{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Post processing and visualization\n",
"\n",
"\n",
"\n",
"*Figure 1*: Heat flux computed from the solution to the heat equation on\n",
"the unit square, see previous example: Heat equation."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Introduction\n",
"\n",
"After running a simulation, we usually want to postprocess and visualize the results in\n",
"different ways. Ferrite provides several tools to facilitate these tasks:\n",
"\n",
" - L2 projection of (discrete) data onto FE interpolations using the `L2Projector`\n",
" - Evalutation of fields (solutions, projections, etc) at arbitrary, user-defined, points\n",
" using the `PointEvalHandler`\n",
" - Builtin functionality for exporting data (solutions, cell data, projections, etc) to\n",
" the VTK format\n",
" - [Makie.jl](https://docs.makie.org/) based plotting using\n",
" [FerriteViz.jl](https://ferrite-fem.github.io/FerriteViz.jl/)\n",
"\n",
"This how-to demonstrates the VTK export, the `L2Projector` for projecting discrete\n",
"quadrature point data onto a continuous FE interpolation, and the `PointEvalHandler` for\n",
"evaluating the FE solution, and the projection, along a user-defined cut line through the\n",
"domain."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"> **Custom visualization**\n",
">\n",
"> A common assumption is that the numbering of degrees of freedom matche the numbering\n",
"> of the nodes in the grid. This is *NOT* the case in Ferrite. If the available tools\n",
"> don't suit your needs and you decide to \"roll your own\" visualization you need to be\n",
"> aware of this and take it into account. For the specific case of evaluating the\n",
"> solution at the grid nodes you can use `evaluate_at_grid_nodes`.\n",
"\n",
"This example continues from the Heat equation example, where the temperature field was\n",
"determined on a square domain. In this example, we first compute the heat flux in each\n",
"integration point (based on the solved temperature field) and then we do an L2-projection\n",
"of the fluxes to the nodes of the mesh. By doing this, we can more easily visualize\n",
"integration points quantities. Finally, we visualize the temperature field and the heat fluxes along a cut-line.\n",
"\n",
"The L2-projection is defined as follows: Find projection $q(\\boldsymbol{x}) \\in U_h(\\Omega)$ such that\n",
"$$\n",
"\\int v q \\ \\mathrm{d}\\Omega = \\int v d \\ \\mathrm{d}\\Omega \\quad \\forall v \\in U_h(\\Omega),\n",
"$$\n",
"where $d$ is the quadrature data to project. Since the flux is a vector the projection function\n",
"will be solved with multiple right hand sides, e.g. with $d = q_x$ and $d = q_y$ for this 2D problem.\n",
"In this example, we use standard Lagrange interpolations, and the finite element space $U_h$ is then\n",
"a subset of the $H^1$ space (continuous functions).\n",
"\n",
"Ferrite has functionality for doing much of this automatically, as displayed in the code below.\n",
"In particular `L2Projector` for assembling the left hand side, and\n",
"`project` for assembling the right hand sides and solving for the projection."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Implementation\n",
"\n",
"Start by simply running the Heat equation example to solve the problem"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"include(\"../tutorials/heat_equation.jl\");"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Next we define a function that computes the heat flux for each integration point in the domain.\n",
"Fourier's law is adopted, where the conductivity tensor is assumed to be isotropic with unit\n",
"conductivity $\\lambda = 1 ⇒ q = - \\nabla u$, where $u$ is the temperature."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "compute_heat_fluxes (generic function with 1 method)"
},
"metadata": {},
"execution_count": 2
}
],
"cell_type": "code",
"source": [
"function compute_heat_fluxes(cellvalues::CellValues, dh::DofHandler, a::AbstractVector{T}) where {T}\n",
"\n",
" n = getnbasefunctions(cellvalues)\n",
" cell_dofs = zeros(Int, n)\n",
" nqp = getnquadpoints(cellvalues)\n",
"\n",
" # Allocate storage for the fluxes to store\n",
" q = [Vec{2, T}[] for _ in 1:getncells(dh.grid)]\n",
"\n",
" for (cell_num, cell) in enumerate(CellIterator(dh))\n",
" q_cell = q[cell_num]\n",
" celldofs!(cell_dofs, dh, cell_num)\n",
" aᵉ = a[cell_dofs]\n",
" reinit!(cellvalues, cell)\n",
"\n",
" for q_point in 1:nqp\n",
" q_qp = - function_gradient(cellvalues, q_point, aᵉ)\n",
" push!(q_cell, q_qp)\n",
" end\n",
" end\n",
" return q\n",
"end"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Now call the function to get all the fluxes."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"q_gp = compute_heat_fluxes(cellvalues, dh, u);"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"Next, create an `L2Projector` using the same interpolation as was used to approximate the\n",
"temperature field. On instantiation, the projector assembles the coefficient matrix `M` and\n",
"computes the Cholesky factorization of it. By doing so, the projector can be reused without\n",
"having to invert `M` every time."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"projector = L2Projector(ip, grid);"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"Project the integration point values to the nodal values"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"q_projected = project(projector, q_gp, qr);"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"## Exporting to VTK\n",
"To visualize the heat flux, we export the projected field `q_projected`\n",
"to a VTK-file, which can be viewed in e.g. [ParaView](https://www.paraview.org/).\n",
"The result is also visualized in *Figure 1*."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"VTKGridFile(\"heat_equation_flux\", grid) do vtk\n",
" write_projection(vtk, projector, q_projected, \"q\")\n",
"end;"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"## Point evaluation\n",
"\n",
"\n",
"*Figure 2*: Visualization of the cut line where we want to compute\n",
"the temperature and heat flux."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Consider a cut-line through the domain like the black line in *Figure 2* above.\n",
"We will evaluate the temperature and the heat flux distribution along a horizontal line."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"points = [Vec((x, 0.75)) for x in range(-1.0, 1.0, length = 101)];"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"First, we need to generate a `PointEvalHandler`. This will find and store the cells\n",
"containing the input points."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"ph = PointEvalHandler(grid, points);"
],
"metadata": {},
"execution_count": 8
},
{
"cell_type": "markdown",
"source": [
"After the L2-Projection, the heat fluxes `q_projected` are stored in the DoF-ordering\n",
"determined by the projector's internal DoFHandler, so to evaluate the flux `q` at our points\n",
"we give the `PointEvalHandler`, the `L2Projector` and the values `q_projected`."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"q_points = evaluate_at_points(ph, projector, q_projected);"
],
"metadata": {},
"execution_count": 9
},
{
"cell_type": "markdown",
"source": [
"We can also extract the field values, here the temperature, right away from the result\n",
"vector of the simulation, that is stored in `u`. These values are stored in the order of\n",
"our initial DofHandler so the input is not the `PointEvalHandler`, the original `DofHandler`,\n",
"the dof-vector `u`, and (optionally for single-field problems) the name of the field.\n",
"From the `L2Projection`, the values are stored in the order of the degrees of freedom."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"u_points = evaluate_at_points(ph, dh, u, :u);"
],
"metadata": {},
"execution_count": 10
},
{
"cell_type": "markdown",
"source": [
"Now, we can plot the temperature and flux values with the help of any plotting library, e.g. Plots.jl.\n",
"To do this, we need to import the package:"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"import Plots"
],
"metadata": {},
"execution_count": 11
},
{
"cell_type": "markdown",
"source": [
"Firstly, we are going to plot the temperature values along the given line."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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"</svg>\n"
]
},
"metadata": {},
"execution_count": 12
}
],
"cell_type": "code",
"source": [
"Plots.plot(getindex.(points, 1), u_points, xlabel = \"x (coordinate)\", ylabel = \"u (temperature)\", label = nothing)"
],
"metadata": {},
"execution_count": 12
},
{
"cell_type": "markdown",
"source": [
"*Figure 3*: Temperature along the cut line from *Figure 2*."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Secondly, the horizontal heat flux (i.e. the first component of the heat flux vector) is plotted."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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]
},
"metadata": {},
"execution_count": 13
}
],
"cell_type": "code",
"source": [
"Plots.plot(getindex.(points, 1), getindex.(q_points, 1), xlabel = \"x (coordinate)\", ylabel = \"q_x (flux in x-direction)\", label = nothing)"
],
"metadata": {},
"execution_count": 13
},
{
"cell_type": "markdown",
"source": [
"*Figure 4*: $x$-component of the flux along the cut line from *Figure 2*."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"---\n",
"\n",
"*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
],
"metadata": {}
}
],
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