{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Step 4 : build a Spectral Deferred Correction solver\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", "tEnd = 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 = tEnd/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) # step update" ] }, { "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 **step update** using $u^{K}$ values\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, tEnd, 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) # step update" ] }, { "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.solvers.sdc import solveDahlquistSDC\n", "uNum = solveDahlquistSDC(lam, u0, tEnd, nSteps, nSweeps, Q, QDelta, weights)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and we observe how the solution evolves with each sweeps :" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for nSweeps, sym in zip([1, 2, 3], ['o', 's', '>']):\n", " uNum = solveDahlquistSDC(lam, u0, tEnd, 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.solvers.sdc import errorDahlquistSDC\n", "\n", "for nSweeps in [1, 2, 3, 4, 5, 6, 8, 9]:\n", " err = errorDahlquistSDC(lam, u0, tEnd, 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, tEnd, 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 }