topFiniteDiff.ipynb

{
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  {
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   "source": [
    "using SparseArrays\n",
    "using LinearAlgebra\n",
    "using Plots\n",
    "using Statistics\n",
    "using SuiteSparse\n",
    "using FiniteDifferences\n",
    "E0 = 1;\n",
    "Emin = 1e-9;\n",
    "nu = 0.3;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "finite_difference_jacobian (generic function with 6 methods)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using FiniteDiff\n",
    "FiniteDiff.finite_difference_jacobian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "topFD (generic function with 5 methods)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function topFD(nelx,nely,objectif ,volfrac = 0.4 ,penal = 3,rmin = 2.5 ,ft = 1)\n",
    "        \n",
    "    A11 = [12  3 -6 -3;  3 12  3  0; -6  3 12 -3; -3  0 -3 12]\n",
    "    A12 = [-6 -3  0  3; -3 -6 -3 -6;  0 -3 -6  3;  3 -6  3 -6]\n",
    "    B11 = [-4  3 -2  9;  3 -4 -9  4; -2 -9 -4 -3;  9  4 -3 -4]\n",
    "    B12 = [ 2 -3  4 -9; -3  2  9 -2;  4  9  2  3; -9 -2  3  2]\n",
    "    KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11])\n",
    "\n",
    "    nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx); #number of the nodes in columns\n",
    "    edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1) ;#1st dof of each element (x top left)\n",
    "    edofMat = zeros(nelx*nely, 8); #every line i contains the 8 dof of the ith element\n",
    "    noeudsvoisins = [0 1 2*nely.+[2 3 0 1] -2 -1];\n",
    "    for i = 1:8\n",
    "        for j = 1:nelx*nely\n",
    "            edofMat[j,i]= edofVec[j]+ noeudsvoisins[i] ;\n",
    "        end\n",
    "    end\n",
    "    #maillage\n",
    "    iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1);# line to build  K\n",
    "    jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1);# columns\n",
    "    #F = spzeros(2*(nely+1)*(nelx+1),1); F[2,1] = -1;   impossible to solve with F sparse in Julia\n",
    "    F = zeros(2*(nely+1)*(nelx+1),1); F[2,1] = -1; \n",
    "    U = zeros(2*(nely+1)*(nelx+1),1);\n",
    "    fixeddofs = union(1:2:2*(nely+1),[2*(nelx+1)*(nely+1)]);\n",
    "    alldofs = 1:2*(nely+1)*(nelx+1);\n",
    "    freedofs = setdiff(alldofs,fixeddofs);\n",
    "    #filtering is linear + chain's rule -> matricial opration with operator H\n",
    "    iH = ones(nelx*nely*(2*(convert(Int64,ceil(rmin)-1))+1)^2);#lines H\n",
    "    jH = ones(size(iH));# columns\n",
    "    sH = zeros(size(iH));# values\n",
    "    k = 0;\n",
    "    for i1 = 1:nelx\n",
    "        for j1 = 1:nely\n",
    "            e1 = (i1-1)*nely+j1;\n",
    "            for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)\n",
    "                for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)\n",
    "                    e2 = (i2-1)*nely+j2;\n",
    "                    k = k+1;\n",
    "                    iH[k] = e1;\n",
    "                    jH[k] = e2;\n",
    "                    sH[k] = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2));\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    H = sparse(iH,jH,sH);# matrix of the Hei\n",
    "    Hs = [sum(H[i,:]) for i = 1:(size(H)[1])];# sum of the Hei for e fixed -> coeffs used to divide in the filter\n",
    "    #variables\n",
    "    x = volfrac*ones(nely,nelx);\n",
    "    xPhys = x;#new variable for the density filter\n",
    "    loop = 0;\n",
    "    change = 1;\n",
    "    cValues = []\n",
    "    while change > 0.01\n",
    "        loop = loop + 1;\n",
    "        \n",
    "        sK = [j*((i+Emin)^penal) for i in ((E0-Emin)*xPhys[:]') for j in KE[:] ];#new values EF\n",
    "        K = sparse(iK[:],jK[:],sK); K = (K+K')/2;# force to be symmetric\n",
    "        KK = cholesky(K[freedofs,freedofs]);\n",
    "        U[freedofs] = KK\\F[freedofs];\n",
    "        \n",
    "        # analyse, objective function \n",
    "        edM = [convert(Int64,i) for i in edofMat] ;#to index by int\n",
    "        mat = (U[edM]*KE).*U[edM];\n",
    "        ce = reshape([sum(mat[i,:]) for i = 1:(size(mat)[1])],nely,nelx);\n",
    "\n",
    "        #new\n",
    "        c = objectif(xPhys,ce) #sum(sum((Emin*ones(size(xPhys)).+(xPhys.^penal)*(E0-Emin)).*ce));\n",
    "        push!(cValues,c)\n",
    "        \n",
    "\n",
    "        #dc = central_fdm(5,1)(x -> objectif(x,ce), xPhys) \n",
    "        dc = -FiniteDiff.finite_difference_gradient(x -> objectif(x,ce), xPhys)\n",
    "\n",
    "        dv = ones(nely,nelx);\n",
    "        \n",
    "        #filtering : maybe other filters are needed if the objective function is not the sensitivity\n",
    "        if ft == 1\n",
    "            dc[:] = H*(x[:].*dc[:])./Hs./max(1e-3,maximum(x[:]));\n",
    "        elseif ft == 2\n",
    "            dc[:] = H*(dc[:]./Hs);\n",
    "            dv[:] = H*(dv[:]./Hs);\n",
    "        end\n",
    "        #Lagrangian multiplicators research, upload of the density x\n",
    "        l1 = 0; l2 = 1e9; move = 0.2;\n",
    "        xnew = zeros(nely, nelx);\n",
    "        while (l2-l1)/(l1+l2) > 1e-3\n",
    "            lmid = 0.5*(l2+l1);\n",
    "            RacBe = sqrt.(-dc./dv/lmid) ;\n",
    "            XB = x.*RacBe ;\n",
    "            for i = 1:nelx\n",
    "                for j = 1:nely\n",
    "                    xji = x[j,i];\n",
    "                    xnew[j,i]= max(0.001,max(xji-move,min(1,min(xji+move,XB[j,i]))));\n",
    "                end\n",
    "            end  \n",
    "            if ft == 1\n",
    "                xPhys = xnew;\n",
    "            elseif ft == 2 # if we chose the density filter\n",
    "                xPhys[:] = (H*xnew[:])./Hs;\n",
    "            end\n",
    "            if sum(xPhys[:]) > volfrac*nelx*nely\n",
    "                l1 = lmid;\n",
    "            else \n",
    "                l2 = lmid; \n",
    "            end\n",
    "        end\n",
    "        change = maximum(abs.(x-xnew));\n",
    "        x = xnew;\n",
    "        println(\"loop = \", loop, \"Change = \", change ,\" c = \", c , \" densité struct = \", mean(x) )\n",
    "        if loop == 25\n",
    "            return heatmap(x), loop, cValues\n",
    "        end\n",
    "    end\n",
    "    return heatmap(x ), loop , cValues\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loop = 1Change = 0.2 c = 240.55295821333357 densité struct = 0.49985205408529515\n",
      "loop = 2Change = 0.20000000000000007 c = 142.29012811626535 densité struct = 0.49995425634059665\n",
      "loop = 3Change = 0.20000000000000007 c = 101.2904274436662 densité struct = 0.5002055990426127\n",
      "loop = 4Change = 0.20000000000000007 c = 80.66559466002106 densité struct = 0.5000701664445731\n",
      "loop = 5Change = 0.20000000000000007 c = 70.50380077833101 densité struct = 0.4999593510384339\n",
      "loop = 6Change = 0.20000000000000007 c = 62.76373410430314 densité struct = 0.5001263850754951\n",
      "loop = 7Change = 0.20000000000000007 c = 57.56945696626541 densité struct = 0.5001217270840642\n",
      "loop = 8Change = 0.20000000000000007 c = 53.32531773669797 densité struct = 0.49999885198096816\n",
      "loop = 9Change = 0.20000000000000007 c = 50.25849153006335 densité struct = 0.5000234491491705\n",
      "loop = 10Change = 0.20000000000000007 c = 48.810735379919066 densité struct = 0.4999699894660608\n",
      "loop = 11Change = 0.20000000000000007 c = 48.1194088739407 densité struct = 0.49999081745384777\n",
      "loop = 12Change = 0.19999999999999996 c = 47.70674372180917 densité struct = 0.4999929488048652\n",
      "loop = 13Change = 0.19999999999999996 c = 47.47118108646299 densité struct = 0.5000210418173404\n",
      "loop = 14Change = 0.20000000000000007 c = 47.34348568960219 densité struct = 0.49999779468003813\n",
      "loop = 15Change = 0.20000000000000007 c = 47.23921451317546 densité struct = 0.5000143109745661\n",
      "loop = 16Change = 0.20000000000000007 c = 47.1279737927421 densité struct = 0.4999847218865917\n",
      "loop = 17Change = 0.20000000000000007 c = 46.99585047321044 densité struct = 0.5000125224959064\n",
      "loop = 18Change = 0.20000000000000007 c = 46.7967007201364 densité struct = 0.500008328552291\n",
      "loop = 19Change = 0.18506657538666071 c = 46.53871601377493 densité struct = 0.4999995570801443\n",
      "loop = 20Change = 0.19999999999999996 c = 46.304486446611065 densité struct = 0.5000122816861852\n",
      "loop = 21Change = 0.14493077289916978 c = 46.234969316392935 densité struct = 0.4999942754916024\n",
      "loop = 22Change = 0.16818798437036797 c = 46.18414432816459 densité struct = 0.5000030431248687\n",
      "loop = 23Change = 0.15922827976834586 c = 46.137793947707465 densité struct = 0.49999559646772507\n",
      "loop = 24Change = 0.17029346386485533 c = 46.09535345946886 densité struct = 0.49999868398891223\n",
      "loop = 25Change = 0.19999999999999996 c = 46.05217117865928 densité struct = 0.500002506987699\n"
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2268.76, 60.8953)\" x=\"2268.76\" y=\"60.8953\">1.0</text>\n",
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       "<polyline clip-path=\"url(#clip9400)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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       "  2256.76,479.746 2232.76,479.746 2232.76,335.579 2256.76,335.579 2232.76,335.579 2232.76,191.411 2256.76,191.411 2232.76,191.411 2232.76,47.2441 2256.76,47.2441 \n",
       "  2232.76,47.2441 \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "penal = 3\n",
    "sensi( x, ce)= sum(sum((Emin*ones(size(x)).+(x.^penal)*(E0-Emin)).*ce));# example of the sensitivity to see if the results do match\n",
    "\n",
    "\n",
    "x,l,values= topFD(100,100,sensi ,0.5,3,2)\n",
    "\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25-element Array{Any,1}:\n",
       " 240.55295821333357\n",
       " 142.29012811626535\n",
       " 101.2904274436662\n",
       "  80.66559466002106\n",
       "  70.50380077833101\n",
       "  62.76373410430314\n",
       "  57.56945696626541\n",
       "  53.32531773669797\n",
       "  50.25849153006335\n",
       "  48.810735379919066\n",
       "  48.1194088739407\n",
       "  47.70674372180917\n",
       "  47.47118108646299\n",
       "  47.34348568960219\n",
       "  47.23921451317546\n",
       "  47.1279737927421\n",
       "  46.99585047321044\n",
       "  46.7967007201364\n",
       "  46.53871601377493\n",
       "  46.304486446611065\n",
       "  46.234969316392935\n",
       "  46.18414432816459\n",
       "  46.137793947707465\n",
       "  46.09535345946886\n",
       "  46.05217117865928"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loop = 1Change = 0.2 c = 181.02944558470028 densité struct = 0.49995144878779085\n",
      "loop = 2Change = 0.20000000000000007 c = 87.70747377684549 densité struct = 0.5001614594868655\n",
      "loop = 3Change = 0.20000000000000007 c = 51.26685651882993 densité struct = 0.49987273232035623\n",
      "loop = 4Change = 0.20000000000000007 c = 37.10721159727915 densité struct = 0.5000877844104062\n",
      "loop = 5Change = 0.20000000000000007 c = 33.47226983913973 densité struct = 0.5000324695599102\n",
      "loop = 6Change = 0.20000000000000007 c = 31.701271772493342 densité struct = 0.5000380824619575\n",
      "loop = 7Change = 0.20000000000000007 c = 30.680779001468615 densité struct = 0.49997259945477746\n",
      "loop = 8Change = 0.20000000000000007 c = 30.056612345002414 densité struct = 0.49999482642033216\n",
      "loop = 9Change = 0.20000000000000007 c = 29.697007825654886 densité struct = 0.4999901098995677\n",
      "loop = 10Change = 0.20000000000000007 c = 29.509405338009124 densité struct = 0.499996767948452\n",
      "loop = 11Change = 0.20000000000000007 c = 29.383561353119056 densité struct = 0.5000018557397305\n",
      "loop = 12Change = 0.20000000000000007 c = 29.29202082961404 densité struct = 0.5000056018701495\n",
      "loop = 13Change = 0.20000000000000007 c = 29.242405074895736 densité struct = 0.49999839735472196\n",
      "loop = 14Change = 0.20000000000000007 c = 29.207364277585675 densité struct = 0.5000011946106242\n",
      "loop = 15Change = 0.20000000000000007 c = 29.187038349280073 densité struct = 0.5000010568890492\n",
      "loop = 16Change = 0.20000000000000007 c = 29.176465503915487 densité struct = 0.49999900433590294\n",
      "loop = 17Change = 0.19999999999999996 c = 29.168046285463177 densité struct = 0.5000009118309621\n",
      "loop = 18Change = 0.19999999999999996 c = 29.159652740717632 densité struct = 0.5000036463264281\n",
      "loop = 19Change = 0.20000000000000007 c = 29.15149758003836 densité struct = 0.4999997716669185\n",
      "loop = 20Change = 0.20000000000000007 c = 29.144847968579956 densité struct = 0.5000036970530275\n",
      "loop = 21Change = 0.20000000000000007 c = 29.13885151473317 densité struct = 0.5000031427584027\n",
      "loop = 22Change = 0.20000000000000007 c = 29.133919109470277 densité struct = 0.5000032437017103\n",
      "loop = 23Change = 0.19999999999999996 c = 29.129077257989596 densité struct = 0.5000028236402674\n",
      "loop = 24Change = 0.20000000000000007 c = 29.123976203995678 densité struct = 0.4999958847695187\n",
      "loop = 25Change = 0.20000000000000007 c = 29.11866208203476 densité struct = 0.5000009010643596\n",
      "116.370186 seconds (106.86 M allocations: 192.019 GiB, 9.99% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(Plot{Plots.GRBackend() n=1}, 25, Any[181.02944558470028, 87.70747377684549, 51.26685651882993, 37.10721159727915, 33.47226983913973, 31.701271772493342, 30.680779001468615, 30.056612345002414, 29.697007825654886, 29.509405338009124  …  29.176465503915487, 29.168046285463177, 29.159652740717632, 29.15149758003836, 29.144847968579956, 29.13885151473317, 29.133919109470277, 29.129077257989596, 29.123976203995678, 29.11866208203476])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time x,l,values= topFD(100,100,sensi ,0.5,3,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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