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genkuroki/Wave equation on the pentagon Version 3 Part 2.ipynb

Last active May 30, 2021 06:08
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Wave equation on the pentagon Version 3 Part 2
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Wave equation on the pentagon Version 3 Part 2.ipynb
{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@show VERSION\n@time using DifferentialEquations\n@time using Plots\n@time using ProgressMeter\n@time using Parameters\n@time using Fmt",
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": "VERSION = v\"1.7.0-DEV.1129\"\n 8.195601 seconds (18.92 M allocations: 1.416 GiB, 5.15% gc time)\n 3.705994 seconds (7.99 M allocations: 575.859 MiB, 8.32% gc time, 0.58% compilation time)\n 0.008682 seconds (7.40 k allocations: 541.883 KiB)\n 0.000537 seconds (251 allocations: 16.391 KiB)\n 0.005529 seconds (5.58 k allocations: 473.102 KiB)\n",
"name": "stdout"
},
{
"output_type": "stream",
"text": "WARNING: Wrapping `Vararg` directly in UnionAll is deprecated (wrap the tuple instead).\n",
"name": "stderr"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "x ⪅ y = x < y || x ≈ y\n\nfunction isin_ngon(n, R, x, y)\n α = 2π/n\n θ = mod(angle(x + im*y), α)\n r = √(x^2 + y^2) / R\n X, Y = r*cos(θ), r*sin(θ)\n (1 - cos(α))*Y ⪅ sin(α)*(1 - X)\nend\n\nisin_unit_pentagon(x, y) = isin_ngon(5, 1, x, y)\n\nx = -1:0.1:1\ny = -1:0.1:1\nD = isin_unit_pentagon.(x, y')\nheatmap(x, y, D'; colorbar=false, size=(200, 200))",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
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},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "module My\n\nusing Parameters: @unpack\n\nstruct Param{TX, TY, TH, TV, TE, TV_dic}\n x::TX\n y::TY\n h⁻²::TH\n V::TV\n E::TE\n V_dic::TV_dic\nend\n\nBase.length(p::Param) = length(p.V)\nBase.size(p::Param) = (length(p.x), length(p.y))\n\nmystep(x::AbstractVector) = x[2] - x[1]\nmystep(x::StepRangeLen) = step(x)\n\nfunction Param(isin_func, x::AbstractVector, y::AbstractVector)\n @assert mystep(x) == mystep(y)\n h⁻² = 1/mystep(x)^2\n I, J = eachindex(x), eachindex(y)\n D = isin_func.(x, y')\n V = Tuple{Int64, Int64}[]\n E_mat = [Tuple{Int64, Int64}[] for i in I, j in J]\n B_mat = zeros(Int64, length(I), length(J))\n for j in J, i in I\n if D[i, j]\n push!(V, (i, j))\n for q in (-1, 1), p in (-1, 1)\n if i+p in I && j+q in J && D[i+p, j+q]\n push!(E_mat[i, j], (i+p, j+q))\n end\n end\n end\n end\n V_dic = Dict(V[k] => k for k in eachindex(V))\n E = [getindex.(Ref(V_dic), E_mat[V[k]...]) for k in eachindex(V)]\n Param(x, y, h⁻², V, E, V_dic)\nend\n\nfunction vec2mat!(p::Param, u, U)\n @unpack V = p\n for k in eachindex(V)\n U[V[k]...] = u[k]\n end\n U\nend\n \nfunction vec2mat(p::Param, u; default_value=NaN)\n U = fill(eltype(u)(default_value), size(p))\n vec2mat!(p, u, U)\nend\n\nfunction mat2vec!(p::Param, U, u)\n @unpack V_dic = p\n for t in keys(V_dic)\n u[V_dic[t]] = U[t...]\n end\n u\nend\n\nfunction mat2vec(p::Param, U)\n u = similar(eltype(U)[], length(p))\n mat2vec!(p, U, u)\nend\n\nend\n\nx = -1:0.1:1\ny = -1:0.1:1\np = My.Param(isin_unit_pentagon, x, y)\n\n@unpack h⁻², V, E = p\n@show h⁻²\n@show V[50]\n@show E[50]\n@show V[E[50]]\n\nu0 = collect(1.0:length(V))\nU0 = My.vec2mat(p, u0; default_value=0)\n@show My.mat2vec(p, U0) == u0\nU0'",
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": "h⁻² = 99.99999999999999\nV[50] = (7, 7)\nE[50] = [34, 36, 65, 67]\nV[E[50]] = [(6, 6), (8, 6), (6, 8), (8, 8)]\nMy.mat2vec(p, U0) == u0 = true\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "21×21 adjoint(::Matrix{Float64}) with eltype Float64:\n 0.0 0.0 0.0 0.0 0.0 0.0 … 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 18.0 19.0 20.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 31.0 32.0 33.0 34.0 … 45.0 0.0 0.0 0.0 0.0\n 0.0 0.0 46.0 47.0 48.0 49.0 60.0 61.0 0.0 0.0 0.0\n 0.0 0.0 62.0 63.0 64.0 65.0 76.0 77.0 0.0 0.0 0.0\n 0.0 0.0 78.0 79.0 80.0 81.0 92.0 93.0 94.0 0.0 0.0\n 0.0 0.0 95.0 96.0 97.0 98.0 109.0 110.0 111.0 112.0 0.0\n 0.0 0.0 113.0 114.0 115.0 116.0 … 127.0 128.0 129.0 130.0 131.0\n 0.0 0.0 132.0 133.0 134.0 135.0 146.0 147.0 148.0 149.0 0.0\n 0.0 0.0 150.0 151.0 152.0 153.0 164.0 165.0 166.0 0.0 0.0\n 0.0 0.0 167.0 168.0 169.0 170.0 181.0 182.0 0.0 0.0 0.0\n 0.0 0.0 183.0 184.0 185.0 186.0 197.0 198.0 0.0 0.0 0.0\n 0.0 0.0 199.0 200.0 201.0 202.0 … 213.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 214.0 215.0 216.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 … 0.0 0.0 0.0 0.0 0.0"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "function anim_sol2D(sol; L = 101, clim=(-0.03, 0.03), color=:bwr, bg=:lightgray)\n @unpack prob, u = sol\n @unpack tspan, p = prob\n @unpack x, y = p\n ts = range(tspan...; length=L) |> r -> [fill(r[1], 20); r; fill(r[end], 20)]\n prog = Progress(length(ts), 0)\n @gif for t in ts\n U = My.vec2mat(p, sol(t).x[2])\n heatmap(x, y, U'; colorbar=false, clim, color, bg)\n title!(f\"t = {$t:4.2f}\"; titlefontsize=12)\n plot!(size=(420, 440), xlim=extrema(x), ylim=extrema(y), aspectratio=1)\n next!(prog)\n end\nend\n\nfunction plot_sol(sol, t;\n color=:bwr, bg=:lightgray, camera=(30, 85), size=(720, 540), kwargs...)\n @unpack prob, u = sol\n @unpack tspan, p = prob\n @unpack x, y = p\n U = My.vec2mat(p, sol(t).x[2])\n surface(x, y, U'; colorbar=false, color, bg, camera, size)\n title!(f\"t = {$t:5.2f}\"; titlefontsize=12)\n plot!(; kwargs...)\nend\n\nfunction anim_sol(sol; L=101, fps=10, fn=\"tmp.gif\",\n color=:bwr, bg=:lightgray, camera=(30, 85), size=(720, 540), kwargs...)\n @unpack prob, u = sol\n @unpack tspan, p = prob\n @unpack x, y = p\n umin = minimum(minimum(u.x[2]) for u in u)\n umax = maximum(maximum(u.x[2]) for u in u)\n ts = range(tspan...; length=L) |> r -> [fill(r[1], 20); r; fill(r[end], 20)]\n prog = Progress(length(ts), 0)\n anim = @animate for t in ts\n plot_sol(sol, t; color, bg, camera, size, kwargs...)\n next!(prog)\n end\n gif(anim, fn; fps)\nend",
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": "anim_sol (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "function g_neumanｎ!(dv, v, u, p, t)\n @unpack h⁻², E = p\n @inbounds for k in eachindex(dv)\n dv[k] = h⁻² * sum(u[l] - u[k] for l in E[k])\n end\nend",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": "g_neumanｎ! (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "x = y = range(-1, 1; length=401)\np = My.Param(isin_unit_pentagon, x, y)\ntspan = (0.0, 1.0)\n\nF(a, b, c, x, y) = exp(-((x-a)^2+(y-b)^2)/(2c^2))\nf(x, y) = F(0.5, 0, 0.01, x, y) + F(-0.2, 0.4, 0.01, x, y) + F(-0.2, -0.4, 0.01, x, y)\nU0 = f.(x, y')\nV0 = zero(U0)\n\nu0 = My.mat2vec(p, U0)\nv0 = My.mat2vec(p, V0)\n\n@time prob = SecondOrderODEProblem(g_neumanｎ!, v0, u0, tspan, p)\n\nsol = nothing; GC.gc()\n@time sol = solve(prob)\n\n@unpack u = sol\numin = minimum(minimum(u.x[2]) for u in u)\numax = maximum(maximum(u.x[2]) for u in u)\numin, umax",
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"text": " 0.326729 seconds (1.15 M allocations: 103.016 MiB, 5.57% gc time, 99.16% compilation time)\n 12.537843 seconds (31.34 M allocations: 5.681 GiB, 9.05% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 6,
"data": {
"text/plain": "(-0.3315672956313261, 1.0)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "anim_sol2D(sol)",
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"text": "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:33\u001b[39m\n┌ Info: Saved animation to \n│ fn = C:\\Users\\genkuroki\\OneDrive\\Math\\Math0052\\tmp.gif\n└ @ Plots C:\\Users\\genkuroki\\.julia\\packages\\Plots\\iYDwd\\src\\animation.jl:104\n",
"name": "stderr"
},
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
"text/plain": "Plots.AnimatedGif(\"C:\\\\Users\\\\genkuroki\\\\OneDrive\\\\Math\\\\Math0052\\\\tmp.gif\")",
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