{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Step 4 : build a Spectral Deferred Correction type time-stepper\n", "\n", "📜 _Now that we can approximate the_ $Q$ _matrix from our time-stepping scheme :_\n", "\n", "$$\n", "\\begin{array}\n", " {c|c}\n", " \\tau & Q \\\\\n", " \\hline\n", " & w^\\top\n", "\\end{array}\n", "$$\n", "\n", "_with a given_ $Q_\\Delta$ _approximation, we can build a SDC-type time-stepper._\n", "\n", "> 💡 While SDC was originally built with a collocation method, nothing prevent to use exactly the same approach with any other type of $Q$-coefficients ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider (again) the _Dahlquist problem_ :\n", "\n", "$$\n", "\\frac{du}{dt} = \\lambda u, \\quad t \\in [0, T], \\quad u(0)=u_0,\n", "$$\n", "\n", "with $\\lambda=i$ (imaginary unit), $T=4\\pi$, and $u_0=e^{\\frac{i\\pi}{6}}$ :" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "lam = 1j\n", "T = 4*np.pi\n", "u0 = np.exp(1j*np.pi/6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let say we want to solve it numerically, using $12$ time-steps of the a SDC time-stepper using a $Q_\\Delta$ based on Backward Euler steps between the nodes. This is how we can do it with `qmat` :" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from qmat import Q_GENERATORS, QDELTA_GENERATORS\n", "\n", "coll = Q_GENERATORS[\"coll\"].getInstance() # use default input parameters for the Collocation class\n", "nodes, weights, Q = coll.genCoeffs()\n", "QDelta = QDELTA_GENERATORS[\"BE\"](nodes=nodes).getQDelta() # simple Backward Euler based approximation \n", "\n", "nSteps = 12\n", "uNum = np.zeros(nSteps+1, dtype=complex)\n", "uNum[0] = u0\n", "\n", "dt = T/nSteps\n", "A = np.eye(nodes.size) - lam*dt*Q # all-at-once system\n", "P = np.eye(nodes.size) - lam*dt*QDelta # preconditioner\n", "\n", "nSweeps = 4\n", "for i in range(nSteps):\n", "\n", " uNodes = np.ones(nodes.size)*uNum[i] # initial guess\n", " for k in range(nSweeps):\n", " r = uNum[i] - A @ uNodes # compute residuals\n", " d = np.linalg.solve(P, r) # solve with preconditioner\n", " uNodes += d # update solution\n", "\n", " uNum[i+1] = uNum[i] + lam*dt*weights.dot(uNodes) # prolongation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's explain a bit ... as for a [RK-type time-stepper](./02_rk.ipynb), we build the all-at-once system $A := I - \\lambda\\Delta{t}Q$ and its preconditioner $P:= I - \\lambda\\Delta{t}Q_\\Delta$. Then for each time-step, we define a number of iterations or **sweeps** $K=4$, and :\n", "\n", "1. starts with $u_n := [u_n, \\dots, u_n]^T$ as **initial guess** for the node solutions\n", "2. update the node solutions $u^k$ to $u^{k+1}$ for $k \\in \\{0, \\dots, K-1\\}$:\n", " - compute the **residuals** $r = u_n - A u^k$\n", " - solve with the preconditioner to retrieve the **defect** $d = P^{-1}r$\n", " - update the node solution with the defect $u^{k+1} = u^k + d$\n", "3. update the step solution with the **prolongation** applied on $u^{K}$\n", "\n", "And here is the obtained numerical solution and associated $L_\\infty$ error :" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L_inf error : 0.00535\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(uNum.real, uNum.imag, 'o-')\n", "plt.axis(\"equal\")\n", "\n", "times = np.linspace(0, T, nSteps+1)\n", "uExact = u0 * np.exp(lam*times)\n", "plt.plot(uExact.real, uExact.imag, ':', c=\"k\")\n", "print(\"L_inf error : {:1.5f}\".format(np.linalg.norm(uNum-uExact, ord=np.inf)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the error is not as small as the [collocation solution in tutorial 2](./02_rk.ipynb), this is still more accurate compared to the RK4 method in the same tutorial. In fact, SDC's accuracy depends on the number of **sweeps** performed within each steps; if we write the full **sweep update** (iteration) :\n", "\n", "$$\n", "u^{k+1} = u^{k} + P^{-1} \\left[u_n - A u^{k}\\right],\n", "$$\n", "\n", "we can see that **if it converges** to a fixed point solution $u^{\\infty}$ (which we assume for now), then its is simply the solution of the all-at-once system as $u_n - A u^{\\infty} = 0$.\n", "\n", "And if we look at the structure of $P$ here :" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P :\n", "[[1.-0.09276909j 0.+0.j 0.+0.j 0.+0.j ]\n", " [0.-0.09276909j 1.-0.3360236j 0.+0.j 0.+0.j ]\n", " [0.-0.09276909j 0.-0.3360236j 1.-0.39604236j 0.+0.j ]\n", " [0.-0.09276909j 0.-0.3360236j 0.-0.39604236j 1.-0.22236249j]]\n" ] } ], "source": [ "print(\"P :\")\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\Rightarrow$ this is a lower triangular matrix, which means that we don't need to solve the system _all-at-once_, but we can solve it line by line as it is done for classical RK method (_c.f_ [tutorial 2](./02_rk.ipynb)).\n", "\n", "However, this comes with some drawback : since it's an **iterative process**, one should do enough sweeps to retrieve a satisfying accuracy. To look deeper into it, we simplify the node solution update by\n", "replacing in it $P$ and $A$ by their expression :\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", "This update formula is more stable from a numerical perspective and simpler from an implementation perspective. \n", "So our SDC time-steppers becomes :" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "nSweeps = 4\n", "for i in range(nSteps):\n", "\n", " uNodes = np.ones(nodes.size)*uNum[i] # initial guess\n", " for k in range(nSweeps):\n", " # nodes solution update\n", " b = uNum[i] + lam*dt*(Q-QDelta) @ uNodes\n", " uNodes = np.linalg.solve(P, b) \n", "\n", " uNum[i+1] = uNum[i] + lam*dt*weights.dot(uNodes) # prolongation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, some convenience functions are provided by `qmat` directly, so we compute the SDC solution with : " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from qmat.sdc import solveDahlquistSDC\n", "uNum = solveDahlquistSDC(lam, u0, T, nSteps, nSweeps, Q, QDelta, weights)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and we observe of the solution evolves with each sweeps :" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for nSweeps, sym in zip([1, 2, 3], ['o', 's', '>']):\n", " uNum = solveDahlquistSDC(lam, u0, T, nSteps, nSweeps, Q, QDelta, weights)\n", " plt.plot(uNum.real, uNum.imag, sym+'-', label=f\"K={nSweeps}\")\n", "plt.axis(\"equal\")\n", "plt.legend()\n", "plt.plot(uExact.real, uExact.imag, ':', c=\"k\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the first sweep, the numerical solution is very far from the exact solution. \n", "And as expected, doing more sweeps corrects it toward the exact solution.\n", "\n", "This can be illustrated more rigorously looking at the $L_\\infty$ error :" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "nSweeps=1, err=0.84538\n", "nSweeps=2, err=0.14365\n", "nSweeps=3, err=0.02750\n", "nSweeps=4, err=0.00535\n", "nSweeps=5, err=0.00106\n", "nSweeps=6, err=0.00021\n", "nSweeps=8, err=0.00002\n", "nSweeps=9, err=0.00001\n" ] } ], "source": [ "from qmat.sdc import errorDahlquistSDC\n", "\n", "for nSweeps in [1, 2, 3, 4, 5, 6, 8, 9]:\n", " err = errorDahlquistSDC(lam, u0, T, nSteps, nSweeps, Q, QDelta, weights)\n", " print(f\"nSweeps={nSweeps}, err={err:1.5f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In particular, for the $Q_\\Delta$ based on Backward Euler, it takes $K=9$ sweeps to reach a similar accuracy as this of the underlying collocation method (cf [tutorial 2](./02_rk.ipynb)).\n", "\n", "The choice of $Q_\\Delta$ for the preconditioner has actually a big impact on how fast SDC converges to the solution of the all-at-once system, hence the different $Q_\\Delta$-generators provided by `qmat`.\n", "For instance, using those _magical_ `MIN3` coefficients introduced in [tutorial 2](./03_qDelta.ipynb) ..." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "nSweeps=1, err=1.62904\n", "nSweeps=2, err=0.05860\n", "nSweeps=3, err=0.00558\n", "nSweeps=4, err=0.00036\n", "nSweeps=5, err=0.00002\n", "nSweeps=6, err=0.00001\n", "nSweeps=8, err=0.00001\n", "nSweeps=9, err=0.00001\n" ] } ], "source": [ "QDelta = QDELTA_GENERATORS[\"MIN3\"](nNodes=coll.nNodes, nodeType=coll.nodeType, quadType=coll.quadType).getQDelta()\n", "for nSweeps in [1, 2, 3, 4, 5, 6, 8, 9]:\n", " err = errorDahlquistSDC(lam, u0, T, nSteps, nSweeps, Q, QDelta, weights)\n", " print(f\"nSweeps={nSweeps}, err={err:1.5f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... makes SDC converge way faster to the solution of the _all-at-once system_ !\n", "However, evaluating the quality of a given $Q_\\Delta$ for more complex problems\n", "can be difficult as usually no exact solution is known beforehand to compute the error.\n", "\n", "But SDC also provides a built-in indicator to estimate the error,\n", "by [monitoring the residuals after each sweeps ...](./05_residuals.ipynb)" ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 2 }