JuliaFEM.jl/notebooks/2015-06-14-data-structures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data structures\n",
    "\n",
    "**Author(s)**: Jukka Aho\n",
    "\n",
    "**Abstract**: Description of data structures.\n",
    "\n",
    "## Revision history\n",
    "\n",
    "### 2015-06-14\n",
    "- Initial version.\n",
    "\n",
    "### 2015-09-25\n",
    "- Complete rewrite. The main ideas proposed in earlier version didn't work."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data fields on elements\n",
    "\n",
    "Typical element structure so far:\n",
    "\n",
    "    type MySuperElement <: Element\n",
    "        connectivity :: Array{Int, 1}  # describes how dofs of this element is connected to another elements\n",
    "        fields :: ???\n",
    "    end\n",
    "\n",
    "- Fields must be interpolable, in space $\\mathbb{C}^n \\times \\mathbb{R}$, i.e. $f(\\boldsymbol{\\xi}, t) = \\sum_i \\phi_i(\\boldsymbol{\\xi}) f_i(t) = \\sum_i \\phi_i(\\boldsymbol{\\xi}) \\sum_j \\varphi_j(t) f_{ij}$, where $f_{ij}$ is scalar, tensor or vector defined in element area $e$ by some basis functions $\\phi(\\boldsymbol{\\xi})$ and $\\varphi(t)$. Parameter $t$ is normally considered as \"time\" and $\\xi$ is dimensionless coordinate. Parameter $t$ has not necessarily to be time, it could be for example angle $\\alpha \\in [-2\\pi, 2\\pi]$ or similar.\n",
    "- We store mainly three fields, scalar field, vector field, tensor field. Field may or may not be dependent from parameters $\\xi$ or $t$.\n",
    "- $t$ is discretized to several steps $\\{t_0, t_1, \\ldots, t_n\\}$. Each discrete time $t_i$ may contain several iterations until convergence. We want to save and get access to all of this data if needed.\n",
    "- So in practice we have a set of fields $f(\\boldsymbol{\\xi})$ over time domain $t$. Typically some fields, like Geometry, is introduced only in time $t_0$. Some other fields, like boundary load, may be \"active\" only on some time $\\hat{t} \\subset t$. Some care must be taken of how to extrapolate field variables.\n",
    "- In the simplest case (simple nonlinear quasistatic analysis), we have for instance $t \\in [0, 1]$ where boundary conditions are set in $t_0$ and load is set in $t_1$. We may use adaptive strategies to shorten time if convergence issues araises."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Without time domain\n",
    "\n",
    "Without time we have something like this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using ForwardDiff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "type Field{T}\n",
    "    time :: Float64\n",
    "    increment :: Int64\n",
    "    values :: Array{T, 1}\n",
    "end\n",
    "\n",
    "type Basis\n",
    "    basis :: Function\n",
    "    dbasisdxi :: Function\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "* (generic function with 158 methods)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Field(time, values)\n",
    "    Field(time, 1, values)\n",
    "end\n",
    "function Basis(basis)\n",
    "    Basis(basis, ForwardDiff.jacobian(basis))\n",
    "end\n",
    "call(b::Basis, xi) = b.basis(xi)\n",
    "Base.(:*)(x::Array{Float64, 1}, f::Field) = sum(x .* f.values)\n",
    "Base.(:*)(b::Basis, f::Field) = (x) -> b(x)*f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can do something like this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field{Float64}(0.0,1,[0.0,1.0])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = Basis((ξ) -> [0.5*(1.0-ξ[1]), 0.5*(1.0+ξ[1])])\n",
    "u = Field(0.0, [0.0, 1.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N([0.0])*u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(N*u)([0.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extending to time domain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we want to interpolate over time domain. Maybe something like this would do the job:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field{Float64}(0.0,1,[0.0,3.0])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Base.(:*)(k::Float64, f::Field) = Field(f.time, k*f.values)\n",
    "u1 = Field(0.0, [0.0, 1.0])\n",
    "3.0*u1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field{Float64}(0.0,1,[1.0,3.0])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Base.(:+)(f1::Field, f2::Field)\n",
    "    @assert(f1.time == f2.time, \"Cannot add fields: time mismatch, $(f1.time) != $(f2.time)\")\n",
    "    Field(f1.time, f1.values + f2.values)\n",
    "end\n",
    "u1 = Field(0.0, [0.0, 1.0])\n",
    "u2 = Field(0.0, [1.0, 2.0])\n",
    "u1 + u2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field{Float64}(0.0,1,[0.5,1.5])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u1 = Field(0.0, [0.0, 1.0])\n",
    "u2 = Field(0.0, [1.0, 2.0])\n",
    "\n",
    "t = Basis((t) -> [1-t, t])\n",
    "u = Field[u1, u2]\n",
    "Base.(:*)(x::Array{Float64, 1}, f::Array{Field}) = sum(x .* f)\n",
    "Base.(:*)(b::Basis, f::Array{Field}) = (t) -> b(t)*f\n",
    "(t*u)(0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Semisummary\n",
    "\n",
    "Putting this together so far:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ϕ = Basis((ξ) -> [0.5*(1.0-ξ[1]), 0.5*(1.0+ξ[1])])\n",
    "φ = Basis((t) -> [1-t, t])\n",
    "u1 = Field(0.0, [0.0, 1.0])\n",
    "u2 = Field(0.0, [1.0, 2.0])\n",
    "# interpolate displacement u1 in mid-point ξ=[0.0] on element\n",
    "(ϕ*u1)([0.0]) # => 0.5\n",
    "# interpolate displacement field [u1, u2] in time t=0.5\n",
    "(φ*Field[u1, u2])(0.5) # => Field{Float64}(:displacement,[0.5,1.5])\n",
    "# interpolate displacement in element area ξ and time t\n",
    "d(ξ, t) = (ϕ*(φ*Field[u1, u2])(t))(ξ)\n",
    "d([0.0], 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Makes sense, since deformation from $u_1$ to $u_2$ at $t=0.5$ is $\\begin{bmatrix}0.5 & 1.5\\end{bmatrix}$ and taking the midpoint of this makes exactly $1.0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Towards generalization\n",
    "\n",
    "So at this point we are able to interpolate $u(\\xi)$ in time $t$. This is a set of discrete fields and needs to figure out which fields are needed to interpolate. So we have $u_0, u_1, \\ldots, u_i$ fields. Each time needs to be aware of it's time $t_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Field{"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Return a field in some time t.\n",
    "\"\"\"\n",
    "function call(fields::Array{Field, 1}, t::Float64)\n",
    "    if t <= fields[1].time\n",
    "        return fields[1]\n",
    "    end\n",
    "    if t >= fields[end].time\n",
    "        return fields[end]\n",
    "    end\n",
    "    i = length(fields)\n",
    "    while fields[i].time >= t\n",
    "        i -= 1\n",
    "    end\n",
    "    if fields[i].time == t\n",
    "        return fields[i]\n",
    "    end\n",
    "    #Logging.debug(\"doing linear interpolation between fields $i and $(i+1)\")\n",
    "    f1 = fields[i]\n",
    "    t1 = f1.time\n",
    "    f2 = fields[i+1]\n",
    "    t2 = f2.time\n",
    "    dt = t2 - t1\n",
    "    nw = (t2-t)/dt*f1.values + (t-t1)/dt*f2.values\n",
    "    f = Field(t, nw)\n",
    "    return f\n",
    "end\n",
    "function call(field::Field, t::Float64)\n",
    "    Field(t, field.increment, field.values)\n",
    "end\n",
    "\n",
    "u1 = Field(0.0, [0.0, 0.0])\n",
    "u2 = Field(1.0, [1.0, 2.0])\n",
    "u3 = Field(2.0, [0.5, 1.5])\n",
    "u = Field[u1, u2, u3]\n",
    "for f in [u(-Inf), u(0.0), u(0.5), u(1.0), u(1.5), u(2.0), u(Inf)]\n",
    "    println(f)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Handling of derivatives in multidimensional case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "* (generic function with 163 methods)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "∂(h::Basis) = h.dbasisdxi\n",
    "diff(h::Basis) = h.dbasisdxi\n",
    "derivative(h::Basis) = h.dbasisdxi\n",
    "Base.(:*)(df::Function, fld::Field) = (ξ) -> df(ξ)*fld\n",
    "Base.length(f::Field) = length(f.values)\n",
    "Base.getindex(f::Field, i::Int64) = f.values[i]\n",
    "Base.(:*)(x::Array{Float64, 2}, fld::Field) = sum([fld[i]*x[i,:] for i in 1:length(fld)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: could not import Base.help into PyCall\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Float64}(0.0,1,[0.0,0.0])\n",
      "Field{Float64}(0.0,1,[0.0,0.0])\n",
      "Field{Float64}(0.5,1,[0.5,1.0])\n",
      "Field{Float64}(1.0,1,[1.0,2.0])\n",
      "Field{Float64}(1.5,1,[0.75,1.75])\n",
      "Field{Float64}(2.0,1,[0.5,1.5])\n",
      "Field{Float64}(2.0,1,[0.5,1.5])\n"
     ]
    }
   ],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpolate midpoint of some field in function of time, i.e., construct $x(\\xi, t)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       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"
      ],
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f031d473250>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ϕ = Basis((ξ) -> [0.5*(1.0-ξ[1]), 0.5*(1.0+ξ[1])])\n",
    "u1 = Field(0.0, [0.0, 0.0])\n",
    "u2 = Field(1.0, [1.0, 2.0])\n",
    "u3 = Field(2.0, [0.5, 1.5])\n",
    "u = Field[u1, u2, u3]\n",
    "x(ξ, t) = ϕ(ξ)*u(t)\n",
    "t = linspace(-1.0, 4.0, 200)\n",
    "midpnt = zeros(length(t))\n",
    "for i =1:length(t)\n",
    "    midpnt[i] = x([0.0], t[i])\n",
    "end\n",
    "plot(t, midpnt, \"-k\", label=\"midpoint of some field\")\n",
    "legend()\n",
    "grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multidimensional interpolation $x(\\boldsymbol\\xi, t)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       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"
      ],
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f0326c86e10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-0.5,2.0,0.0,2.0)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = Basis((xi) ->\n",
    "    [(1-xi[1])*(1-xi[2])/4\n",
    "     (1+xi[1])*(1-xi[2])/4\n",
    "     (1+xi[1])*(1+xi[2])/4\n",
    "     (1-xi[1])*(1+xi[2])/4])\n",
    "X = Field(0.0, Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]])\n",
    "u1 = Field(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])\n",
    "u2 = Field(1.0, Vector[[-0.3, 0.2], [0.2, 0.0], [1.0, 0.0], [0.0, 1.0]])\n",
    "u = Field[u1, u2]\n",
    "N = 5\n",
    "x(ξ, t) = h(ξ)*(X(t) + u(t))\n",
    "for t in linspace(0, 1, N)\n",
    "    m = [x([-1, -1], t) x([1, -1], t) x([1, 1], t) x([-1, 1], t) x([-1, -1], t)]\n",
    "    midpnt = x([0, 0], t)\n",
    "    plot(m[1,:][:], m[2,:][:], \"-o\", label=\"t=$t\")\n",
    "    #plot(midpnt[1], midpnt[2], \"ko\")\n",
    "end\n",
    "legend()\n",
    "axis(\"equal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To interpolate field $X$ using basis $h$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.5\n",
       " 0.5"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(h*X)([0.0, 0.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.5\n",
       " 0.5"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h([0.0, 0.0])*X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To interpolate derivatives of field $X$ using basis $h$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 0.5  0.0\n",
       " 0.0  0.5"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(∂(h)*X)([0.0, 0.0])  # ∂(⋅) is equivalent to diff(⋅) and derivative(⋅)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 0.5  0.0\n",
       " 0.0  0.5"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "∂(h)([0.0, 0.0])*X"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.0-dev",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}