plot - create histograms

Author: jeremylt

papers/high-order-bddc-2023/img/lumpedBDDCHighOrderEigenvalues.png

@@ -31,7 +31,7 @@
    "outputs": [],
    "source": [
     "# setup\n",
-    "p = 8\n",
+    "p = 4\n",
     "mesh = Mesh2D(1.0, 1.0)\n",
     "\n",
     "# diffusion operator\n",
@@ -73,18 +73,83 @@
     "    if sqrt(abs(θ[1])^2 + abs(θ[2])^2) > π/128\n",
     "        A = computesymbols(bddc, ω, θ)\n",
     "        currenteigenvalues = [abs(val) for val in eigvals(I - A)]\n",
-    "        push!(eigenvalues, currenteigenvalues)\n",
+    "        append!(eigenvalues, currenteigenvalues)\n",
+    "    end\n",
+    "end\n",
+    "\n",
+    "# plot\n",
+    "histogram(\n",
+    "    eigenvalues,\n",
+    "    title=\"Lumped BDDC Eigenvalues, p = 4\",\n",
+    "    legend=false,\n",
+    "    color=:cividis,\n",
+    "    normed=:true,\n",
+    "    bins=range(1.0, ceil(maximum(eigenvalues)), length=100)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "savefig(\"lumpedBDDCModerateOrderEigenvalues\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# setup\n",
+    "p = 8\n",
+    "\n",
+    "# diffusion operator\n",
+    "diffusion = GalleryOperator(\"diffusion\", p + 1, p + 2, mesh)\n",
+    "\n",
+    "# bddc smoother\n",
+    "bddc = LumpedBDDC(diffusion)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# full operator symbols\n",
+    "numbersteps = 4\n",
+    "maxeigenvalue = 0\n",
+    "θ_min = -π/2\n",
+    "θ_max = 3π/2\n",
+    "θ_step = 2π/(numbersteps-1)\n",
+    "θ_range = θ_min:θ_step:θ_max\n",
+    "\n",
+    "# compute and plot smoothing factor\n",
+    "# setup\n",
+    "ω = [1.0]\n",
+    "eigenvalues = []\n",
+    "\n",
+    "# compute\n",
+    "for i in 1:numbersteps, j in 1:numbersteps\n",
+    "    θ = [θ_range[i], θ_range[j]]\n",
+    "    if sqrt(abs(θ[1])^2 + abs(θ[2])^2) > π/128\n",
+    "        A = computesymbols(bddc, ω, θ)\n",
+    "        currenteigenvalues = [abs(val) for val in eigvals(I - A)]\n",
+    "        append!(eigenvalues, currenteigenvalues)\n",
     "    end\n",
     "end\n",
     "\n",
     "# plot\n",
     "histogram(\n",
     "    eigenvalues,\n",
-    "    title=\"Lumped BDDC Eigenvalues\",\n",
+    "    title=\"Lumped BDDC Eigenvalues, p = 8\",\n",
     "    legend=false,\n",
-    "    aspect_ratio=:equal,\n",
     "    color=:cividis,\n",
-    "    normed=true\n",
+    "    normed=:true,\n",
+    "    bins=range(1.0, ceil(maximum(eigenvalues)), length=100)\n",
     ")"
    ]
   },
@@ -100,15 +165,15 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.9.2",
+   "display_name": "Julia 1.11.2",
    "language": "julia",
-   "name": "julia-1.9"
+   "name": "julia-1.11"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.9.2"
+   "version": "1.11.2"
   }
  },
  "nbformat": 4,