{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Step 5 : residuals of SDC sweeps\n", "\n", "📜 _Once we have defined our SDC method after choosing :_\n", "\n", "- _some_ $Q$_-coefficients (underlying time-stepping method, cf. [step 1](./01_qCoeffs.ipynb)),_\n", "- _one_ $Q_\\Delta$ _approximation (preconditioner for SDC, cf. [step 3](./01_qCoeffs.ipynb)),_\n", "\n", "_we need to evaluate the quality of this new time-integration method._ \n", "_For that, we use the **residuals**._\n", "\n", "\n", "Starting from the SDC sweep formula\n", "\n", "$$\n", "u^{k+1} - \\lambda\\Delta{t}Q_\\Delta u^{k+1} = u_n + \\lambda\\Delta{t}(Q-Q_\\Delta)u^k,\n", "$$\n", "\n", "the residual at sweep $k$ for the Dahlquist problem is defined as :\n", "\n", "$$\n", "r^k = u_n - A u^{k} = u_n + \\lambda\\Delta{t}Q u^k - u^k.\n", "$$\n", "\n", "From an implementation perspective, it can be interpreted as the \n", "**difference of the SDC solution versus the solution obtained with the underlying time-integration method**\n", "defined by the $Q$-coefficients.\n", "\n", "For instance, if the $Q$-coefficients are obtained using a collocation method, \n", "then the numerical solution at node $u_m := u(t_0 + \\tau_m\\Delta{t})$ should satisfy :\n", "\n", "$$\n", "u_m = u_0 + \\int_{t_0}^{t_m} \\lambda u(s)ds,\n", "$$\n", "\n", "where the integral is approximated with the quadrature rule stored in the $Q$ matrix. \n", "Hence if we note $u^C$ the collocation solution, then we have\n", "\n", "$$\n", "u^C = u_n + \\lambda\\Delta{t}Q u^C,\n", "$$\n", "\n", "which means that the SDC residuals for this solution are zeros.\n", "\n", "> ⚠️ **Residuals** and **time-integration errors** are not the same, \n", "> since the underlying method for SDC has its own time discretization error, \n", "> even if the underlying method is usually chosen to be very accurate.\n", "\n", "Let's setup (as before) the Dahlquist problem ..." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Problem settings\n", "lam = 1j\n", "tEnd = 4*np.pi\n", "u0 = np.exp(1j*np.pi/6)\n", "\n", "nSteps = 12\n", "dt = tEnd/nSteps\n", "times = np.linspace(0, tEnd, nSteps+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and the definition of our SDC method :" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from qmat import Q_GENERATORS, genQDeltaCoeffs\n", "\n", "coll = Q_GENERATORS[\"coll\"](nNodes=4, nodeType=\"LEGENDRE\", quadType=\"RADAU-RIGHT\")\n", "nodes, weights, Q = coll.genCoeffs()\n", "\n", "QDelta = genQDeltaCoeffs(\"BE\", qGen=coll)\n", "P = np.eye(nodes.size) - lam*dt*QDelta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We build our SDC loop, and this time store the residuals for each sweeps, time-steps and nodes, \n", "along with the numerical error versus the analytical solution :" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "nSweeps = 4\n", "uNum = np.zeros(nSteps+1, dtype=complex)\n", "residuals = np.zeros((nSweeps+1, nSteps, nodes.size), dtype=complex)\n", "error = np.zeros((nSweeps+1, nSteps, nodes.size), dtype=complex)\n", "\n", "uNum[0] = u0\n", "for i in range(nSteps):\n", "\n", " uNodes = np.ones(nodes.size)*uNum[i] # initial guess\n", "\n", " # Initial residuals & error\n", " residuals[0, i] = uNum[i] + lam*dt*Q @ uNodes - uNodes\n", " error[0, i] = uNodes - u0*np.exp(lam*(times[i] + dt*nodes))\n", "\n", " # Sweeps\n", " for k in range(nSweeps):\n", " b = uNum[i] + lam*dt*(Q-QDelta) @ uNodes\n", " uNodes = np.linalg.solve(P, b)\n", "\n", " # Residual & error after sweep\n", " residuals[k+1, i] = uNum[i] + lam*dt*Q @ uNodes - uNodes\n", " error[k+1, i] = uNodes - u0*np.exp(lam*(times[i] + dt*nodes))\n", "\n", " uNum[i+1] = uNum[i] + lam*dt*weights.dot(uNodes) # step update" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we take the $L_\\infty$ norm on each nodes ..." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "residuals = np.linalg.norm(residuals, axis=-1, ord=np.inf)\n", "error = np.linalg.norm(error, axis=-1, ord=np.inf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and plot this versus time for each sweeps :" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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WlkYdOnQQPdybNKmY26U6Fi9eLDat1nqeF8/gL9ydGThrA/KIcpQSHI8oRynB8ehf5egTAdHAgQNt9ro39/jjj4vNk6ZNmyY249TfAAAA4J98vg8RAAAAgLsQEAEAAEDAQ0AEAAAAAQ8BEQAAAAQ8BEQAAAAQ8BAQOcBD7tu1a0c9e1asSAwAAAD+BwGRAzzk/uTJk7R///7a+0YAAACg1iEgAgAAgICHgAgAAAACHgIiAAAACHgIiAAAACDgISACAACAgIeACAAAAAIeAiIHMA8RAABAYEBA5ADmIQIAAAgMCIgAAAAg4CEgAgAAgICHgAgAAAACHgIiAAAACHgIiAAAACDgISACAACAgIeACAAAAAIeAiIAAAAIeAiIHMBM1QAAAIEBAZEDmKkaAAAgMCAgAgAAgICHgAgAAAACHgIiAAAACHgIiAAAACDgISACAACAgIeACAAAAAIeAiIAAAAIeAiIAAAAIOAhIAIAAICAh4DIASzdAQAAEBgQEDmApTsAAAACAwIiAAAACHgIiAAAACDgISACAACAgIeACAAAAAIeAiIAAAAIeAiIAAAAIOAhIAIAAICAh4AIAAAAAh4CIgAAAAh4CIgAAAAg4CEgAgAAgICHgMgBLO4KAAAQGBAQOYDFXQEAAAIDAiIAAAAIeAiIAAAAIOAhIAIAAICAh4AIAAAAAh4CIgAAAAh4SndKQK1WU3p6OhUVFVH9+vUpOjo64AsUAAAAAqCGqKCggD7++GMaOHAgRUZGUtOmTaldu3YiIGrSpAlNmTKF9u/fXzO5BQAAAPB2QPT++++LAGjZsmV000030dq1a+nw4cN0+vRp+u233+jVV18ljUZDQ4YMoWHDhtHff/9dE3kGAAAA8F6T2d69e2n79u3UsWNHm6/36tWLJk2aREuXLqXly5fTzp07qVWrVp7KKwAAAID3A6Jvv/3WpXTBwcH0+OOPVzdPAAAAALUKo8wAAAAg4Lk1yqykpISOHj1KGRkZpNPpLF4bMWJEwBcuAAAA+HlAtHnzZho/fjxlZmZWek0mk5FWq3U3bwAAAADSbjKbPn063XfffZSWliZqh8w3BEMAAAAQEAERN5PNmjWLGjRo4NkcAQAAAPhKQHTvvffSjh07PJsbAAAAAF/qQ/Thhx+KJrPdu3eLeYlUKpXF608++ST5usWLF4sNTYAAAAD+rdoB0YoVK2jLli0UGhoqaoq4I7UR3/eHgGjatGliy8vLE8uUAAAAgH+qdkD0r3/9i+bMmUPPP/88yeWYzggAAAB8V7UjmbKyMho9ejSCIQAAAAjcgGjChAm0evVqz+YGAAAAwJeazLij8dtvvy36EXXq1KlSp+qFCxd6In8AAAAA0g2Ijh07Rl27dhX3jx8/bvGaeQdrAAAAAL8MiNRqtbj9+OOPqXXr1p7OEwAAAID0+xBx8xjXCqEmCAAAAAK6UzUv7Lp8+XLP5gYAAADAl/oQ8bD7Tz/9lLZt20Y9evSg8PBwi9fRqRoAAAD8PiDiJrNu3bqJ+2fOnLF4DU1pAAAAEBAB0fbt2z2bEwAAAAAvwZobAAAAEPCqXUPEcnJyRMfqU6dOiWaytm3b0uTJk7EQKgAAAARGDdGBAweoRYsW9P7771N2djZlZmaK+/zcoUOHPJtLAAAAACnWED311FM0YsQIWrZsGSmVht1oNBp6+OGHaebMmbRr1y5P5hMAAABAegER1xCZB0NiZ0olPfvss2IYPgAAAIDfN5lFRETQ5cuXKz2fnJxMdevWdTdfAAAAANIPiEaPHi06UK9evVoEQSkpKbRq1SrRZDZmzBjP5hIAAABAik1m7777rhhZxkt4cN8h4xpnjz32GL311luezCMAAACANAOioKAg+uCDD2j+/Pl07tw50uv11LJlSwoLC/NsDgEAAACkPA8R4wCoY8eOnskNAAAAgK8FRD///LPYMjIySKfTWbz22WefuZs3AAAAAGkHRK+//jrNmTNHDLFPSEjAgq4AAADgs6odEC1dupS++OILGjduHPmrxYsXi02r1Xo7KwAAACDFYfdlZWXUt29f8mfTpk2jkydP0v79+72dFQAAAJBiQMTzDa1YscKzuQEAAADwpSazkpIS+uSTT+inn36iTp06iTmIzC1cuNAT+QMAAACQbkB09OhR6tKli7h//Phxi9d4wkYAAAAAvw+Itm/f7tmcAAAAAPhaHyIAAAAAf4GACAAAAAIeAiIAAAAIeAiIAAAAIOAhIAIAAICAh4AIAAAAAp5bq91b+/HHH8UWFhZGTZs2penTpwd8AQMAAECABUQffvgh/e9//yOlUkmDBw9GQAQAAACB12T2+OOPiyBo5syZNGrUKE/u2n+d2070YS/DrVQhjyhHKcHxiHKUEhyPflOOHg2I5HI5FRUVUXR0NBUWFnpy1/5Jryf6+XWizNOGW34sNcgjylFKcDyiHKUEx6NflaNHA6LFixfT559/Tq+88gpt2rTJk7v2T+d+Jkr903Cfb/mx1CCPKEcpwfGIcpQSHI9+VY4yvd5zodjGjRtp27ZtolN1kyZN6JFHHiF/kJeXR5GRkZSbm0sRERGe2SkX+7JBFQcBC6pDlNCFV8eteG7gC0RN+xnun99JtOsd+/vs/xRRy8GG+5f/IPrlDftpr3+c6LrhhvtpR4i2vGR6SafXU1ZWFsVER5M8/QhRWUHF++q3JQqLscyjuS4PEnUZY7iffYHohyfs56HjvUTdJxru56URrZ1iP+11txNdP9Vwvyib6L/jK8ox7bBlHus2JJp10pDHsiKiFQ6ab5sOIBr4XPkfriP6zwj7aRN7Et38asXj/9xFpNOYHur0OsrKyqaYmGiS8/c4bF5FHt9qQlSaa/u7jm1NdPvCite+nUhUmGk7D/WaEN21uOLx2keJclNsp63bgOjezyoe//AkUdY522lDIonyUysfj/GdK3/XqhCisWsqHm99mejKIdv75fdO3FDx+Je5RJf2WiThcsvOzhY1y/Lx3xMpgw0v8LFuXn3O5SiOR7Pa54ZdiaZsJ/rtQ6LTDv4Rdt8XRHXiDPf3LSM6sc5+2ruXEtVrbLh/6D9Eh1faTzvi30SxrQz3j/6XaP9nRFePWuYxKJyoQSei294hiu9oeO7k90S/L7W/36FvECX2MNw/s4Voz/s2k/FvdW/wIOo9+mlSqVSG8tq5wP5+B8w2nCMqnXs4jx0tv+s+04na3m64z2k3PW9/v72mGH7PLOMU0f9m2k/bbRxR17GG+9nnidY9VjkNf9dXjxOpzcqxQQciVZj9c0/bEUR9p1ecI1bebzcL2hY304bcNjR8+HBS6cuIvrrbfn6b3Uh000sV54jPbqnIY8ZJyzyGxxHNPlORx89vI9KW2d5vwy5Ew83O51+NJCrNs522/nVEd35Y8XjlA0SFGbbTRjUluufTijwuaEpUklPxOpdhXDtDHuvGE43+uuK1dVOJMv+2vd/QKFKPXimu86LcNj9DlH7MdlpVqOXvftNzRCn7bacVEYjO8ng0/q49sFB8Va7fHu1UzYXEG1QxIjbii/qlPZbPFZkFCYX/EF3cbX+fHIwYFWc7Ttve7ARQnGORlqsN6/MdsxjD5J9T5BAHGEbqIsd5aNS94r6mxHHauLYV97Vqx2n5ws7l2/JmIr3Wcdpw8ZdWcJSWLxrm+MKuLbVdbjKzylfOi3kwZP1dq4stX0veT5RnJ8iJy7J8fOUgUdbf9oMncxw4cvBrS3Ck7Txe/rVyWg6UzF09Ufm4NbE6of3zF9Ely31yScUay83832eZZyulrcT4r0kO9Byl1VR8T3TtouO06pKK+znJRJctAzgL5oE4B6bJv9lIU2h4vsTsYpef7ni//Js0Ksggumxjv+VlF9SsZ8UTRVl205rOITbPPZzH3y2f63hfxX3Ou/Xr5oyBEystcJy2xU0V9/nYd5TWHAdIjiR0tjxHJP9hN6ksqgWRoo3hgV7nMC1FNLJ8nLLPfloOUoznHpF2v8U5woIx8DdKPURUfM12Wut6C/4d2ztHmAfjnBfzYMh4Xr5ywPY5IuOk/XMEB3vm/jldsR9n5wgOsvhc5Srj79pYjr5YQ8TOnDlDDz30EP36q5MTWSDXENmqHbIgM4uMze6Lr8rR12VMK6tC2sr7FY/0WnEpsx+fy21H7/ycMRjg/fLJxm4W5FVIa2O/It9a+3+fIqg8fRX360paprP8bFFuOh3J5HJDuckVhn2KfyHa+S5kSsM+Oa3Ffu19d7LKae1+STLX9st5FDVdejv7UFX+ruVKF/Nbntb4fhtp9aQnnVZHcoWcZDI7aR2Wo5xIEcxnM/t5qLRfW9+zzHZ+HR0T5mm1GiJNsf1yVIVXfB8cqOsc7VdhdlzqKh1r5mWn0elJqQoimfjd209ryIacSFNk52+SESlDKv4emYI7hjrNg2m/pr/NeDzZS6uwSqu2+qP0hn8g2S3HUDvnHnnFcWlrv+YfIVNQmUZHQUFBfBF0mNbmfvlW/ENGZ/vv4xpXzqPGTu2QSMfnKFXFYz6+9R5My3ksyTUca7b+JmWY4fs1nieNgaS9410mI70iiMrKSikoKJhknNbR79484LO3X1GOhbZf81AtkddqiJharabff3cx4g9Utv6FZoEvzGYHWlVCVg+kdRwIGXFA4u7nOzjBurNf4xvs/cushpjKzXjhcHSSNdJrDH+bg2tjJVVJW4Uito0vADZO6lUpWydpuczE5VFcQ6vznemItFa1bJLDJ35bVa7u4bITl8lSs1qtauNAxBfKscgj5SYu1zXx5/J5jWvoXaBVhJI6pLwLgjzM9c9wNW24Va220/2GOk8TEmr4lbqS1ogDbXuC6tl+Pi+T6Mx2oiZ9He6am4oVCrN/+LnB4wEROMGBDvejcITbyh/4r0faT6tDXaamok9vo4iSZPuBEedxzGo38qh3vxxXjjY019jToD3R/atqLY9qjYa2b99OgwYNIpVSacjjqjGO8xjHeVzhte/akMcHiDKc5fGb6ufRSSU0l9uOHTto4MCBhnKz9f7VY53ksZ2hL0QN5dGl9/93nKHJwVEeR33l0TyqNWrauXMn3XjjjaRSqpy//9vxzvN435fePR6/neA4j9yP0a086sUxt2vXTrrhBi43ZTXyONFx9wHO472f280jN8yk56spp4S/0xoq66JMQ82MPVyLFCYaq12m1+uptLSUgoODSeaJY8RZHnNlRBcuON1NvXr1KD4+3u08VTkgmjp1KnXv3p26du1KnTp1ElWOUAVc1ckdCR3hvgjhsZXbmGtLcQGFqrMc/0w5j3Xqey+P3CfEXmdio9wrho7FtZVHtZqKg2KJIpP4ny2u5THvClFEgnfL0V5fBIs8Nqy5PKrVVBQcZ+gMyuVWrTymEkUmerkcrzjPY70kz+ZRrabCkDNEMS1tl1118hjVRNrlmJ9GFN3UvTyq1VQQctYwoMFZudnKI/dTdJbHmOZ285ielkY56hyKS4gTg5A8ElyY4yaofxx1KWAKovotLbsBOKHT6aigoIDq1KkjptmpnTw2sZtHDtB4qp+MDEMH84SEhNoNiI4ePUrffPONmGeIq6ratWtH3bp1E0ES37pdSP6O22v5xC06WNppI49sZNmuW9sUQVSkjCGVtshOUCSNPPpCOSKPKEccj/jNmNNqtZSTk0NxcXEUExNTM+cersUKCSrvi2WHMkg0f1Wlpk2n01FZWRmFhIR4ICDyTB5DQw1NdxwUcZm603xW5YBo7969Iir766+/6NChQ6Zt7dq1otMS83i06281RAX/OGiO0RtGgnA6b/0rTVtGIdpcBzVE0sijL5Qj8ohyxPGI34x1P1vGNUM1x0nHdmYaSOGt67XeY3k0liWXba0GRMaAp23btmJ78MGKod7nzp2jgwcP0uHDh6udIb/HF+dHttufZ8Y4FNxbF3GmDKadbV6nm3p3st++LoE8+kI5Io8oRxyP+M3YUqMVB9zEFNvGccAhRkh6sUVH5rk8eqosPdqpukWLFmLDOmZOcFMPbxJWEhRjmNejqu3rtckHyhF5RDlKCn4zgVOO3NxEEu/jq5RWHqsUHl6+fLlKO79yxUnnOAAAAABfC4h69uxJU6ZMoX377M/Uyf2Ili1bRh06dBD9igAAAMB/zJ49m+644w7yN1VqMjt16hTNmzePhg0bJkaY9ejRgxo2bCh6nF+7do1OnjxJJ06cEM+/8847dOutt9ZczgEAAAKYVqenfReyKSO/hOLqhlCvZtGkkNd8J+kjR45Q376OJ0x010cffSTiiLS0NGrfvj0tWrSIBgwwWxrK2wERL7747rvv0ty5c8UCb7t376aLFy9ScXExxcbGig7Wt9xyi6gdAgAAgJqx+Xgavf6/k5SWWzFsPSEyhF69ox0N6+DefDyuBETTpk2jmrJ69WqaOXOmCIr69etHH3/8sahg4UqXxo3LF16uAdXqVM01QiNHjhQbAAAA1G4w9NjXhypNOpKeWyKeXzK2W40FRSkpKZSVlUVdunQRj3lOpXHjxonn1qxZ4/bkiGzhwoU0efJkevjhh8Vjrh3asmULLVmyhObPn081BbMoAgAAeJGYcblM49KWX6KmV3844XApydd+OCnSOdtXddZ2P3bsmFgstVmzZuI+9y3mIIiX3zEPhrh7Dc9o7WjjViZrPPEjT98zdOhQi+f5Mc+DWJOwlhkAAIAXFau11O6VLR7ZF4c46Xkl1PG1rU7TnpxzC4UFVS0MOH78OHXu3JlWrlwpms3eeustevTRR20u8+VsCp5GjRpVei4zM1PM5t2gQQOL5/lxeno61SQERAAAAOASrhXibfr06fTjjz/a7VzNfY55qy7ryRa5NqumV8FAQAQAAOBFoSqFqK1xBY8qm/j5fqfpvniopxh15uxzq+rYsWOi//CKFStE/yF7uMmMN0c2bdpUaeQYD9Di5Tesa4N4rTLrWiNPC5iA6O677xZtnIMHD6bvvvvO29kBAAAQuObD1aarAa3qi9Fk3IHazrLWFB8ZItJ5egh+fn4+Xbp0iR577DHq378/jRkzRvTr4WHxnmoyCwoKEovFb9u2TVy3jfjxnXfeSZINiHghNY7iioqKqH79+m5Vj9W0J598kiZNmkRffvmlt7MCAABQLRzk8NB6Hk3G4Y55UGQMf/j1mpiP6PDhw6L2pl27diJo4XkHeYJGnqyZa3Y81WQ2a9YsMXKN5zTs06cPffLJJ2KlDA6yalKVR5kVFBSIOQEGDhwoepo3bdpUFA4HRE2aNBEzWe/f77w6r7YNGjSI6tat6+1sAAAAuIWH1PPQeq4JMsePa3LI/dGjR6lVq1YUHGxYNHvBggXi+s9NaDw6zFNGjx4thtrPmTNHDO/ftWuXmPuQYwzJBETvv/++CIB4aY6bbrpJLM3BEePp06fpt99+o1dffZU0Gg0NGTJEzGb9999/u7Rf/mM5yuRZr7nqcP369ZXS8ARNPMyP50DiyNTWcD0AAIBAwEHPnuduopVTrqcP7u8ibvlxTU7KOG3aNIuh73K5nDZs2CCu4dzU5UmPP/64mPi5tLRUDMO/4YYbqKZVqcmMC2L79u3UsWNHm6/36tVLNEstXbqUli9fTjt37hTRpDOFhYViGN9DDz1E99xzT7VmreQgiQvO2tatW0WgBQAA4E+4WaxPixhvZ8NvVCkg+vbbb11Kx9VpHN25ioMbR+ueuTJrJUeQnsKBlXlwlZeXZ+ozxZu/M/6NgfC3ehLKDeWGY843ePO3yp/JQ8h1Op3YfIm+fCJHY/6lgvPCeeKy5T5O5qryHXtklNmvv/4qOj8Z2xU9yThr5fPPP19rs1ZykPX666/brG0KCwujQMG9+gHlhuNN+vBb9Z1yUyqVFB8fL/rjerLfTW3Kz88nKeFy5DVVuemOu+2Y40FftRoQce0O9yVq3rw5eZqnZq3kRWcPHTokmucSExNp3bp1YspxW1544QXRy928higpKUkEYREREeTvOKLmEwX3BVOpVN7Ojs9AuaHccMz5Bm/+VktKSig5OVksXcF9Yn2JXq8XwRAPUKrpSRKrWqahoaGin5F1mRpbeGotIKrOeii1PWslN7G5imu6bNV28Q8nkAKEQPt7PQXlhnLDMecbvPFb5X/g87WLOyTz5kt05c1kxvxLBeeF82Tr+6zK9yudv8gOb85aCQAAAIHBIwERj/qqqeDEfNZKc/zY3hoqAAAAAFXhkSYzniyJO4pVF3cuO3v2rOnxhQsXRJ8knuWSh9V7a9ZKAAAACAyS6FR94MABMZO0kbFD84QJE+iLL74Qs1ZmZWWJWSvT0tKoQ4cOtTJr5eLFi8XGbb4AAADgvyTRqZqXAXG2D57XqCpzG3lqVk7euJc6L1MCAAAA/knynaoBAABAOmbPni2W2/I3ku9UDQAAANJx5MgRsehqTXFlfVOvB0TckdmWBx54gMLDwys9f+XKlernDAAAABw7t53ow16G21oMiLp27Vpj+zeub/rhhx9SbapSQMQzO0+ZMoX27dtnN01ubi4tW7ZMdHxeu3atJ/IIAAAA1rjv7c+vE2WeNtzWwiTJKSkpYpCTsYYoJydH1ObwNDg86MlTA7Xmzp1LI0eOJMl2qj516hTNmzePhg0bJmZ/5GHwXKXFU2Vfu3ZNrD5/4sQJ8fw777zjcMFWAAAAKA9s1K6vuWVyfgdR6p+G+3x7eiNR84Guv18VxtNOV+kjjx07JgYZNWvWTNznoIVHia9Zs0bMG2jEsQJvjmzatIkGDBhAUlGlgIjnBXr33XdF5MbD3nfv3k0XL14Ui6rxjNIPPvigWDOMa4f8AYbdAwBAjeNgaF5D9/ez6oGqpX8xlSiocncXR44fPy6as1auXClGYb/11lv06KOPVkrH8wSOGjXK4b4aNWpEPj/snmuEOCqs7eqs2oZh9wAAABW4Voi36dOn048//mh3xQiuQOHNlyiru1Iwr/zOo8tat27t+VwBAAAECm664tqaqjSxfTGcKP04kd5s4mCZgii+A9HEja41hfHnVtGx8mayFStWiP5D9vh9k5kR9x/iarOqrDYPAAAANvC1tCpNV2d/Iko7Uvl5Do74+eTfiVre7PGizs/Pp0uXLtFjjz1G/fv3pzFjxtDevXupffv2gdtkxsaPH0/Lly8X7YcAAABQC7h26Je55YPEdTYSyA2vtxhc5Q7TzvASXQqFgtq1aycWXedBVDzCjEeecz9iTzWZOVvfVHIBUVlZGX366adi1XkeVWY9D9HChQs9kT8AAAAw0pYR5V6xEwwxHVHeFUM6ZbBHy+3o0aPUqlUrCg427HfBggVi9Dk3of30008Wo8zc4Wx9U8kFRNxk1q1bN3H/zJkzFq+hKQ0AAKAGcJDzyHaiwkz7acLrezwYMg40GjduHBnJ5XLasGEDeZor65tKKiDavr32ZsUEAACAcpGJhg2ks9o99zDnfkRcZca1QtyuOGnSJL9ZGR7zEAEAAAQGuTttfC1atKD333+fsrOzKTMzU/Qb4ucOHTpE/oCrB3n27f3793s7KwAAACDFGqKnnnqKRowYIdYtUyoNu9FoNPTwww/TzJkzxWq1AAAAAH4dEHENkXkwJHamVNKzzz4rRp0BAAAA+H2TWUREBF2+fLnS88nJyVS3bl138wUAAAAg/YBo9OjRNHnyZFq9erUIglJSUmjVqlWiyYxnrwQAAADw+yYzXvWeR5bxjNXcd8i4pAdP6Y3ZqwEAACAgAiKekfKDDz6g+fPn07lz58QkSi1btqSwsKovFgcAAADgc01mvNo9T6vNM1RzANSxY0fq1KkTgiEAAAAInIAIq90DAAAEptmzZ4tFXf2N3N3V7v0Zz1TNs2/37NnT21kBAAAQ0grS6GTWSbsbv16Tjhw5Ql26dKmx/XNXHL7u8oj1uLg4uuuuu+j06dNU07DavZOZqnnLy8vzm+VIAADAd3Gwc/v626mMV7O3I0gRRBvu2kAJdRJqLCCaNm0a1ZSdO3eK/XNQxIO2XnrpJRo6dKhYOSI8PLzGPher3QMAAPiIa6XXHAZDjF/ndDUREKWkpFBWVpaphojXNB03bpx4bs2aNZSQ4P5nbt682eLx559/LmqKDh48SDfccAPVFKx2DwAA4EU8SrtYU+xS2hJNicvpitRFDtOEKkPF9DlVcezYMdFi0qxZM3F/5MiRYpAVB0M8+txo3rx5YnNk06ZNNGDAAKefmZubK26jo6OpJimrO8qMq68+/vhjat26tedzBQAAECA4GOq9ordH9zlh8wSnaf544A8KU1Vtqpzjx49T586daeXKlaJZi+cdfPTRRyulmzp1Ko0aNcrhvho1auRSsDhr1izq378/dejQgSQXEGGUGQAAQOA5duyY2KZPn04//vgj9e3b12Y6rs3xRI0Of87Ro0dpz549VNOU7o4yw6zUAAAA1cdNV1xb44q/sv9yqfbny2Ff0nXR1zn93Ko6Vt5MtmLFCtF/yB5PNJk98cQT9MMPP9CuXbsoMTGRahpGmQEAAHgR9+NxtekqRBnicrqqNoc5k5+fT5cuXRJLdHETFq9bunfvXmrfvr1Hm8y4mYyDoXXr1tGOHTtEf6XagFFmAAAA4NThw4dJoVCI+fm6d+9OJ06cEBM07tu3j2JjYz3WZMZ9k7gG6vvvvxdzEaWnp4vnuTN3aGjVa7VchVFmAAAAPiIqOErMM+RsHiJO52lHjx6lVq1aUXBwsHi8YMECOnXqlGhC++mnnyxGmbljyZIl4nbgwIGVht9PnDiRJBcQsd27d4uRZufPn6dvv/1WVH999dVXonqLq9MAAADAc3huIZ50kecZsoeDoZqYg2jatGliziEjuVxOGzZs8PjncJOZN1Q7IOI5B7hgHnzwQTp06BCVlpaa2hi5I9XGjRvJH5bu4E2r1Xo7KwAAAAIHOzU1C3Ugq/ZaZnPnzqWlS5fSsmXLxDB8Ix6CxwGSP+BomKcK379/v7ezAgAAAFIMiHihNVtTaEdERDgcigcAAADgNwERr1dy9uzZSs/z5EnNmzd3N18AAAAA0g+IeKruGTNm0B9//CHmUEhNTaVvvvmGZs+eTY8//rhncwkAAAAgxU7Vzz77rFhwjRd1KykpEc1nPBSPAyKeahsAAADAV7g17P7NN9+kl156SXQ81ul0YrKmOnXqeC53AAAAAFIPiFhYWBj16NHDM7kBAAAA8KU+RAAAAAD+AgERAAAABDwERAAAAD5EV1bmteUtGA+e4kVd/Q0CIgAAAB+hTkujs4Nuoov3jaKC3Xu8EhgdOXKEunTpUmP758VdO3XqJCZ65q1Pnz60adMm8smAKDs7uyZ2CwAAENA02dmkzcqikhMnKHnKFK8ERkeOHKGuXbvW2P4TExPprbfeogMHDojtpptuojvvvJNOnDhBkg6IOIrjNb8OHjwoHp85c4auv/568ge8sCtPJdCzZ09vZwUAAPwUBzO6oiKXNn1JifFN4qbk5EkRGF24517K/+kn0hYWur6vagRRKSkplJWVZaoh4qW6uPmM1zFNS0vzSHnw/oYPH06tW7cWG0/xw1P6/P777yTpYfcTJkyg48ePiwkaBw8eTLt37/abAIIDPd7y8vIoMjLS29kBAAA/pC8uptPdulfvzTqduCk9eZJSpj9Rpbe2OXSQZGFhVXrPsWPHxPWwWbNm4v7IkSPF9X/NmjUUFBRkSjdv3jyxOcLNYAMGDHCYRqvV0rfffkuFhYWi6UxSARFPwMjkckPl0tNPPy1uhw0bRmPGjBFRHC/hAQAAAP7l+PHj1LlzZ1q5cqWoMOCmLV7Ky9rUqVNp1KhRDvfVqFEju69xsMUBEK+EwXHFunXrRIuNpAKi+++/X0SDjz32mOm5ffv20ZQpU+j111+n3377TVRvvffee57OKwAAgN+RhYaK2hpXlJw6RZceHFv5Ba6k0OkouF07qv/EdArv3dulz62qY8eOiY2X6Prxxx9FU5kt0dHRYquuNm3a0OHDh0WTHNc+cWvUzp07azQoqnIfIs7QwIEDTY9PnTpFt912G73xxhv08ssv0wsvvEDfffedp/MJAADgl3iBdHlYmEubLCTE8s3lrTUh7dpR0rJl1GzNd1R30CDX9iWTVTmvx8qbybjmhoMVe7i5jGt2HG3cxcYebn5r2bKlWAlj/vz5olbqgw8+IEnVEHE7nkKhEPcvXbpEt956Ky1YsIAmTZoknktISKDMzEzP5xQAAAAMOJjR60UgVH/GDArv369aAU5V5Ofni+s+txD1799fdJPZu3cvtW/f3uNNZta4A3hpaSlJKiDinuUzZ84UEeLcuXPp8ccfNwVDbPPmzSKqAwAAAM9SxsSQIjaWVPHxtRYIGXETFleIcLNV9+7dxTB4HhHG3WZiY2PJU01mL774oqhsSUpKEkHYqlWraMeOHSK+kFRAtGjRIho9ejS9/fbbdO+999I777wjepxzoLRr1y7Rj2jhwoU1k1sAAIAAxoFQy19+JplKVWuBkNHRo0epVatWFBwcLB5z6xB3m+EKkp9++slilJk7rl69SuPGjRPD+Dm+4Ol9OBgaMmQISSog4va8c+fOmR537NhR9BtKT0+n0NBQmjFjBj3yyCOezicAAABwtyEPBR5VNW3aNBGoGPFo8w0bNnj8c5YvX07e4JF5iMaPH08ZGRkUFRXlsQgRAAAAwGcCIsbVdg0aNPDErgAAAABqHRZ3BQAAgICHgAgAAAACHgIiAACAWlabq9P7O72HyrLafYiKi4tFJsLKF4bjyZqMa40MHTrUI5kDAADwJyqVStwWFRWJkdmBrExbRlq91u7rCpmCghTOB2pxWZqXba0HRHfeeaeYe4Bno+Tpu3v37i0yw7NU8zxE5mudAQAAAImJDevVqydGZjOuVKiJ+YQ42NDpDYux2yKXyV0KNqwXdy8rKxPLdhgXeHcnf5fzLpOe7NfuyEhGjSMa280nV8pwMMRlyWVqXEWj1gOiQ4cO0fvvvy/u89plPMrszz//FIuwvfLKKwiIAADAL6UVpNG10mt2X48KjqKEOgl2X4+Pjxe3xqDI07Q6LWUUZTgNNuLC4kghdz2I0Ov1onWIa7bcDeLUWjX9U/yP03S6UB2pFI5rfjgYMpapVwIijsrq1q0r7m/dulXUFnHEeP3114vmMwAA8K8LeW2Qeh45f7evv13UcNjDNRob7tpgN58cTPC6n3FxcaRWqz2ex7PXztJbR99ymm7hwIXULKqZy/tVq9ViRYobbrjB7eYpzuOCHQvcziPnw92aIbcDIl6vbP369XT33XfTli1b6KmnnjJFvBEREeQPFi9eLDat1n4bJwBAoFzIa5ov5JG/Y0f5Y/w6p3OWR76Qe+pibk4eJKe0sjTnCZVEISEhpodZxVmk1qlJo9NUbHrDrUquouZ1m5NGoxHvOZR5iArKCkitt0zPtVNhqjC6o8Udpv2u+msVXS26akrDn5FZnOlSHvlvMc9jTap2QMTNYg888IAIhAYPHkx9+vQx1RZ17dqV/AFPU85bXl6eWE8FALwDwYa0LuSBmkfuk1OoLnQpLQcGe1P3ilvzwMK4NazTkHon9Dbt97Pjn1UKRrjDMd+2qNeCxlw3xrTv2TtnU4mmxCLAMO6/XUw7uq/1fS7l8eW9L9O6O9eZHo/aMEo0tdnSKqoVrb51tenx3N/n0sW8izbTJtZJtAiI1v69lk5lnyKpq3ZAxAu79u/fXyy+1rlzZ9PzHBxxrREA+AYEG/5/Ia9N3M/EeCG3rmXgLTI4kuoGGbpbcA3D2ZyzpkDgQu4Flz5j/dn1tDNlp6lGgm/7NOxD/Rr1E6+nF6bT+wfft/h8Yzr+rKGNh1IdqmNK+/DWhysCC/N86zR0b+t76YXeL4i02SXZNGnLJJfyyPt6dNujdl8f2mSoKSDi/jwfHPrAbtr+jfpbBES7UnZRsabYZtpQpesj16xHeAXJg0RNkFKuJKVMabgt32JDLFezbxvdluoF17NIY3xfbKhl2lub3UrdG3S3SJddnE3/PfNf8pulO7gTk3VHpl69ermbJwC/uJD7Qh4DrYlCqgGE+b/y+cJdJ6iOuDCxnJIcyijOqFRrwOlLy0qpUFdRY8EBxeGMw5YX9vJghL9rV7y9/21xUZ3UYRL1jO8pnvs97XdaeGChzf3y9lyv5+j25reLtLuv7KZpP0+zu/8Xer1AD7R9QNznWgNXAwxzK/9aWem5YGWwKSAq0hTRxgsb7b6/bVRb4v+MLuXZ7/dapqs49ozfiSs4MGgd1VoMHTcFGeUbP9c2pq1Fn6J7Wt0jRn5ZBxd82ySiSaUy5A7TxjTcMZrv8+fwOcVVr1z/isXjTfdscpjevL/T2ze+7fLnPNThoUrPncw66dsB0axZs1xOy0PvwXfl6HLEyUqptH2I4ELuHIKN2pVZlEnJqmTRp8HUTFF+4e4Y21FcMNiprFOUUpBiUQtgfqHnGgHuA8F2JO+gQ1cPVbxu1ezBgYD1v4Zdwc0jHx3+yBTgWPvq1q+oS1wXcf/7c9/TuwfetbuvieETTff3p++nN35/g9xx8OpBcXtb89tMzxWWFTps8jCvreALtC3GCzZf9I24nJPqJokAgV/n8rDXDGNuUOIgig2LNQUXvN9ucd1Mr8eExNDsHrNNn2kdYDQKa0Rnr54VaaNDounLYV9aBCvm7wlXhZv2GxEUQV/f+jWN3TTWaR6VCiWtGbGGXPVa39dcTnt3K8etMBxsuMJ4nEM1AiIeVu+KmphTwZ9IvtagMI0W5S0izWaN3TSoNfC9mg0e5soXdt6MtQz/FDkf9sr2pe2jy/mXxXv4IjGs6TDTaxvPb6TUwlSbzQ2c9pmez5jSfnzkYzqRdcIiWOF8ZeZn0srNK2nVHatMaV/b+5poFuG+Eq6Y9ov9Wok99+8RTTVs9enVtOZv+xeqoU2Hmi4U+9L30Vcnv7Kb9rEuj1UrIOI+I6XaUruvc1ka8QWZL9rWTRjGi3dQWcUcLY3qNKIbEm+olJYv8HllebTt0janeXuk4yOUFJFEnetXdIXoHNeZlty8xCKoMA8a6ofVN6XlWiUub/MghIMgW9eF9jHtaePIjRYX8tEbRjvN49QuU0VfGXv4u57QfoLDmo6zdNZ0LuvWoCKYcoT/BmdDwME1fJ3jsndWO12VGq9aDYi2b99eczkJEL5Qa5BTmkMash8M+XoTRVUuWuY1CHzx4aYMYzPH+dzzFq+XqEvonPoc/Zr6K8WGx1r8S9iR7Ze3W5zc39n/DuWX5VsGDeWBTOO6jenF3i+a0k79aSpdLTSM3rBuzuBq9m+Gf2NKO/KHkS7969uW9w6+Z7rPF2fzgIirvY21Cta46cU8IDr8z2Hac2WPzbQp2SmiXI0XTr6A80gUV/GFly9WtgIH86n9m0Y0FbUJtpomeDOfBK5ng54kJ6tmDLNgIDo4mqqDO71yvwpbeTU2gRhxjRVv9i7sGzdWBBTcZGRsNrLGwYYrAdHgJoMrBRsc9HE/FlfwdxCpwCAUb5JisGGNrx18nZNS5YBbfYjA92sNahJfmPmiZl1rYOwrwdXa8eGGPmg8cuNA+gHD63q1qDUwb6JoE9XG9K843ufqvypGOzjC+52ydYrdDp6DkgbRrB6zTNX+A1cPNKWxnuV1SJMhYk4Mo7u+v8vmZ36+43NxUXqy65Mu5ZGbZaZ1rajd2HB+g+i8aUt2tOXzF3Mv0pWCKzbT5pXmWTw2NhkZcYDHQZt5bYQ9reu1pojgCLEPbjYwN6DRABGo2bqwByuCLdJyx9CbGt9kUcvAc8cdOXSEevc0dDA1eqr7U/Rop0dF/46ndz7tNI/f3PaNw1oDo4kdJorNFYMaDxKbp3ENhrHGCnwLgg3P4WuclK5zbgdEJ0+epMuXL4vpvM2NGDHC3V0HNK6l4dEPfNI0jhrILc2l5PxkU1Bh3UTB/SSMBxen45EItgIBDjaGNB1iqhI/c+0MLT+23JSOe/+7wjiCwvwz+ML+cMeHxfOnr52m+zfcb/f9UzpOoSe7GYIGnqNi+i/T7aYd23asKSAqUhfR2rNrXcoj1wxwh1B7+HON+CLNnTHtMQ8cuBaDAzpmXitRXFBMUZFRlFQniVxl7LhqNLnDZNGR01btAdfOmHuz/5umpinzQIQDjRCl5dwdXw//Woxm4de4BoKDIVebKN7o/4bdYGNyx8ku/63cnGOrlqP0WCn1a9jPolmF+5YwR2sdgX9dyH0hj1Ks2fCFYMMXVDsgOn/+vBhef+zYMXESM1ZJG09omMzQPcZgY9GgRTS48WDT6I0XdhuGf9oyr/88uqPOHaYg56199mcq5fVhjAERT8blaESGo6DNGl+crTtX8oXXVsdG886KYcow0Z+gUtOETCUCDh6tYcTvu6XpLbTl4haneeSgYP6A+aZ9We/fGNSI/MqVtPHujaYRG9YBhvUU9ztG77DZfDH81uFi9lRXOzbe3sIwOsdofPvx5Coeyuoq8/IGz8KF3DMQbIBPBkQzZsygZs2a0U8//UTNmzenffv2UVZWFj399NP07rv2R0RAFb4cmdKi2aaOqo5oYrIOLoyPo0Iq/tXE6ThosO4fYUxrHmBwn4pnejxjSpNekE7Lji9zmr+3B7xNraNbW+TFOL8I4884Mv6IS31pOL+rbq/oUOsIfwYPCXYlIOJ8GYcDO8PBPHcmBWlBsBFYtQa+kEfwT9UOiH777Tf65ZdfqH79+mINM954osb58+fTk08+6fKINLBt1W2rqH1se4vnBiYNFJsruLbl3RtdC0z55GNeK3H06lGXAqImkU3EDKqOAgz+D6QdbHCQ7KgfUVXnNvE0Pj4/G/oZJRck203DTZS4iPr+CFeGPKIcfa5TNTeJ1aljGHETGxtLqamp1KZNG2rSpAmdPn3ak3n0KzxXiiu4GctbXB3ZI/6WihanWsX9oDyZLlDz6Av4Ajlp6yRJj8z0hdGjyCPKEcejY66NC7ahQ4cOdPToUXG/d+/e9Pbbb9Ovv/5Kc+bMEU1oYFue2nLkj7vpvMqLlT+uzgXizTlDfCGPXFvgbJQZv+6oVkFKIzO9BXlEOZrD8eibv5lq1xD961//osJCw5Txc+fOpdtvv50GDBhAMTExtGqVa31BApH1kGV7ZHqZ3aHXTt/rZqTC69m4IlgeLJYVqC53JvDkNZBcTcej82oDrwJdrCsW0wIodUqX88hTA/B7qsud75tH7LmiWF3s8t9T1e9ajDLTl4pyUFHl4NDemk3WeAJHV/8eT3N18kiejNHVv8cVao2ayvRlYp8ameO5wxxNBGl9EXL17/H077oqtarOLqaOaLQVk4JWtVqA3+tSuvLRwN5gPrjFEeOM7lXZr7Z8UleZzr0uETqd5bQmUiDTm89Y5qbs7GyKioryu5mqjavd5+bmUkSEawGNPa4OcwYAAAh0q29f7dL8Yp64fle7hoibxhx55RXLReMAAAAApKraAdG6desqVXtfuHBBLAbaokULBEQeGGXmTlTsDh5lNnbLWJfyaL5ic1W4WzHJC3SO2TjGaboVw1dUP488hXIV8G9g86bNNOzWYWIeIs7jgxsfdPq+b279ptp5dJfI4ybneeQFLWuqHEW5bd5Mw4YZys3aX1l/ubSYJi+Iel30dTWSR2f+yv6Lxm9yPn8ULyJa3TzaK7stW7fQLUNvsVl21nmcsNn++l5GXwz7wqN5rArO48TNzmcR/+KWL6hNdJtqf9dcbtu2baMhQ4Y4LTdrp7NP00NbKq/ebu2zWz6rfh7dPD9yHidvdT5h6vKhy6uUR7Ub5VbdPPpEQGRrWD1XTU2cOFFM2AjuEUPWvdT06OrncjpX1+uq/GZyC0/z4ArjJIu1Qm5YDoOHqRvne3IFr4rtrY7V/Nmu4PyZr/HlSXKdXEyayct82CoHV8uG82c9O3dtsV6ixB7OnydXGFeTmoJlwWKfzi5QrpYNz4zvrUk8jbPyO02nCjWtK1gdapmaQmQhYk6zql7YXf3+uAxd7TPqaa6WDaeryhIyarmawuRh4j3uBkTufH+SG2VmC7fPcVPayy+/7MndAgAAAPhOQMRycnJE5yVwPOuuI95eq6decD1SOqk89HYefaEckUeUozkcj/jN4Nwj7fNjtdsS/v3vf1dq80xLS6OvvvpK9AUA312rJyE8gWZGzKSufbuKPmGSzKMvlCPyiHI0g+MRvxmce6R9fqx2QPT+++9X6tPBy3hMmDCBXnjB/gKk4Btr9dST16O20W3dbicO9HJEHlGOUoLjEeUoJQkSO4dXOyDiEWUAAAAA/sDjfYgAAAAAfE2VaohmzZrlctqFCxeSr1u8eLHYeCFbAAAA8F9Kd+YeOnjwoAgWeJV7dubMGVIoFNS9e3fyB9OmTRObcepvAAAA8E9VCoi2b99uUQNUt25d+vLLL8X6ZezatWv00EMPiUVeAQAAAPy+D9F7771H8+fPNwVDjO/zyvf8GgAAAIDfB0TcjHT16tVKz2dkZFB+fr67+QIAAACQfkDE65Vx89h3331HKSkpYuP7kydPppEjR3o2lwAAAABSnIdo6dKlNHv2bBo7dqxYAVfsTKkUAdE777zjyTwCAAAASDMgCgsLo48++kgEP+fOnRNLd7Rs2ZLCw72zSjIAAABArQdERhwAderUyd3dAAAAAPjOxIxvvPGGCIKcTdLoDxMzAgAAQGCo8sSMxv5C1pM0mpPJZO7nDAAAAEDqEzOa3wcAAAAIyGH3xcXFVFRUZHp86dIlWrRoEW3dutVTeQMAAACQdkB055130n/+8x9xPycnh3r16iVmqObnlyxZ4sk8AgAAAEgzIDp06JBpzTKekDE+Pl7UEnGQ9O9//9uTeQQAAACQZkDEzWW8uCvjZjKenVoul9P1118vAiMAAAAAvw+IeBLG9evXU3JyMm3ZsoWGDh1qWsssIiLCk3kEAAAAkGZA9Morr4ilO5o2bUq9e/emPn36mGqLunbt6sk8AgAAAEhzpup7772X+vfvT2lpadS5c2fT84MHDxYLvwIAAAAExNId3JGaN3M82gwAAAAgIJrM2O7du8Vq99xcduXKFfHcV199RXv27PFU/gAAAACkGxCtWbOGbrnlFgoNDRXLeJSWlorn8/Pzad68eZ7MIwAAAIA0A6K5c+fS0qVLadmyZaRSqUzP9+3bV8xRBAAAAOD3AdHp06fphhtuqPQ8D7nnmasBAAAA/D4gSkhIoLNnz1Z6nvsPNW/e3N18AQAAAEg/IHr00UdpxowZ9Mcff5BMJqPU1FT65ptvxNxEjz/+uGdzCQAAACDFYffPPvss5ebm0qBBg6ikpEQ0nwUHB4uAaPr06Z7NJQAAAIDUAiK1Wi2W6vj444/ppZdeopMnT5JOp6N27dpRnTp1PJ9LAAAAAKkFRDyq7Pjx46KpLCwsjHr06OH5nAEAAABIvQ/R+PHjafny5Z7NDQAAAIAv9SEqKyujTz/9lLZt2yZqiMLDwy1eX7hwoSfyBwAAACDdgIibzLp16ybunzlzxuI1bkoDAAAA8PuAaPv27Z7NCQAAAIAvLu4KAAAA4A8QEAEAAEDAQ0AEAAAAAS8gAqLk5GQaOHCgmDiyU6dO9O2333o7SwAAAOAPnap9iVKppEWLFlGXLl0oIyNDjI4bPnx4pakCAAAAIDAFRECUkJAgNhYXF0fR0dGUnZ2NgAgAAACk02S2a9cuuuOOO6hhw4ZiDqP169dXSvPRRx9Rs2bNKCQkhLp37067d++u1mcdOHBArLuWlJTkgZwDAABAdejKykiv15NUSCIgKiwspM6dO9OHH35o8/XVq1fTzJkzxUKyf/75Jw0YMIBuvfVWunz5sikNB0kdOnSotKWmpprSZGVliSVHPvnkk1r5uwAAAKAydVoanR10E128bxQV7N4jicBIEk1mHNzwZg8vAzJ58mR6+OGHxWPuD7RlyxZasmQJzZ8/Xzx38OBBh59RWlpKd999N73wwgvUt29fp2l5M8rLyxO3arVabP7O+DcGwt/qSSg3lBuOOd+A36r3y60kI4O0WVmkzc6m5ClTKLh9e4p+YjqF9e3r0dUuqpJXmV4KYZkZLoh169bRXXfdZVozLSwsTIwM44DGaMaMGXT48GHauXOn033yn/jAAw9QmzZt6LXXXnOantO8/vrrlZ5fsWKFyAsAAICUyTQa0isUfFElydHpKPTCRUoya63Ry2QckFBJYiJlDh1KRa1beSTvRUVF4vqfm5tLERER0q8hciQzM5O0Wi01aNDA4nl+nJ6e7tI+fv31V9HsxkPujf2TvvrqK+rYsaPN9FyLNGvWLIsaIu5zNHToUKcF6g84ouZFe4cMGUIqlcrb2fEZKDeUG4453+Dvv1V1ejql3D+GlPHxHq11UVuVm76sjLR5eaTLzSVtbi7ptVoK69nTlD57yVIqO3/eIg3f6vLzSREbS1qzfXMwxEJSUynxs89EjVHMjBkU1ud6t/JsbOFxheQDIiPrL5NrfVz9gvv37y86UrsqODhYbNb4APDHH489gfb3egrKDeWGY843+OtvVZOXZ2qOSpv6GIV06ED1Z8yg8P79bF43tQWFpMvNEQFLxZYnbmUqFcU8NNGUtuGX/6ErC98XQY6+uNhiP8qEBGq1/RfT4+Jff6XiI0ds5lFXUGA78+XX6tITJyhzwQJq8eMGckdVvl/JB0SxsbGkUCgq1QbxfELWtUYAAAC1MTqKAwVP9nWpEeW1LiUnToh+Oop69UiVlERBzZpSo7ffNiW7eN99VHbhgs1dcJBjHhApCgpIc/VqRQK5nBR165K8XiSpGsRbvDfqwQco4rbhpIiMJHlkJCkiIklRL1I8Vqek0MXR91f+QLlcBEUcxMXNeopqk+QDoqCgIDGCjKvpzPsQ8eM777zTq3kDAIDAGx114d77SJWQ4LDWxR260lLS5uSIJqkgsylisr/6Wnw+vyY2rskpv6+Kj6dma75zGBgZ05acOkX17rqLwssHGHGAIgsKErccsIjgJbIeKSIiSBkXZ7GrjLvupH59+1JwTIwh0KlTh2QcxNgQOWKEw2Y9m4FQu3Y1Vq4+ERAVFBTQ2bNnTY8vXLggOkzzBIqNGzcW/XnGjRtHPXr0oD59+ohh8zzkfurUqV7NNwAABBZNdrbF6ChHzVF6jUY0LZkCmBxuglJSnQEDTGnSXn6Zyi4nWwQ3+pIS8VpwmzbU/PuKefmurVhhtyaHa6xc/yM0lP7mPFNzVJP/fCkCIleUNmpEIe3be66pkctMr/dqICSpgIgnSxw0aJDpsbFD84QJE+iLL76g0aNHizmE5syZQ2lpaWJ+oY0bN1KTJk1qNF+LFy8WG3fqBgCAwG2O0pWUkPbaNSo7f8Fmc5R5YMRNQRy4cOdha8GtW1sEREUHDtoOcmyMEIu8c4To22OoyalntkWSIirK+R9hpznK1WDIk5RcwxQbK2q2vB0ImfJEEsALrzob/f/444+LrTZNmzZNbNxLPTIyslY/GwAg0NRGc5S50tOnqSwvjzTXrpH2Wo4IeMSWk0PKBg2owXPPmtKeHXyzqBmqxBgYnTxpCow0mZkWwZC8bl1T8ML9d8zx36lXqysCm/J0oinK6m+PrW6riASao6xxINTyl58lFfxKIiACAACoSnOUEQcT5s1FeZs3kyYzyyK40eZcI821HArmzsQLF5rSpj7yqPgsW4JbtSIyC4g4SOHmL3l4OOlycuyOjio5fpxUiYnUfOOPhuAmIoJkSvuX2ohht9TcFy+h5ihb5F6omXIEAREAQICQanOUiVpjs9aFa2tC2rYlWWioGB7OwY0IdK5do9AOHajJ11+ZdpE+903SZmba3r+mfP/lglq0IB2PZObAJSqKFFGG2hllVBQp4w0Lghs1++5bkoWEiDxdvOdep81Rwc2bk7dIsTnKFyAgAgAIALXdHMXdIHSFRaS9li0CF5IrKLRDe9Praa++JoZva8TrOaKmptLcNOW1LpyuwHyotxltrmVtDffP0RUVWQQ3Itjh+/XrW6Rt9NlylzsHy0ND7byA5ih/gYAIACAAVKc5yhzPQixGTPF+srNFvxt5WDjV6d/PlCb50amk5jWquKkqO1sMGzcK7dGdmn79telx/i8/k/YfOzU5DvAw8IQ355KinrFGx7IzccP586hWoDnK7yAgAgAIJFbNUUEtW1LEHbeTKqGh6BujiI6myNtvMyU/f/dI0qSni2Hhxhobo9Du3S0CIt6n5p9/LNJwM5MiOoqUMbEWz9d/4glxq4yOFp/JgY0mI4MuT6yYBNBec5Rx/hxvQHOU/0JA5ACG3QOAr/TPETU4PJdNVhZpsrgWx3Cryc4iVVwchXTqZJVhQ3BTdvYsZb6/yCLIMQ+IRK0SN3mVk/NkfdwEFR1NIW3aWOwy/vXXRAdiRVS0aKZSRkeR3M6C2FGjRlV6TldcZPkEmqOgFiEgcgDD7gHAW/1zDH1wCg0BjrGZqrzJiwMd/qyIcWNNaU/36FlpbSmj0G7dKgdENvAIqvB+lrUviR/+H8mCQ0Rww/1wHE0AWPemm8gj0BwFXoCACACglvrncODCzU+mGhzxPkMtDt+qGidRfbP51v7u28+iH4650K5dTQERfwYHK5riYsOkfTExhqYovo2JpqDmLexn3klzVKgLgZSnoDkKvAkBEQBInreboxzhIEedmmp8YDF7MU/IF96vHzV6f6Ep7+eG3Ur60lKb+wrt0sUUEIkgJyaGdLm54lb0w4mOIUVMtLgNatbM4r3N1q4hBU/mZ6cGp/jECcsn0BwFYAEBEQBIWm0PFzcGOWUXLxqaqzJ5yyRNViZpy+8HNW9GDZ55xpT+yqynrXcgbni24vzNm+liSoqp9oXn1OG1qipqcQwBDt8GNbZcjqjFls0OJ69Tq9Wm+9yvxyVojgKwCQERAPj1cHGXg5xmzajBsxVBzoW7R5oW2bQWkl2xhAPngYM19eXLdj+bZy82LqbJQY6r+fbkTL5ojgJwDAERAPgGG2tGxc54klQNG5FOjKgqD3REkJMp7gc1bWpaj4qDkAsj77Hb8TjEbJ0qThvUuDHpSkvEcHFlLG9cixNDytj6FJSUaPFebhJzZfZi4769QYprRwFICQIigAAntf45ouNxRgZpMv4Rc9oUHzlie82okycpZcojpiYgW0I6drR4LIKckuLKQU5MLKmsgpzmP3xf/T9Cgv1zpLh2FICUICByAPMQgb+rzf45vJwCBzhi4xqc8oCn7OpViiksJBo+XKTjzz9363DSFxU52WH5JIEcDKmUFNqxk2gWUtaPtR/kfL+eapTE++cAgH0IiBzAPETg79xezkGvF4tsmgKd8o2brHhxydgpU0xp/+5vWGPKlvBGjSwec4DG61rx2lM803HxgQOV34TZiwHAgxAQAUDl/jnt21PUhPEU1LSZoT9OeaDDc91Ej33QYp4c81mMzQW3a2sREHFww+tc8a3YuMmKA56YaDputTp58w3/MwVkPFzcon+OBJuj0D8HwPchIAIIpP45Op2oDVLzKuMZGVT852Hb/XNOnKC0Z5+zGeSYB0Q8CSAHRIaVxA0BjnFTNbEcQt7s+/UkCw6uVBY8dLxg40aL52yWl8Sbo9A/B8C3ISAC8IP+OWKZh4IC0pQHOsx8xuHLkyZR6fkLou8OaTRV2jcHMWL+nPr1xagtc02++VpMPuhKMCAPCaHqwHBxAKgNCIgAJD5/jq60VDRX8Zw4wS1bmp5Pe/U1KrtwQQRBan7drH9O8HXXUfP160yP1elXxZIRglxu6HwcF0eysDAq3r+/2v1zeD81Dc1RAFAbEBABeGH+HA6MwvpcL4IYRUSEKWnmsmVi8kAxAqu8toc7LbPgNm0sRkkVHThAZefOWXyUWIk8rj4FNbOsyUl4Y45ouuNZkjmI4RXJfaV/jsgWhosDQA1DQARQW4z9c44fF4ERUyUmUsuftpmS5H7/PZWdtQxymCwoyBTEGNV/YjrpNVoRAKk40Klfn+RhYTY/Oqx7d8d5k3j/HACAmoaACHyWNzssl6VcIU1aKqnT08WmSUunsrQ0anzmDF1Zu5aafvmlS/sxLQpaLmrUKNIWFBgCnLg4UsbxbX3Radn674wYNsztvwP9cwAADBAQgU+qqQ7LHGSJWZLT0gz9bq6mkzotnUghp/gXXzSlS576qM2aHO42XJqf71JtDDeBxc22XBQ0evx4qk3onwMAYICAyAHMVO1fHZatgx19aQnVu7ei/8ylseNEvxxbeHi5eUAU1KQp6dVqUsUnkCq+ASkbxJM8rj4dTk6m62+7zXamjf1z2reXVLMU+ucAACAgcggzVfteh+WgFi2owfPPm4KNq/PnU9GBg2LeHZ5g0Jw8MtIiIOIZkcVtUBApE+JJ1SCelPENRNDDtzy03RjAJC3+sFJWeD6dwo0bKbhtW8sX0D8HAEDyUEMEPid3w49UsGuXzQ7LPOrKWGPEw8V57h2eZNDIPNhRJcSTXqslmUJRMRIrJMRmf53qQP8cAADfgYAIbJJpNKJGpLZosrJInZwsOhkbtjTTfV1hIbX8+SdT2tz166lwzx6H++ORXOlvzqP4V16hqDFjDM1aCQkOgx3uj+RJ6J8DAOA7EBBBJTxqqtn8tyhlxUqKmznT7b4uou8OBzfcd4dvr6SSJjuLEl57zZQm9bnnHQY52oJCUtQJF/fr3jyY5JERlP+j5XIPNicU7N3Lq98w+ucAAPgGBERQCXdUVhYUUKnVRIL2AiNtXp4Idngm5Do33mh6Pn3ePMrbtIm0/1j23TGKm/2MKcgJapxEpQ0TSNWwIakSGhpuxWZ4Th5asexD1P33U0jHjpYBkUQnFAQAAN+AgAiqNMNyeL9+pM3LJQ03aZXX+PAaWkZtDh4gebghyNGXlJqCIe6bYwpyEhJI1aghpzC9r8HLL4vmrSpDh2UAAPAABEQgJgLk/jtl3Icn5QoV/fmn7RmWT54UfXNs4b45HOxwbZExIIqeOJHqjRolankUUVEOa2yqWpuDDssAAOBJCIgCYIZlfVmZqMkpS04h9ZUUUqekUOy0aSQPDRWvZyxYQDnffud8R+WBEVPExlLD+fMMNT7x8aYgyFxw82ZUU9BhGQAAPAkBkR/MsKzX6cRq6OaLduasWUu569ZRWUqKWCTU2PxlFHnnnRTcqpW4r2qUSIroaFIlJVJQo0TSB6kof/331V4BvbagwzIAAHgKAiIfmGHZfP0snlOHa3i4pkfU+Ij7V0QtUPMfN1BwixaGz/knw2LWZVloKAUlNhLBjyopSTw2inn0EYqd+qjpcf6RI5YBETosAwCAn0NA5K2lO6w6LAe3by9GTykbxJHmyhVTsBP3zGwKSkoSafP+9wP988G/be9PoRDLUhgDojo33USqxCRDEJSYSAquPbITcNkNxNBhGQAAAgQCIm8v3VHeL6f0xAlKf/nlSi/Xu2ekKSDiJq6Qzp1EsxbX8qgSG1FQYvn9Bg1EvySjkNatxVYdyuho0tSpQ+FNmnhkHiIAAACpQ0AkQbKwMKp37z0i2OG1uYzq3nyz2GqaMj6eLrzwPA274w4KCgqq8c8DAADwNgREUiGxDst6pRK1QgAAEDAQEHkbOiwDAAB4HQIib0GHZQAAAMlAQFTbBR4TI0Z8eXIeIn9Y7d4XJrisDuQR5SglOB5RjlKik9g5XO7tDAQcvV4EGlIONkyr3Y95gAp275FkXnmCy7ODbqKL941CHlGOXofjEeUoJTgeqwcBkRcmZtRlZ5tWkpfiBd16tXsp5tE4wSVPVIk8ohy9DccjyhHnR9//zaDJzFusJmYMatmCosaModAuXbxefai+cMFOHltS1AMezKMb+yi7eNF+Hh98kEK7eqocXd+HRqOmoLR0Kj1zhrRKFZVdumw/j2M5j109kkd39qG+nGw7j61aUfTYsRTazTN5dESj0VDQ1atUdu4c6cqXnrHIY7KDPI7jPHbz+vHIs8XbzeP48R7MY+WyU/3zj/g92Co7izymptrMY3BrzuMECu3uoTy6QZOaZiePrSl6wngK7d7dI3nUaLWkysoSxxaPqK3Se9PT7edx4kQK7dHd68cjT9JrM49t2pTnsUe18qjRqEmZnW1YHUFZMe9d9fL4j808VmX1Bk+T6aUU1kqUcWLG3NxcioiIcGtfxSdO0MV77vVY3gAAAPyG3LNT0FTl+o0aIilSKEgZG1u993ogvtWp1aS7ds15HqOjyVv0ajVpc3IcJ1IoSBEd5caHVDW9nkpLSyk4OFj8606v0ZDOWR7lclJEuZNH975vkce8POd5dGemdid55FfVZWWkCgqyWR8n8lhQ4DyPdeuSt+i1WpfyKHcnj7bKUa8ntUZNKv7XupN/TXMe9YWFzvMYHu7ZPFbl7ZzH4mLHiWQykoeFufc55bVrSp5vrTp5LClxnkez9SKrkz93F/wmF/IoCwmp6p5Jq9GSQqlwO5Mij2VldldvKDl+nNLfnEctftxAtQUBkVRIaGJGXtw1ZfT9ks6j3Zo2L+ZRrVbTxo0bafjw4aRSqSSZR2tSyKN1uUkxj854K4/Oyk4KeayK2spjVcrNW3l0R03lUe1GuVU3j7UJAZG3Fnf1pYkZkUeUo5TgeEQ5SgmOR78pRwRE3lrc1RcmZkQeUY5SguMR5SglOB79rhwREHljYsbYWFLFx3v9y/fl1e59ohyRR5SjhOB4RDlKiVKC50cERLWMv/yWv/wsqdk5fXG1e18oR+QR5SglOB5RjlKikuA5HAGRF8glGmT42mr3vlCOyCPKUUpwPKIcpUQusXM4ZqoGAACAgIeACAAAAAIeAiIAAAAIeAiIAAAAIOAhIAIAAICAh4AIAAAAAh4CIgAAAAh4CIgAAAAg4CEgAgAAgICHmapdoNfrxS0v8hoI1Go1FRUVib9XpVJ5Ozs+A+WGcsMx5xvwWw2ccssrv24br+OOICByQX5+vrhNSkpy97sBAAAAL1zHIyMjHaaR6V0JmwKcTqej1NRUqlu3ruTX9/JURM3BX3JyMkVERHg7Oz4D5YZywzHnG/BbDZxy0+v1Ihhq2LAhyeWOewmhhsgFXIiJiYkUaPiA95WDXkpQbig3HHO+Ab/VwCi3SCc1Q0boVA0AAAABDwERAAAABDwERFBJcHAwvfrqq+IWXIdyqx6UW/Wh7FButSnYz68N6FQNAAAAAQ81RAAAABDwEBABAABAwENABAAAAAEPAREAAAAEPAREIMyfP5969uwpZuOOi4uju+66i06fPo3SqUY58mzmM2fORNm54MqVKzR27FiKiYmhsLAw6tKlCx08eBBl54BGo6F//etf1KxZMwoNDaXmzZvTnDlzxIz6YGnXrl10xx13iFmK+Xe5fv36SrMYv/baa+J1LsuBAwfSiRMnAr4YdzkoN17P7LnnnqOOHTtSeHi4SDN+/HixmoOvQ0AEws6dO2natGn0+++/07Zt28RJd+jQoVRYWIgSctH+/fvpk08+oU6dOqHMXHDt2jXq16+fWCRy06ZNdPLkSXrvvfeoXr16KD8HFixYQEuXLqUPP/yQTp06RW+//Ta988479H//938oNyt8/urcubMoK1u47BYuXChe599vfHw8DRkyxLR+ZaAqdFBuvLjroUOH6OWXXxa3a9eupTNnztCIESPI5/FaZgDWMjIyeI07/c6dO1E4LsjPz9e3atVKv23bNv2NN96onzFjBsrNieeee07fv39/lFMV3XbbbfpJkyZZPDdy5Ej92LFjUZYO8Pls3bp1psc6nU4fHx+vf+utt0zPlZSU6CMjI/VLly5FWdopN1v27dsn0l26dEnvy1BDBDbl5uaK2+joaJSQC7h27bbbbqObb74Z5eWiH374gXr06EH33XefaKbt2rUrLVu2DOXnRP/+/ennn38W/ypnR44coT179tDw4cNRdlVw4cIFSk9PFzXhRjzh4I033kh79+5FWVbxesFNa75eu4vFXaES/kfBrFmzxIm3Q4cOKCEnVq1aJaqOucodXHf+/HlasmSJONZefPFF2rdvHz355JPiosR9EsA27r/BF6DrrruOFAoFabVaevPNN2nMmDEosirgYIg1aNDA4nl+fOnSJZSli0pKSuj555+nBx54wKcWfLUFARFUMn36dDp69Kj4Vyc4lpycTDNmzKCtW7dSSEgIiqsKuBMw1xDNmzdPPOYaIu7QykESAiL7Vq9eTV9//TWtWLGC2rdvT4cPHxad+Llz64QJE3AMVhHXbFj/g9D6ObCNO1jff//94rf80Ucfka9DQAQWnnjiCdGUwaMMEhMTUTpO8IiojIwM6t69u+k5/hc7lx93SCwtLRX/iofKEhISqF27dhbPtW3bltasWYPicuCZZ54R/yLnCxHj0T5co8EjHBEQuY47UBtrivhYNOLfs3WtEdgOhkaNGiWaHn/55Refrx1i6EMEpn8Vcc0Qjxjgg5uH9IJzgwcPpmPHjol/pRs3rvV48MEHxX0EQ/bxCDPrqR24X0yTJk1w6DnAo3zkcstTNx9nGHZfNXyO46CIR9UalZWViRG3ffv2xTHoQjD0999/008//SSmzfAHqCECU6dgroL//vvvxVxExvb1yMhIMT8H2MZlZd3Piufm4BME+l859tRTT4kLDzeZ8cmV+xDxtAW8gX08Pwz3GWrcuLFoMvvzzz/F0PFJkyah2KwUFBTQ2bNnTY+5NoP/ocKDRbj8uKmRj79WrVqJje/zfFjcHyaQFTgoN26avffee0W/yQ0bNogaceP1gl8PCgoin+XtYW4gDXwo2No+//xzb2fN52DYvev+97//6Tt06KAPDg7WX3fddfpPPvmkBr8Z/5CXlyemdWjcuLE+JCRE37x5c/1LL72kLy0t9XbWJGf79u02z2sTJkwwDb1/9dVXxfB7PgZvuOEG/bFjx/SBbruDcrtw4YLd6wW/z5fJ+H/eDsoAAAAAvAl9iAAAACDgISACAACAgIeACAAAAAIeAiIAAAAIeAiIAAAAIOAhIAIAAICAh4AIAAAAAh4CIgAAAAh4CIgAwG/t2LFDrFyek5Pj7awAgMRhpmoA8BsDBw6kLl260KJFi0yLdWZnZ4vVyzkwAgCwB4u7AoDf4oUmeUVzAABn0GQGAH5h4sSJtHPnTvrggw9EbRBvX3zxhUWTGT+uV6+eWKW7TZs2YmVzXrm7sLCQvvzyS2ratClFRUXRE088IVbxNuKapmeffZYaNWpE4eHh1Lt3b9EcBwD+AzVEAOAXOBA6c+YMdejQgebMmSOeO3HiRKV0RUVF9O9//5tWrVpF+fn5NHLkSLFxoLRx40Y6f/483XPPPdS/f38aPXq0eM9DDz1EFy9eFO9p2LAhrVu3joYNG0bHjh2jVq1a1frfCgCeh4AIAPxCZGSkaCLjWh9jM9lff/1VKZ1araYlS5ZQixYtxGOuIfrqq6/o6tWrVKdOHWrXrh0NGjSItm/fLgKic+fO0cqVKyklJUUEQ2z27Nm0efNm+vzzz2nevHm1/JcCQE1AQAQAAYUDJmMwxLjDNTeVcTBk/lxGRoa4f+jQIdLr9dS6dWuL/ZSWllJMTEwt5hwAahICIgAIKCqVyuIx9zGy9ZxOpxP3+VahUNDBgwfFrTnzIAoAfBsCIgDwG9xkZt4Z2hO6du0q9sk1RgMGDPDovgFAOjDKDAD8Bjd9/fHHH6IDdGZmpqmWxx3cVPbggw/S+PHjae3atXThwgXav38/LViwQHTCBgD/gIAIAPwGd3bmZi3uGF2/fn26fPmyR/bLnac5IHr66afFcP0RI0aIwCspKckj+wcA78NM1QAAABDwUEMEAAAAAQ8BEQAAAAQ8BEQAAAAQ8BAQAQAAQMBDQAQAAAABDwERAAAABDwERAAAABDwEBABAABAwENABAAAAAEPAREAAAAEPAREAAAAQIHu/wEIEawMgOivEQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "for k, sym in zip(range(nSweeps+1), [\"o\", \"^\", \"s\", \">\"]):\n", " p = plt.semilogy(times[1:], residuals[k], sym+'-', label=f\"$k={k}$\")\n", " plt.semilogy(times[1:], error[k], sym+'--', c=p[0].get_color())\n", "plt.grid(); plt.xlabel(\"time\"); plt.ylabel(r\"residuals & error(--) ($L_\\infty$ norm)\"); plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that residuals are a good approximation of the numerical error for the first sweeps,\n", "but we also see some discrepancies for the last sweeps.\n", "While the residuals are relatively constant over time, the time-discretization error increases for the last sweeps,\n", "which is not shown by the residuals.\n", "\n", "This is because we only did 4 SDC sweeps here, so the SDC approach is way less accurate than the underlying collocation\n", "method using 4 Legendre Radau-Right nodes (order 7).\n", "This can be observed more in details by looking at different total numbers of sweeps $K$. \n", "For that, we can use the `monitor` parameter of the `solveDahlquistSDC` function (simpler code), \n", "extract the maximum $L_\\infty$ norm over all time-steps,\n", "and plot this versus the sweeps :" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qmat.solvers.sdc import solveDahlquistSDC\n", "\n", "for nSweeps, sym in zip([10, 8, 6, 4], [\"^\", \"o\", \"s\", \">\"]):\n", "\n", " uNum, monitors = solveDahlquistSDC(\n", " lam=lam, u0=u0, tEnd=tEnd, nSteps=nSteps, nSweeps=nSweeps,\n", " Q=Q, QDelta=QDelta, weights=weights,\n", " monitors=[\"residuals\", \"errors\"] # list of data we want to monitor for all nodes, time-steps and sweeps\n", " )\n", "\n", " # Extract maximum residuals and errors over time\n", " residuals = np.max(np.linalg.norm(monitors[\"residuals\"], axis=-1, ord=np.inf), axis=-1)\n", " errors = np.max(np.linalg.norm(monitors[\"errors\"], axis=-1, ord=np.inf), axis=-1)\n", "\n", " p = plt.semilogy(residuals, sym+'-', label=f\"$K={nSweeps}$\")\n", " plt.semilogy(errors, sym+'--', c=p[0].get_color())\n", "\n", "plt.grid(); plt.xlabel(\"sweeps\"); plt.ylabel(r\"max. residuals & error(--) ($L_\\infty$ norm)\")\n", "plt.ylim(1e-6, 2); plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here 8 sweeps are required to reach an accuracy below $1e^{-4}$, which is the accuracy of the collocation method.\n", "While the residuals decrease is almost identical when $K$ varies, this is not the same for the errors, \n", "that follows the residuals decrease only when $K$ is large enough.\n", "\n", "> 💡 If the time-discretization error of the underlying method is known a priori, then targeting a \n", "> **residual level close to the time-discretization error level** can be an acceptable stopping criterion.\n", "\n", "In practice, residuals can be also monitored to evaluate the quality of a $Q_\\Delta$ approximation. \n", "For instance, if we use the same SDC method, but using a trapezoidal rule for $Q_\\Delta$, \n", "and monitor residuals & errors ... " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "QDelta = genQDeltaCoeffs(\"TRAP\", qGen=coll)\n", "\n", "for nSweeps, sym in zip([10, 8, 6, 4], [\"^\", \"o\", \"s\", \">\"]):\n", "\n", " uNum, monitors = solveDahlquistSDC(\n", " lam=lam, u0=u0, tEnd=tEnd, nSteps=nSteps, nSweeps=nSweeps,\n", " Q=Q, QDelta=QDelta, weights=weights, monitors=[\"residuals\", \"errors\"])\n", "\n", " residuals = np.max(np.linalg.norm(monitors[\"residuals\"], axis=-1, ord=np.inf), axis=-1)\n", " errors = np.max(np.linalg.norm(monitors[\"errors\"], axis=-1, ord=np.inf), axis=-1)\n", "\n", " p = plt.semilogy(residuals, sym+'-', label=f\"$K={nSweeps}$\")\n", " plt.semilogy(errors, sym+'--', c=p[0].get_color())\n", "\n", "plt.grid(); plt.xlabel(\"sweeps\"); plt.ylabel(r\"max. residuals & error(--) ($L_\\infty$ norm)\");\n", "plt.ylim(1e-6, 2); plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... we can see that with this preconditioner, the SDC iteration converges **way faster to the collocation accuracy** (only two sweeps), and this is visible in some residuals value that decrease very quickly.\n", "\n", "Comparing the residuals evolution for different types of approximations can then give some first insights on the efficiency of different SDC variants, for instance when we compare the Backward-Euler sweep from the original SDC methods,\n", "the Trapezoidal rule and the `MIN-SR-NS` diagonal approximation from [[Caklovic et al., 2024]](https://arxiv.org/pdf/2403.18641>) :" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nSweeps = 4\n", "for qDelta, sym in zip([\"BE\", \"TRAP\", \"MIN-SR-NS\"], [\"o\", \">\", \"s\"]):\n", "\n", " QDelta = genQDeltaCoeffs(qDelta, qGen=coll)\n", "\n", " uNum, monitors = solveDahlquistSDC(\n", " lam=lam, u0=u0, tEnd=tEnd, nSteps=nSteps, nSweeps=nSweeps,\n", " Q=Q, QDelta=QDelta, weights=weights, monitors=[\"residuals\", \"errors\"])\n", "\n", " residuals = np.max(np.linalg.norm(monitors[\"residuals\"], axis=-1, ord=np.inf), axis=-1)\n", " errors = np.max(np.linalg.norm(monitors[\"errors\"], axis=-1, ord=np.inf), axis=-1)\n", "\n", " p = plt.semilogy(residuals, sym+'-', label=f\"{qDelta}\")\n", " plt.semilogy(errors, sym+'--', c=p[0].get_color())\n", "\n", "plt.grid(); plt.xlabel(\"sweeps\"); plt.ylabel(r\"max. residuals & error(--) ($L_\\infty$ norm)\");\n", "plt.ylim(1e-6, 2); plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the `MIN-SR-NS` coefficients require $K=4$ sweeps to reach the collocation accuracy, \n", "which is better than the `BE`-based sweep, but still twice larger as the `TRAP`-based SDC.\n", "\n", "However, measuring the number of iterations to a given accuracy is **not sufficient** to assess the efficiency of\n", "a SDC variant. Here for instance, since the `MIN-SR-S` approximation is diagonal, this enable some parallelism across\n", "the sweep update that can improve the time-to-solution.\n", "\n", "Also, we looked at convergence only for one $\\lambda$ value, and only considered the accuracy. \n", "While this is interesting for a first look, analyzing other numerical aspects of SDC variants is critical\n", "for a fair comparison, _e.g_ numerical stability for the problem of interest." ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 2 }