content:\n",
    "* [Create, refine and assign topology to geometry](#geometry)\n",
    "* [Build stiffness matrix](#k)\n",
    "* [Assign Dirichlet Boundary Conditions](#bc)\n",
    "* [Solving system of equations](#solve)\n",
    "* [Post-processing](#post)\n",
    "    * [plot](#plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='geometry'></a>\n",
    "## 1) Create geometry - Anticline model; refine and assign topology"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygeoiga.nurb.nurb_creation import NURB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create multipatch structure\n",
    "cp1 = np.array([[[0., 0.], [0.,  50.], [0., 100.]],\n",
    "                [[250., 0.], [250., 180.], [250., 250.]],\n",
    "                [[500.,   0.], [500.,  50.], [500., 100.]]])\n",
    "knot1 = [[0, 0, 0, 1, 1, 1],[0, 0, 0, 1, 1, 1]]\n",
    "\n",
    "nrb1 = NURB(cp1, knot1)\n",
    "cp2=np.array([[[0., 100.], [0., 200.], [0., 300.]],\n",
    "                       [[250., 250.], [250., 350.], [250., 400.]],\n",
    "                       [[500., 100.], [500., 200.], [500., 300.]]])\n",
    "knot2= [[0, 0, 0, 1, 1, 1],[0, 0, 0, 1, 1, 1]]\n",
    "nrb2 = NURB(cp2, knot2)\n",
    "\n",
    "cp3 = np.array([[[0., 300.], [0., 400.], [0., 500.]],\n",
    "                        [[250., 400.], [250., 450.], [250., 500.]],\n",
    "                        [[500., 300.], [500., 400.], [500., 500.]]])\n",
    "knot3 = [[0, 0, 0, 1, 1, 1],[0, 0, 0, 1, 1, 1]]\n",
    "\n",
    "nrb3 = NURB(cp3, knot3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygeoiga.nurb.multipatch_NURBS import Multipatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "mult = Multipatch()\n",
    "# Kappa is the thermal conductivity of the patch\n",
    "mult.add_patch(nrb1, \"Bottom\", position=(1,1), kappa = 2, color=\"red\")\n",
    "mult.add_patch(nrb2, \"Middle\", position=(2,1), kappa = 3.1, color=\"green\")\n",
    "mult.add_patch(nrb3, \"Top\", position=(3,1), kappa = 0.8, color=\"blue\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "model_id": "79cbe454ed644debbdfc8bae70bd25cc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Inserting knots by patch:   0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Inserting single knot:   0%|          | 0/9 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Inserting single knot:   0%|          | 0/9 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
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       "version_minor": 0
      },
      "text/plain": [
       "Inserting single knot:   0%|          | 0/9 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eb1b638a8e2a4748b2cd98d12ade62e3",
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       "version_minor": 0
      },
      "text/plain": [
       "Inserting knots by patch:   0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Inserting single knot:   0%|          | 0/9 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "version_minor": 0
      },
      "text/plain": [
       "Inserting single knot:   0%|          | 0/9 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "version_minor": 0
      },
      "text/plain": [
       "Inserting single knot:   0%|          | 0/9 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knot_ins = np.arange(0.1, 1, 0.1)\n",
    "\n",
    "mult.global_knot_insertion(knot_ins, direction =0)\n",
    "mult.global_knot_insertion(knot_ins, direction =1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assign connection between faces\n",
    "mult.define_topology()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Global degrees of freedom:  408\n"
     ]
    }
   ],
   "source": [
    "gDoF = mult.fill_topological_info()\n",
    "print(\"Global degrees of freedom: \", gDoF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='k'></a>\n",
    "## 2) Assemble stiffness matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set empty the stiffness matrix\n",
    "K = np.zeros((gDoF, gDoF))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assemble stiffnes matrix\n",
    "from pygeoiga.analysis.MultiPatch import form_k_IGA_mp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "765c263245a9441f8b98226c5a62bbd2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Assembling global stiffness matrix:   0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Depending to the degrees of freedoms this can take a while\n",
    "K = form_k_IGA_mp(mult.geometry, K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fadbde3a400>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the stiffness matrix shape\n",
    "fig, ax = plt.subplots(figsize=(5,5))\n",
    "ax.spy(K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='bc'></a>\n",
    "## 3) Assign Boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = np.zeros(gDoF) # Force vector\n",
    "a = np.zeros(gDoF) # Solution vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "T_t = 10  # [°C]\n",
    "T_b = 25  # [°C]\n",
    "T_l = None  # 10\n",
    "T_r = None  # 40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygeoiga.analysis.MultiPatch import boundary_condition_mp\n",
    "bc, a = boundary_condition_mp(mult.geometry, a, T_t, T_b, T_l, T_r)\n",
    "bc[\"gDOF\"] = gDoF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='solve'></a>\n",
    "## 4) Solve:  Ka = f\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygeoiga.analysis.common import solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, f = solve(bc, K, f, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25., 25., 25., 25., 25., 25., 25., 25., 25., 25.])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Temperatures\n",
    "a[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='post'></a>\n",
    "## 5) Post-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygeoiga.analysis.MultiPatch import map_MP_elements\n",
    "# Map solution to geometry\n",
    "mult.geometry = map_MP_elements(mult.geometry, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='plot'></a>\n",
    "### Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pygeoiga.plot.solution_mpl import p_temperature\n",
    "fig, ax = plt.subplots(figsize=(10,10))\n",
    "for patch_id in mult.geometry.keys():\n",
    "    x = mult.geometry[patch_id].get(\"x_sol\")\n",
    "    y = mult.geometry[patch_id].get(\"y_sol\")\n",
    "    t = mult.geometry[patch_id].get(\"t_sol\")\n",
    "    ax = p_temperature(x,\n",
    "                       y,\n",
    "                       t, \n",
    "                       vmin = np.min(a), \n",
    "                       vmax = np.max(a), \n",
    "                       levels=50, \n",
    "                       show=False, \n",
    "                       colorbar=True, \n",
    "                       ax=ax,\n",
    "                       point = False, \n",
    "                       fill=True, \n",
    "                       contour=False)\n",
    "    ax = p_temperature(x,\n",
    "                       y,\n",
    "                       t, \n",
    "                       vmin = np.min(a), \n",
    "                       vmax = np.max(a), \n",
    "                       levels=10, \n",
    "                       show=False, \n",
    "                       colorbar=True, \n",
    "                       ax=ax,\n",
    "                       point = False, \n",
    "                       fill=False, \n",
    "                       contour=True)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optionally you can use the solution plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "debd43b5e66e400480f77dae928f06e6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Plotting solutions:   0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1440 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mult.plot_solution()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}