FEM_global_matrices_pipe_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### This is a [jupyter](https://jupyter.org/) notebook that contains text, equations, images and executable code in one document."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sy\n",
    "import ipywidgets as ipw\n",
    "%matplotlib inline\n",
    "sy.init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finite Elements: Global Matrices for Pipe Example\n",
    "In this example, we will use the one-dimensional linear elements to calculate the sound field inside a pipe. First we take a look a the problem at hand. The pipe has a length $l$, and the fluid inside the pipe has a speed of sound $c$. The domain where the sound field is of interest is one-dimensional and it is partitioned into $N$ elements. The partition does not need to be equidistant. Therefore we allow a certain randomness to generate the FE mesh. The function _generate1D_ generates the node coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cd2acdd6a72d4821929279f75071c4a8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=10, description='N', max=30, min=-10), FloatSlider(value=0.0, descriptio…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate1D(N, l=1, randomness=0): \n",
    "    x = (np.ones(N+1)+np.random.normal(size=N+1)*randomness).cumsum()\n",
    "    x -= x[0]\n",
    "    return x*l/x[-1]\n",
    "\n",
    "def plot_nodes(x):\n",
    "    plt.plot(x,np.zeros_like(x),'o')\n",
    "    for i,xi in enumerate(x):\n",
    "        plt.text(xi,x[-1]/20,'%i' % i,horizontalalignment='center')\n",
    "    plt.axis('equal')\n",
    "    plt.axis('off')\n",
    "\n",
    "@ipw.interact(N=10,rn=0.0)    \n",
    "def plot_nodes_interact(N,rn):\n",
    "    plt.figure(1,(10,2))\n",
    "    plot_nodes(generate1D(N,1.0,rn))    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $N$ elements each have two nodes. Because our example is so extremely simple, we can easily say which nodes belong to a certain element and which length the element has. We store this information in three arrays. In a more practical application we would have decide about a clever way to handle this information, especially when different element types are used within one mesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "element 0 has nodes [0 1] and length 0.097\n",
      "element 1 has nodes [1 2] and length 0.113\n",
      "element 2 has nodes [2 3] and length 0.105\n",
      "element 3 has nodes [3 4] and length 0.111\n",
      "element 4 has nodes [4 5] and length 0.096\n",
      "element 5 has nodes [5 6] and length 0.084\n",
      "element 6 has nodes [6 7] and length 0.097\n",
      "element 7 has nodes [7 8] and length 0.094\n",
      "element 8 has nodes [8 9] and length 0.104\n",
      "element 9 has nodes [ 9 10] and length 0.100\n"
     ]
    }
   ],
   "source": [
    "def get_element_information(x):\n",
    "    le = x[1:]-x[:-1]\n",
    "    n1_index = np.arange(x.shape[0]-1)\n",
    "    n2_index = n1_index+1\n",
    "    return np.vstack((n1_index,n2_index)).T,le\n",
    "\n",
    "# example with 10 finite elements\n",
    "for nidx, le in zip(*get_element_information(generate1D(10,1.0,0.1))):\n",
    "    print(\"element %i has nodes %s and length %.3f\" % (nidx[0],nidx,le))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As this information is now available, we can compute all the element matrices. We know the entries of those from the derivation of the element mass matrix $\\mathbf{M_{el}}$ and the element stiffness matrix $\\mathbf{K_{el}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Kel(le):\n",
    "    return np.array(((1,-1),(-1,1)))[np.newaxis]/le[:,np.newaxis,np.newaxis] # dimensions Nx2x2\n",
    "\n",
    "def Mel(le, c=344):\n",
    "    return np.array(((2,1),(1,2)))[np.newaxis]*le[:,np.newaxis,np.newaxis]/6/c**2 # dimensions Nx2x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The global matrices $\\mathbf K$ and $\\mathbf M$ can now be assembled. The overall dimension of that matrices is $(N+1) \\times (N+1)$. As it will turn out that these matrices have only few nonzero elements, sparse matrix structures will be used to store the matrices. The assembly process just add each element matrix to the rows and columns that correspond to the node numbers for the element. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<11x11 sparse matrix of type '<class 'numpy.float64'>'\n",
       " \twith 31 stored elements in List of Lists format>,\n",
       " <11x11 sparse matrix of type '<class 'numpy.float64'>'\n",
       " \twith 31 stored elements in List of Lists format>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kgjlCAOqpzPyiEQIaw9rGXWMAailtftmeJWlY0ssRcfx0+9IIAQ3CHCEAdZU4v86StE7Szp125OMj0BDjz+rptAFA1eTNrzwZZnuxpOMkXZnn2JwRApoiWtfZAaB2usuvhbaH214PRcRQ2+tLJJ0naUGewWiEgAbhrjEAddVFfm2KiGWTfcP28ZI2RsQa24fnGYxGCGiIYLI0gJpKmF+HSTrB9kclzZW0s+1vRsSnpvoBUhNokIjOGwBUUZ786pRhEfGliFgcEUslnSzpO9M1QRJnhIBG4a4xAHXFytIACml9WqIRAlA//civiLhf0v2d9uPSGNAgqW6ft3217Y22n2x7bzfbd9t+Nvt11779hwAYOKlun+8WjRDQIAnnCF0j6dgJ750v6d6I2FfSvdlrAEgixRyhXgz8pbFX/+jQJOP8/qF7JRlHkr7wwB1JxvnKB45IMo4kbTjpV5KNhf4IWWOJ7hqLiAdsL53w9omSDs++vlatU85fTHJA9GS77z6WZJzrzzsuyTiS9FdfuyzJOF/c+sdJxpGk7e94JNlY6I+U+dWtgW+EgCbp801he0bEqCRFxKjtPfp7OACDpKybWmmEgKbIP9mw06qsADCzSrzZg0YIaJJ8H6mmXJW1g1dsL8rOBi2StLGHMQBgciWdEmKyNNAgEe64FXCbpFOzr0+VdGvhggEgkye/+nHWqPAZIduzJA1Lejkiji9eEoBehKSxsTQhYft6tSZGL7Q9IukCSRdKutH2aZJelHRSkoOViPwCqiFlfnUrxaWxsyStk7RzgrEA9CokJfq0FBHLp/jWUUkOUB3kF1AFCfOrW4UujdleLOk4SVemKQdAETxrLD/yC6iWstYRKjpH6BJJ50kaK14KgMIix4Zxl4j8AqojT35VqRGyfbykjRGxpsN+K2wP2x7e+sbrvR4OQEflTDSso17ya4venKHqgEGUL7/6kWFFzggdJukE2y9IukHSkba/OXGniBiKiGURsWz2jvMLHA5AR5wRyqvr/JqjHWa6RmCw1O2MUER8KSIWR8RSSSdL+k5EfCpZZQC6E1KMueMG8guonJz51Y8MY0FFoFFodADUVX1vn1dE3K/WAxgBlIlLX10jv4CKKCm/OCMENAmNEIC6ohECUEiJC5IBQCEl5heNENAgLJgIoK7Kyi8aIaBJuCsMQF3V+FljkDR6wnuSjfWVDxyRZJxzV9+fZBxJuvhDadZQSfn7hHcyZ4TQg7mrHk421he3/nGScf7yisuTjCNJXzjz9CTjpPx9wjuVlV80QkBTsGAigLoqMb9ohIDGMJOlAdRUeflFIwQ0CWeEANQVZ4QAFMZz1AHUVUn5RSMENAXrCAGoK9YRApACd40BqCvuGgNQHI0QgLpKlF+250p6QNIOavU5KyPigqn2pxECAABN8qakIyPiX23PkfSg7W9HxPcm25lGCGgQLo0BqKtU+RURIelfs5dzsm3K0WmEgKYIJVui3vYLkjZL2iZpa0QsSzIwAEymu/xaaHu47fVQRAy172B7lqQ1kv69pMsiYvVUg9EIAU2S9ozQERGxKemIADCV/Pm1qdOHs4jYJukg27tIusX2ARHx5GT7btdNjQCqzdF5A4AqypNf3WZYRPxY0v2Sjp1qHxohoEkix5adVm7bVkwx0l2210zxfQBIK09+5WiEbO+enQmS7R0lHS3p6an259IY0CT5Pi11PK0s6bCIWG97D0l32346Ih4oXB8ATCXdGetFkq7N5gltJ+nGiFg11c40QkBDpLz0FRHrs1832r5F0iFqrcsBAMklzq/vSzo47/5cGgOaZMydtw5sz7e9YPxrSR+RNOkkQwBIJk9+Jbozth1nhIAGSfSJak+17rKQWhnx9xFxR5KRAWAKPGIDQHEJgiQinpd0YPGRAKALNEIYt+GkX0kyzsUf2iHJOJL02fseTDLO1Ueluxo7evySZGM1ArfHowK2v+ORJON84czTk4wjSTdcfnGScX531jlJxpGkHW99ONlYjVBiftEIAU1CIwSgrmiEABTlsbIrAIDelJVf3DUGAAAGFmeEgCbh0hiAuiopvwqdEbK9i+2Vtp+2vc72oakKA9ClPjynp+nIMKAicuZXPzKs6BmhSyXdERGfsL29pHkJagLQKxqdbpFhQFXUbbK07Z0lfUjSZyQpIt6S9FaasgD0hEYoNzIMqJgaXhr7JUmvSvo724/ZvjJbjh9ACazWXRedNryNDAMqIm9+9SPDijRCsyW9T9IVEXGwpNclnT9xJ9srbA/bHt76xusFDgdgWswR6lbHDGvPry16s4wagcFQ4hyhIo3QiKSRiFidvV6pVqj8gogYiohlEbFs9o582AL6KnJsGNcxw9rza47SrdQOYBJ58qtKjVBEbJD0ku39sreOkvRUkqoA9IZGKDcyDKiYkhqhoneNnSnpuuxui+cl/V7xkgD0iktfXSPDgIqo5bPGIuJxScvSlAKgMBqhrpBhQIXUsRECUCHBXWEAaqrE/KIRApqEM0IA6oozQgCKYo4QgLqq5RwhABVDIwSgrmiEkNroCe9JNtbVRxV6Pu/bzrn/20nGkaSLDvnNJONs+OR+nXeqA26PR4PMXfVwsrF+d9Y5Scb5m0u+lmQcSTr756cnGWf7O4eTjFO6EvOLRghoCItLYwDqqcz8ohECGoRGCEBdlZVfaa53AKiGRKuy2j7W9jO2n7P9jmcIAkBydXvEBoAKShAitmdJukzSb0naX9Jy2/v3p2AAyNAIASgk3ZObD5H0XEQ8HxFvSbpB0on9LB3AgKvp0+cBVE2+T1MLbQ+3bSsmjLK3pJfaXo9k7wFA/yQ6I2R7ie37bK+zvdb2WdPtz2RpoEFyLlG/KSKme76WJ3mPadgA+irhIza2Sjo3Ih61vUDSGtt3R8RTk+1MIwQ0SKLTxiOSlrS9XixpfZKRAWAKqS57RcSopNHs682216l1VnvSRohLY0BTpJto+IikfW3vY3t7SSdLuq0PFQNAS978ynd5/222l0o6WNLqqfbhjBDQJAk+UUXEVttnSLpT0ixJV0fE2uIjA8A08udXp8v7kiTbO0n6lqTPR8RPp9qPRghoiJQrs0bE7ZJuTzMaAEwv9crStueo1QRdFxE3T7cvjRDQIB5jTjOAekqVX7Yt6SpJ6yLi4k77M0cIaIqSFiMDgMK6myPUyWGSTpF0pO3Hs+2jU+3MGSGgQXjWGIC6Snhp/0FNvgzIpGiEgCahEQJQVyXlF40Q0CCcEQJQV2XlF40Q0CQ0QgDqikYIQCGRdIl6AJg5JeYXjRByGT1+SeedcrjokN9MMo4knfbQcJJxrjpulyTjbDh6zyTj9Cr1OhxAU+x468NJxjn756cnGUeSbr7yb5KMc/w5ZycZZ6ebplx4eUaUmV80QkCTBJ0QgJoqKb9ohIAG4YwQgLrijBCAYlgwEUBdlZhfNEJAgzBZGkBdlZVfhR6xYfts22ttP2n7ettzUxUGoHse67zh35BhQHXkya9+ZFjPjZDtvSV9TtKyiDhA0ixJJ6cqDECXQq3Jhp02SCLDgErJm199yLCil8ZmS9rR9hZJ8yStL14SgF4xWbprZBhQEWXlV89nhCLiZUlflfSipFFJP4mIuybuZ3uF7WHbw1vfeL33SgF0xtPnc8uTYe35tUVvllEmMDjSPX2+K0Uuje0q6URJ+0jaS9J825+auF9EDEXEsohYNnvH+b1XCmBa4wuSddrQkifD2vNrjnYoo0xgIOTNr35kWJHJ0kdL+mFEvBoRWyTdLOk30pQFoGsR8ljnDW8jw4CqyJlf/ciwIo3Qi5I+aHuebUs6StK6NGUB6AmXxrpBhgFVUtKlsZ4nS0fEatsrJT0qaaukxyQNpSoMQPe49JUfGQZUSy1Xlo6ICyRdkKgWAEWEJC59dYUMAyqixPwqtKAigIqZgdPKtv/U9su2H8+2jxYfFcDAq9ulMQDVM4Onlv86Ir46Y0cD0Hi1vDQGoFq4KwxAXZWVX1waA5oi/2nlheOLBGbbih6Odobt79u+OluPBwB6lze/uDSGutvwyf2SjXXVcbskGeeT//vBJOPcdMT7kowjSU/08DOtBclypcSmiFg27Vj2PZLePcm3/kTSFZL+TK1I+jNJF0n6bFfFAjW0/Z3DycY6/pyzk4zzT5d+I8k4h//sD5KMI0latbLrH+kiv5KjEQKaJNGTmSPi6Dz72f5bSavSHBXAQOvDk+XzoBECGmQmPlHZXhQRo9nLj0t6su8HBdB4nBECUMzMrRz9FdsHZUd7QdIfzshRATRXiSvf0wgBjTEzzxKLiFP6fhAAA6a8ZyFy1xjQJBGdNwCoojz5lSPDsrtZN9rOddmeRghoipA81nkDgMrJmV85M+waScfmPTSXxoAm4YwPgLpKlF8R8YDtpXn3pxECmoQ+CEBd5c+vhbbbF3UaioihXg9LIwQ0iMe49gWgnrrIr46LwnaDRghoilBpC5IBQCEl5heNENAQVpS2IBkAFFFmfnHXGNAk3D4PoK7S3T5/vaSHJO1ne8T2adPtzxkhoElodADUVbq7xpZ3sz+NENAUzBECUFfMEQKQAneNAairsvKLRghoDOYAAair8vKLRghoihCNEIB6KjG/aISAJuHKGIC6Yo4Q0J0NR++ZZJybjnhfknH+36W7JxlHknRSbz/GOkJAPex00+ok4xz+sz9IMs76/5iwHVjV24+VlV80QkCT0AgBqCsaIQCFREjbuDYGoIZKzC8aIaBJOCMEoK44IwSgMBohAHVV1WeN2b7a9kbbT7a9t5vtu20/m/26a3/LBNBRSBqLztuAIcOAGsibX33IsDwPXb1G0rET3jtf0r0Rsa+ke7PXAEoVUox13gqyfZLttbbHbC+b8L0v2X7O9jO2jyl8sDSuERkGVFzO/EqQYRN1bIQi4gFJr014+0RJ12ZfXyvpY2nLAtC1UGuyYaetuCcl/bakB9rftL2/pJMl/ZpajcfltmelOGARZBhQA3nzqw8TqnudI7RnRIxKUkSM2t5jqh1tr5C0QpLm7MTZZ6CvZuAae0SskyTbE791oqQbIuJNST+0/ZykQyQ91Peiupcrw9rza67mzWB5wACq6hyhoiJiKCKWRcSy2TvO7/fhgMEW0XmTFtoebttWJDr63pJeans9kr1XW+35NUc7lF0O0Gx58qsPzVKvZ4Resb0o+yS1SNLGlEUB6EXukNgUEcum28H2PZLePcm3/iQibp3qxyYvqpLIMKBS6vfQ1dsknSrpwuzXqYIRwEwJSWNprp9HxNE9/NiIpCVtrxdLWp+koPTIMKBKEuZXt/LcPn+9Wtf497M9Yvs0tcLjw7aflfTh7DWAspVwWrnNbZJOtr2D7X0k7Svp4X4eMA8yDKiJql4ai4jlU3zrqMS1AChkZpaot/1xSV+TtLukf7T9eEQcExFrbd8o6SlJWyWdHhHb+l5QB2QYUAc8YgNAUSFFH9bYeMdhIm6RdMsU3/tzSX/e9yIANMsM5ddkaISAJhnAlaMBNERJ+UUjBDQJzxoDUFc1u2sMQNVElHbXBQAUUmJ+zWgj9MarI5ueuPzcf+6w20JJm2aini5QUz61rOmJVEc6KfeeeX6f3tNTDZwR6pvN+tGme2Jlp/ySqvfvoGr1SNSUV+eaVq1Mc6RVufdsXH7NaCMUEbt32sf2cKfF3mYaNeVDTfn0r6ZQbCv9Jq3GypNfUvX+zlWtHoma8hqsmsrLLy6NAU0RYrI0gHoqMb9ohIAmKen2UwAorKT86vtDV3swVHYBk6CmfKgpn77UFJJiLDpu6Luq/Z2rWj0SNeU1MDXlza88GWb7WNvP2H7O9vkd9w8mVwKNsLN3iw/O/kjH/e7e+g9rqjbvAMBgy5tf0vQZZnuWpP+r1qNzRiQ9Iml5RDw11XhcGgMahMnSAOoqUX4dIum5iHhekmzfIOlEtR79MykaIaAhNutHd94TKxfm2LVqtwgDGHBd5JckzbU93PZ6KCLGL9ntLemltu+NSPrAdIPRCAENERHHll0DAPQiYX55suGn+4EqTpYGAADoxYikJW2vF0taP90P0AgBAICmeETSvrb3sb29pJMl3TbdD3BpDAAANEJEbLV9hqQ7Jc2SdHVErJ3uZ7h9HgAADCwujQEAgIFFIwQAAAYWjRAAABhYNEIAAGBg0QgBAICBRSMEAAAGFo0QAAAYWP8fgBF4mFNC0tYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.sparse as sp\n",
    "def assemble_global(X):\n",
    "    nidx,le = X\n",
    "    N = le.shape[0]\n",
    "    K = sp.lil_matrix((N+1,N+1),dtype='float')\n",
    "    M = sp.lil_matrix((N+1,N+1),dtype='float')\n",
    "    Ke = Kel(le)\n",
    "    Me = Mel(le)\n",
    "    for i in range(N):\n",
    "        K[np.ix_(nidx[i],nidx[i])] += Ke[i]\n",
    "        M[np.ix_(nidx[i],nidx[i])] += Me[i]\n",
    "    return K,M\n",
    "\n",
    "# example with 10 finite elements\n",
    "K,M = assemble_global(get_element_information(generate1D(10,1.0,0.1)))        \n",
    "fig, axarr = plt.subplots(1,2,figsize=(10,4))    \n",
    "msk = axarr[0].matshow(K.toarray()) \n",
    "fig.colorbar(msk,ax=axarr[0])\n",
    "msm = axarr[1].matshow(M.toarray()) \n",
    "fig.colorbar(msm,ax=axarr[1])\n",
    "K,M    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note, that both matrices are sparse and banded. The latter is not necessarily the case if the FE model has a different topology. However, the matrices columns and/or rows can be switched to get matrix where the non-zero elements concentrate around the main diagonal (form a band). This property can be of advantage for the numerical solution of the equations that arise in FE analysis.\n",
    "\n",
    "#### Modal extraction (numerical modal  analysis)\n",
    "\n",
    "Now that we have the global stiffness and mass matrices, we can compute the eigenfrequencies of the pipe. We assume both ends of the pipe to be rigidly terminated. Thus, all elements of the rhs vector are zero:\n",
    "\\begin{equation}\n",
    "\\mathbf{K}\\mathbf{p}-\n",
    "\\omega^2 \\mathbf{M} \\mathbf{p} = 0\n",
    "\\end{equation}\n",
    "This is equivalent to the (generalized) eigenvalue problem\n",
    "\\begin{equation}\n",
    "\\mathbf{K}\\mathbf{p} =\n",
    "\\omega^2 \\mathbf{M} \\mathbf{p},\n",
    "\\end{equation}\n",
    "where $\\omega^2$ is the eigenvalue and $\\mathbf p$ the eigenvector. Generally we can expect to get up to $N+1$ pairs of eigenvalue and eigenvector.\n",
    "\n",
    "Let us now see the result for one case with $N=10$ identical elements and $l=1$m. The speed of sound is assumed to be 344 m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eigenfrequencies: [6.73236948e-06 1.72708167e+02 3.49682886e+02 5.35244046e+02\n",
      " 7.33625330e+02 9.48285700e+02 1.17993265e+03 1.42200037e+03]\n"
     ]
    }
   ],
   "source": [
    "from scipy.sparse.linalg import eigsh\n",
    "from scipy.linalg import eig\n",
    "x = generate1D(10,1.0,0.0)\n",
    "K,M = assemble_global(get_element_information(x))\n",
    "om2, evec = eigsh(K,M=M,sigma=1,k=8)\n",
    "freq =(om2**0.5)/2/np.pi\n",
    "print(\"eigenfrequencies:\", freq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correct values can be computed from\n",
    "\\begin{equation}\n",
    "f_n = n\\frac{c}{2l}\\qquad p_n(x)=p_{0n}\\cos(\\frac{\\pi nx}{l})\n",
    "\\end{equation}\n",
    "and used for comparison with the values from FEM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# N correct results\n",
    "def correct(N,l,c=344):\n",
    "    xn = np.linspace(0,l,100) # to discretize the correct result\n",
    "    pn = np.cos(np.pi*xn[:,np.newaxis]/l*np.arange(N)[np.newaxis])\n",
    "    fn = np.arange(N)*c/2/l\n",
    "    return fn, pn.T, xn\n",
    "# compare first six results\n",
    "fn,pn,xn = correct(6,1)\n",
    "pfem  = evec.T\n",
    "fig, axarr = plt.subplots(2,3,figsize=(10,5))\n",
    "for i in range(6):\n",
    "    axarr.flat[i].plot(xn,pn[i])\n",
    "    axarr.flat[i].set_title('%.1f Hz vs %.1f Hz' % (fn[i],freq[i]))\n",
    "    axarr.flat[i].plot(x,pfem[i]/pfem[i,0])    \n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously the error increases with frequency. As the wavelength decreases with frequency and the element size is the same for all frequencies, it is also true that the error becomes small if we have more elements per wavelength. If we define the error for the eigenfrequency as\n",
    "\\begin{equation}\n",
    "\\epsilon = \\frac{\\left|f_{FEM}-f_n \\right|}{f_n}\n",
    "\\end{equation}\n",
    "we can plot this error over the number of elements per wavelength. This time we use 100 elements to get more data that we can plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = generate1D(100,1.0,0.0)\n",
    "K,M = assemble_global(get_element_information(x))\n",
    "om2, evec = eigsh(K,M=M,sigma=1,k=99)\n",
    "freq =(om2[1:]**0.5)/2/np.pi # to avoid zero freq.\n",
    "fn = np.arange(1,99)*172\n",
    "lambda_ = 344/fn\n",
    "el_per_lambda = lambda_*100/1.0\n",
    "error = np.abs(freq-fn)/fn\n",
    "plt.loglog(el_per_lambda,error)\n",
    "plt.grid(True,'both')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From about six elements per wavelength, the error becomes less than 5%. Therefore, a rule of thumb, that is often used, says that elements should not be larger than 1/6 of the wavelength."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are interested, you could try and repeat the last three steps but this time with elements of somewhat different size, e.g. setting the randomness in _generate1D_ to 0.1 ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Harmonic analysis - direct frequency response\n",
    "Now we assume that on one end of tube, a loudspeaker is mounted that excites the fluid with a harmonic acceleration that has a constant magnitude. This means that the first entry in the right hand side $\\mathbf F$ of the equation is nonzero and the equation can be solved for any given frequency $\\omega$:\n",
    "\\begin{equation}\n",
    "\\left(\\mathbf{K}-\n",
    "\\omega^2 \\mathbf{M}\\right) \\mathbf{p} = \\mathbf{F}\n",
    "\\end{equation}\n",
    "In our example, we solve for frequencies from 100 Hz to 800 Hz in steps of 5 Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.sparse.linalg import spsolve\n",
    "x = generate1D(20,1.0,0.0) # 20 elements\n",
    "K,M = assemble_global(get_element_information(x))\n",
    "pl = [] #list of sound pressures to be filled with the results\n",
    "F = np.zeros_like(x)\n",
    "F[0] = 1.0\n",
    "freqs = np.arange(100,801,5)\n",
    "for f in freqs: # loop over all frequencies\n",
    "    A = K-(2*np.pi*f)**2 * M\n",
    "    p = spsolve(A,F)\n",
    "    pl.append(p[6])# store results at node 6\n",
    "pl = np.asarray(pl)\n",
    "plt.plot(freqs,20*np.log10(np.abs(pl)/2e-5))\n",
    "plt.title('SPL at node 6 (x=%.1f)' % x[6]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### License\n",
    "\n",
    "This notebook is an [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use it for your own purposes. The text and the images are licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), and any code under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: Ennes Sarradj, Numerical Acoustics: Finite Elements: Global Matrices Pipe Example, 2019."
   ]
  }
 ],
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