{ "cells": [ { "cell_type": "raw", "id": "c45a2da1", "metadata": { "vscode": { "languageId": "raw" } }, "source": [ "---\n", "title: \"Lecture 05 - Time integration\"\n", "subtitle: \"SSP and symplectic methods\"\n", "author: \"Georgii Oblapenko\"\n", "jupyter: fenicsx\n", "# execute:\n", "# freeze: auto\n", "format:\n", " html:\n", " output-file: 05-notes.html\n", " embed-resources: true\n", " pdf: default\n", " revealjs:\n", " output-file: 05-slides.html\n", " theme: [default, ../styles/theme.scss]\n", " logo: ../images/rwth_acom_en_rgb.png\n", " center: false\n", " smaller: true\n", " slide-number: c/t\n", " show-slide-number: all\n", " sc-sb-title: true\n", " toc: true\n", " toc-depth: 2\n", " toc-title: Contents\n", " slide-level: 3\n", " embed-resources: true\n", " # navigation-mode: vertical\n", "format-links:\n", " - pdf\n", " - revealjs\n", " - href: 05.ipynb\n", " text: Jupyter\n", " icon: journal-code\n", "execute:\n", " echo: true\n", "---" ] }, { "cell_type": "markdown", "id": "d3e67ba4", "metadata": {}, "source": [ "## Objectives\n", "\n", "In this lecture, we will learn about advanced methods for solving time-dependent PDEs and ODEs. In particular, we will be discussing\n", "\n", "1. Stability\n", "2. Monotonicity\n", "3. \"Structure\" preservation" ] }, { "cell_type": "markdown", "id": "8482ae94", "metadata": {}, "source": [ "## ODEs: why?\n", "Want to solve ODE\n", "\n", "$$\n", "d\\frac{u}{dt} = f(u,t),\\quad u \\in \\mathbb{R}^n, \\: t > 0, \\quad u(0) = u^0.\n", "$$\n", "\n", "ODEs come from\n", "\n", "- direct description of system (i.e. biology, chemical reactors)\n", "- semi-discretization of system (i.e. $u$ --- vector of cell values from a FVM discretization, RHS are the fluxes + sources)\n", "\n", "\n", "::: {.callout-note}\n", "**Method of lines**: discretize in space, solve in time. Take PDE\n", "$$\n", "\\partial_t{u(x,t)} + \\sum_{\\alpha} \\partial_{\\alpha} a_{\\alpha} u(x,t) = f(u(x,t),t),\n", "$$\n", "\n", "discretize in space (FD/FVM/FEM/DG): $u(x_i,t)=u_i(t)$, discretize operators in terms of $\\{u_j\\}$, obtain ODEs\n", "$$\n", "\\partial_t{\\mathbf{u}} + \\mathbf{A} \\mathbf{u}(t) = \\mathbf{f}(t).\n", "$$\n", ":::\n", "\n" ] }, { "cell_type": "markdown", "id": "293ebdf1", "metadata": {}, "source": [ "### PDE discretization - remark\n", "\n", "\n", "::: {.callout-important title=\"Alternatives to Method of Lines\"}\n", "Are all discretizations of time-dependent PDEs in time done via Method of Lines?\n", ":::\n", "\n", "\n", "::: {.fragment}\n", "Lax-Wendroff: couples time and space discretization.\n", "For linear advection\n", "$$\n", "\\partial_t u + a_0 \\partial_x u = 0,\\:C = \\frac{a_0 \\Delta t}{\\Delta x}\n", "$$\n", "\n", "$$\n", "u_j^{n+1} = u_j^n + \\frac{C}{2}(1+C)u_{j-1}^n + (1-C^2)u_{j}^n - \\frac{C}{2}(1+C)u_{j+1}^n\n", "$$\n", ":::" ] }, { "cell_type": "markdown", "id": "7d75ace2", "metadata": {}, "source": [ "### ODE solvers: computational cost\n", "\n", "::: {.content-visible when-format=\"revealjs\"}\n", "\n", "We want *best accuracy* and *minimum computational cost*.\n", "\n", "- Cost related to number of evaluations of $f(u,t)$, but also to timestep size\n", "- Harder for adaptive methods, since they change $\\Delta t$ based on error estimate\n", "- Even harder for implicit methods, since they involve solution of non-linear systems\n", ":::\n", "\n", "::: {.content-visible when-format=\"html\" unless-format=\"revealjs\"}\n", "As with any numerical method, we want to achieve best possible accuracy and minimum computational cost.\n", "Cost is easier to quantify, at least for non-adaptive explicit methods: for a given time step $\\Delta t$, how many times do we need to evaluate $f(u,t)$ to compute $u(t+\\Delta t)$, given $u(t)$?. But cost is also related to $\\Delta t$: smaller $\\Delta t$ means more steps to reach final time.\n", "Becomes harder for adaptive methods, i.e. methods that change $\\Delta t$ based on some error estimate. Even harder for implicit methods, since they involve solution of non-linear systems:\n", "depends on linear solver, condition number of Jacobian, etc.\n", ":::" ] }, { "cell_type": "markdown", "id": "f71c6680", "metadata": {}, "source": [ "### ODE solvers: accuracy\n", "\n", "\n", "::: {.fragment}\n", "**Example 1**: you want to model a system of chemical reactions. Which method would you choose?\n", "\n", "1. Method with $\\mathcal{O}(\\Delta t^4)$ error, but still might lead to negative densities\n", "1. Method with $\\mathcal{O}(\\Delta t^2)$ error, but preserves non-negativity of densities\n", ":::\n", "\n", "::: {.fragment}\n", "**Example 2**: you want to model a system of particles. Which method would you choose?\n", "\n", "1. Method with $\\mathcal{O}(\\Delta t^4)$ error, but does not conserve energy\n", "1. Method with $\\mathcal{O}(\\Delta t^2)$ error, but conserves energy\n", ":::\n", "\n", "::: {.fragment}\n", "We therefore will focus on different (not all!) notions of error/accuracy and talk about some problem-specific methods.\n", ":::\n", "\n", "\n", "::: {.content-visible when-format=\"html\" unless-format=\"revealjs\"}\n", "But first, let us recall some classical ODE methods to 1) introduce some notation 2) use them as building blocks for other methods 3) use them as baseline methods for comparisons.\n", ":::" ] }, { "cell_type": "markdown", "id": "344451ad", "metadata": {}, "source": [ "## Recap of some standard methods\n", "\n", "Let's recall some textbook methods first.\n", "\n", "$$\n", "t_n = n \\Delta t, \\quad u^n = u(t_n).\n", "$$\n", "\n", "::: {.content-visible when-format=\"revealjs\"}\n", "\n", "::: {.callout-tip}\n", "Which methods would you name?\n", ":::\n", "\n", ":::\n", "\n" ] }, { "cell_type": "markdown", "id": "3fed7801", "metadata": {}, "source": [ "\n", "### Forward Euler\n", "\n", "Simplest approach:\n", "$$\n", " u^{n+1} = u^n + \\Delta t f(u^n, t^n)\n", "$$\n", "\n", "::: {.callout-tip}\n", "## Properties?\n", "$\\mathcal{O}(\\Delta t)$ error; what else?\n", ":::" ] }, { "cell_type": "markdown", "id": "4b8be743", "metadata": {}, "source": [ "### RK4\n", "\n", "::: {.fragment}\n", "$$\n", " k_1 = \\Delta t f(u^n, t^n),\n", "$$\n", ":::\n", "\n", "::: {.fragment}\n", "$$\n", " k_2 = \\Delta t f(u^n + \\frac{1}{2}k_1, t^n + \\frac{1}{2}\\Delta t),\n", "$$\n", ":::\n", "\n", "::: {.fragment}\n", "$$\n", " k_3 = \\Delta t f(u^n + \\frac{1}{2}k_2, t^n + \\frac{1}{2}\\Delta t),\n", "$$\n", ":::\n", "\n", "::: {.fragment}\n", "$$\n", " k_4 = \\Delta t f(u^n + k_3, t^n \\Delta t),\n", "$$\n", ":::\n", "\n", "::: {.fragment}\n", "$$\n", " u^{n+1} = u^n + \\frac{1}{6}k_1 + \\frac{1}{3}k_2 + \\frac{1}{3}k_3 + \\frac{1}{6}k_4\n", "$$\n", ":::\n", "\n", "::: {.fragment}\n", "::: {.callout-tip}\n", "## Properties?\n", "$\\mathcal{O}((\\Delta t)^4)$ error; what else?\n", ":::\n", ":::" ] }, { "cell_type": "markdown", "id": "9bbe981c", "metadata": {}, "source": [ "## Stability, monotonicity\n", "\n", "Let's discuss stability and monotonicity. These are not identical properties!\n", "\n", "\n", "\n", "::: {.content-visible when-format=\"revealjs\"}\n", "\n", "::: {.callout-tip}\n", "## Question\n", "Which one is stronger?\n", ":::\n", "\n", ":::\n" ] }, { "cell_type": "markdown", "id": "f4dea8f5", "metadata": {}, "source": [ "### Stability\n", "\n", "Linear analysis:\n", "\n", "$$\n", "u' = -\\alpha u,\\: \\alpha \\in \\mathbb{C},\\, Re(\\alpha) > 0 \\Rightarrow u(t) = u_0 e^{-\\alpha t}.\n", "$$\n", "\n", "Expect numerically for $\\alpha: Re(\\alpha) < 0$:\n", "\n", "$$\n", " \\lim_{n \\to \\infty} u^{n} = 0\n", "$$\n", "\n", "I.e. solution does not \"blow up\".\n", "\n", "::: {.callout-note}\n", "## Stability\n", "For forward Euler:\n", "$\\Delta t < \\frac{2}{\\alpha}$\n", ":::\n", "\n", "\n", "::: {.content-visible when-format=\"html\" unless-format=\"revealjs\"}\n", "We can derive the stability condition for the forward Euler method as follows:\n", "\n", "$$\n", "u_{n+1} = u_n + \\Delta t \\cdot (-\\alpha u_n) = (1 - \\alpha \\Delta t) u_n,\n", "$$\n", "\n", "$$\n", "|1 - \\alpha \\Delta t| \\leq 1 \\implies -1 \\leq 1 - \\alpha \\Delta t \\leq 1,\n", "$$\n", "\n", "from which we get\n", "$$\n", "0 < \\Delta t \\leq \\frac{2}{\\alpha}.\n", "$$\n", ":::" ] }, { "cell_type": "markdown", "id": "a6212914", "metadata": {}, "source": [ "### Monotonicity\n", "\n", "\n", "$$\n", "u(t) = u_0 e^{-\\alpha t}: t_2 > t_1 \\Rightarrow |u(t_1)| > |u(t_2)|\n", "$$\n", "\n", "Expect numerically:\n", "$$\n", " |u^{n}| \\leq |u^{n-1}|\n", "$$\n", "\n", "::: {.callout-note}\n", "## Monotonicity\n", "For forward Euler:\n", "$\\Delta t < \\frac{1}{\\alpha}$\n", ":::\n", "\n", "\n", "\n", "::: {.fragment}\n", "Example where monotonicity may be desirable:\n", "\n", "$$\n", " \\mathbf{u} = (\\rho, \\rho v_1, \\rho v_2, \\rho e),\n", "$$\n", "if $\\rho$ or $\\rho e$ become negative - solver might crash or produce meaningless results!\n", ":::\n", "\n", "::: {.fragment}\n", "::: {.callout-note}\n", "## Generalized stability/monotonicity\n", "Consider $G(u^{n})$ instead of $|u^{n}|$, where $G$ is a 1) norm 2) semi-norm or 3) convex functional\n", ":::\n", ":::" ] }, { "cell_type": "markdown", "id": "1071099e", "metadata": {}, "source": [ "### Numerical example\n", "\n", "$$\n", "u' = -\\alpha u,\\: \\alpha > 0,\\: u(0) = u_0\n", "$$\n", "\n", "\n", "::: {.callout-note}\n", "For forward Euler:\n", "Monotonicity: $\\Delta t < \\frac{1}{\\alpha}$, stability: $\\Delta t < \\frac{2}{\\alpha}$.\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "id": "2062109f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| code-line-numbers: true\n", "#| code-fold: true\n", "#| label: linear-stability\n", "#| fig-cap: \"Euler's method for $du/dt = -a u$\"\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "\n", "def forward_euler(alpha, u0, times):\n", " u = np.zeros(len(times))\n", " u[0] = u0\n", " for (i, t) in enumerate(times[1:]):\n", " u[i+1] = u[i] + (times[i+1] - times[i]) * (-alpha * u[i])\n", " return u\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(6.5, 4.2))\n", "\n", "u0 = 2.0\n", "\n", "alpha = 10.0\n", "times = np.linspace(0, 1, 100)\n", "\n", "times_fe1 = np.linspace(0, 1, 5)\n", "dt1 = times_fe1[1] - times_fe1[0]\n", "\n", "times_fe2 = np.linspace(0, 1, 10)\n", "dt2 = times_fe2[1] - times_fe2[0]\n", "\n", "times_fe3 = np.linspace(0, 1, 12)\n", "dt3 = times_fe3[1] - times_fe3[0]\n", "\n", "dts = r\"$\\Delta t$\"\n", "oas = r\"$1/\\alpha$\"\n", "tas = r\"$2/\\alpha$\"\n", "\n", "\n", "ax.plot(times, u0 * np.exp(-alpha * times),\n", " 'k-', label=f\"Analytical\")\n", "ax.plot(times_fe1, forward_euler(alpha, u0, times_fe1),\n", " color='tab:red', label=f\"F.E. ({dts} = {dt1:.3f}; {tas} = {2.0/alpha:.2f})\")\n", "ax.plot(times_fe2, forward_euler(alpha, u0, times_fe2),\n", " color='tab:purple', label=f\"F.E. ({dts} = {dt2:.3f}; {oas} = {1.0/alpha:.2f})\")\n", "ax.plot(times_fe3, forward_euler(alpha, u0, times_fe3),\n", " color='tab:blue',\n", " label=f\"F.E. ({dts} = {dt3:.3f})\")\n", "\n", "ax.legend(fontsize=12)\n", "ax.set_xlabel(\"t\", fontsize=10)\n", "ax.set_ylabel(\"u\", fontsize=10)\n", "ax.tick_params(axis='both', labelsize=8)\n", "\n", "ax.set_yscale(\"log\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f0897868", "metadata": {}, "source": [ "### Region of absolute stability\n", "\n", "Re-write discretization of ODE ($-\\alpha \\to \\lambda$)\n", "\n", "$$\n", "u'(t) = \\lambda u,\\: u^n = R(\\lambda \\Delta t) u^{n-1},\n", "$$\n", "\n", "$R(z), z \\in \\mathbb{C}$ is called the stability function.\n", "\n", "Region of absolute stability:\n", "$$\n", "\\mathcal{S} = \\{ z \\in \\mathbb{C} | |R(z)| < 1 \\}\n", "$$" ] }, { "cell_type": "markdown", "id": "df8ee0a2", "metadata": {}, "source": [ "### Region of absolute stability: examples\n", "\n", "Forward Euler: \n", "$$\n", "R(z) = 1 + z \n", "$$\n", "\n", "Backward (implicit Euler):\n", "$$\n", "u^{n+1} = u^n + \\Delta \\lambda t u^{n+1} \\implies R(z) = \\frac{1}{1 + z}\n", "$$\n", "\n", "RK4:\n", "$$\n", "R(z) = 1 + z + \\frac{1}{2!} z^2 + \\frac{1}{3!} z^3 + \\frac{1}{4!} z^4\n", "$$" ] }, { "cell_type": "markdown", "id": "dbec4189", "metadata": {}, "source": [ "## SSPRK methods\n", "\n", "Strong stability-preserving (Total Variation Diminishing) Runge-Kutta methods:\n", "\n", "- ensure strong stability/monotonicity of solutions **and** have higher order than forward Euler: $||u^{n+1}|| \\leq ||u^n||$ (or a generalized $G(u)$) for all $n$\n", "- *usually* written as convex combination of forward Euler steps" ] }, { "cell_type": "markdown", "id": "7978858a", "metadata": {}, "source": [ "### SSPRK methods: formulation\n", "\n", "An m-stage method for $u' = f(u)$ is written as (*Shu-Osher form*)\n", "$$\n", "u^{(0)} = u^n, \n", "$$\n", "\n", "$$\n", "u^{(i)} = \\sum_{j=0}^{i-1} \\left(\\alpha_{ij} u^{(j)} + \\Delta t \\beta_{ij} f(u^{(j)}) \\right), \\quad i = 1, \\dots, m; \\: \\alpha_{ij} \\geq 0,\n", "$$\n", "\n", "$$\n", "u^{n+1} = u^{(m)}.\n", "$$" ] }, { "cell_type": "markdown", "id": "9e825530", "metadata": {}, "source": [ "### Theorem\n", "::: {.callout-note}\n", "## Theorem\n", "If $||u^{n+1}|| \\leq ||u^n||$ in the forward Euler method with $\\Delta t \\leq \\Delta_{FE}$, then the SSPRK method is stable for $\\Delta t \\leq c_{SSP} \\Delta_{FE}$.\n", ":::\n", "\n", "- $c_{SSP}$ is called the **SSP coefficient**, $c_{SSP} = \\min \\frac{\\alpha_{ij}}{\\beta_{ij}}$\n", "- Most research focused on finding SSPRK methods with largest $c_{SSP}$\n", "- $\\Delta_{FE}$ - depends on spatial discretization, $c_{SSP}$ - on time-stepping scheme" ] }, { "cell_type": "markdown", "id": "2089f856", "metadata": {}, "source": [ "### SSPRK examples\n", "\n", "**SSPRK2**:\n", "$$\n", "u^{(1)} = u^n + \\Delta t f(u^n),\n", "$$\n", "$$\n", "u^{(n+1)} = \\frac{1}{2}u^n + \\frac{1}{2}u^{(1)} + \\frac{1}{2}\\Delta t f(u^{(1)}).\n", "$$\n", "\n", "\n", "**SSPRK3**:\n", "$$\n", "u^{(1)} = u^n + \\Delta t f(u^n),\n", "$$\n", "$$\n", "u^{(2)} = \\frac{3}{4}u^n + \\frac{1}{4}u^{(1)} + \\frac{1}{4}\\Delta t f(u^{(1)}),\n", "$$\n", "$$\n", "u^{(n+1)} = \\frac{1}{3}u^n + \\frac{2}{3}u^{(2)} + \\frac{2}{3}\\Delta t f(u^{(2)}).\n", "$$" ] }, { "cell_type": "markdown", "id": "b4359b46", "metadata": {}, "source": [ "### SSP coefficient, effective CFL\n", "::: {.callout-note}\n", "## Question\n", "What does $c_{SSP} = 1$ (for example, SSPRK3) mean?\n", ":::\n", "\n", "::: {.fragment}\n", "Makes more sense to talk about **effective CFL**: $c_{eff} = c_{SSP} / k$, $k$ - number of evaluations of RHS.\n", "For example, SSPRK3 has $c_{eff} = 1/3$ (but third-order convergence!).\n", "\n", "::: {.callout-important title=\"Stability vs. monotonicity vs. accuracy\"}\n", "SSPRK methods may have same restrictions on $\\Delta t$ to achieve monotonicity, but\n", "\n", "- are more accurate\n", "- have a larger stability region (monotone $\\neq$ stable!)\n", ":::\n", ":::" ] }, { "cell_type": "markdown", "id": "46a35f03", "metadata": {}, "source": [ "## Stability for oscillatory problems\n", "\n", "Consider harmonic oscillator\n", "\n", "$$\n", " \\frac{d}{dt}\n", " \\begin{pmatrix}\n", " u_1 \\\\ u_2\n", " \\end{pmatrix}\n", " = \n", " \\begin{pmatrix}\n", " u_2 \\\\\n", " - \\omega^2 u_1\n", " \\end{pmatrix}\n", "$$\n", "\n", "Analytical solution:\n", "$$\n", "\\begin{pmatrix}\n", " u_1 \\\\ u_2\n", " \\end{pmatrix}\n", " = \n", " c_1 \\begin{pmatrix}\n", " \\cos(\\omega t) \\\\ -\\omega\\sin(\\omega t)\n", " \\end{pmatrix}\n", " + c_2 \\begin{pmatrix}\n", " \\frac{1}{\\omega}\\sin(\\omega t) \\\\ \\cos(\\omega t)\n", " \\end{pmatrix}\n", "$$" ] }, { "cell_type": "markdown", "id": "22004177", "metadata": {}, "source": [ "### Forward Euler\n", "\n", "Energy is given by\n", "$$\n", "E = (\\omega^2 u_1^2 + u_2^2)/2\n", "$$\n", "and is conserved for the analytical solution.\n", "\n", "::: {.callout-note}\n", "## Energy blow-up\n", "For forward Euler we can show that \n", "$E^{n+1} = \\frac{1}{2} (1 + \\omega^2 \\Delta t^2) \\left( \\omega^2 (u_1^n)^2 + (u_2^n)^2 \\right)$.\n", "Eigenvalues of harmonic oscillator system are purely imaginary ($\\pm i\\omega$) and do not lie in stability region of forward Euler.\n", ":::" ] }, { "cell_type": "markdown", "id": "bc871d50", "metadata": {}, "source": [ "### Forward Euler: analysis\n", "\n", "Let's write the forward Euler scheme as a matrix equation\n", "$$\n", " \\begin{pmatrix}\n", " u_1^{n+1} \\\\ u_2^{n+1}\n", " \\end{pmatrix}\n", " = \n", " \\begin{pmatrix}\n", " 1 & \\Delta t \\\\\n", " -\\omega^2 \\Delta t & 1 \n", " \\end{pmatrix}\n", " \\begin{pmatrix}\n", " u_1^{n} \\\\\n", " u_2^{n}\n", " \\end{pmatrix} =: J \\mathbf{u}\n", "$$\n", "\n", "::: {.callout-note}\n", "## Determinant of $J$\n", "Note that $det(J) = (1 + \\omega^2 \\Delta t^2)$ is exactly the energy growth factor!\n", ":::\n", "\n", "::: {.fragment}\n", "Re-write integration step via **growth factor** $\\gamma$:\n", "$$\n", "u_1^{n+1} = \\gamma u_1^n,\\:u_2^{n+1} = \\gamma u_2^n \\implies \n", "\\begin{pmatrix}\n", " \\gamma - 1 & -\\Delta t \\\\\n", " \\omega^2 \\Delta t & \\gamma - 1 \n", " \\end{pmatrix}\n", "\\begin{pmatrix}\n", " u_1^{n} \\\\ u_2^{n}\n", " \\end{pmatrix}\n", " = \n", " \\begin{pmatrix}\n", " 0 \\\\\n", " 0\n", " \\end{pmatrix}\n", "$$\n", "\n", "::: {.callout-note}\n", "## Exercise\n", "Non-trivial solution $\\implies$ $det(LHS) = 0$; can show that $|\\gamma| > 1$, i.e. method is unstable.\n", ":::\n", ":::" ] }, { "cell_type": "markdown", "id": "30a48031", "metadata": {}, "source": [ "### Example - harmonic oscillator" ] }, { "cell_type": "code", "execution_count": 3, "id": "7e18b42c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dE F.E. (dt=0.051) at t=5.0: -1.057e+01\n", "dE F.E. (dt=0.013) at t=5.0: -9.460e-01\n", "dE SSPRK2 (dt=0.063) at t=5.0: -3.250e-02\n", "dE RK2 (dt=0.063) at t=5.0: 3.461e-01\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| code-line-numbers: true\n", "#| code-fold: true\n", "#| fig-cap: \"Harmonic oscillator phase space (left) and energy (right), omega=3\"\n", "def forward_euler_generic(rhs, u0, times, omega):\n", " u = np.zeros((len(times), len(u0)))\n", " u[0,:] = u0\n", " for (i, t) in enumerate(times[1:]):\n", " u[i+1,:] = u[i,:] + (times[i+1] - times[i]) * rhs(u[i,:], omega)\n", " return u\n", "\n", "def ssprk22_generic(rhs, u0, times, omega):\n", " u = np.zeros((len(times), len(u0)))\n", " u[0,:] = u0\n", " for (i, t) in enumerate(times[1:]):\n", " u_1 = u[i,:] + (times[i+1] - times[i]) * rhs(u[i,:], omega)\n", " u[i+1,:] = 0.5 * u[i,:]+ 0.5 * u_1 + 0.5 * (times[i+1] - times[i]) * rhs(u_1, omega)\n", " return u\n", "\n", "def rk2_generic(rhs, u0, times, omega):\n", " # Ralston's method\n", " u = np.zeros((len(times), len(u0)))\n", " u[0,:] = u0\n", " for (i, t) in enumerate(times[1:]):\n", " dt = (times[i+1] - times[i])\n", " k1 = rhs(u[i,:], omega)\n", " k2 = rhs(u[i,:] + 0.75 * k1 * dt, omega)\n", " u[i+1,:] = u[i,:] + dt * (0.25 * k1 + 0.75 * k2)\n", " return u\n", "\n", "def harmonic_rhs(u, omega):\n", " return np.array([u[1], -omega**2 * u[0]])\n", "\n", "def energy(u, omega):\n", " return 0.5 * (u[:,1]**2 + omega**2 * u[:,0]**2)\n", "\n", "fig, axes = plt.subplots(figsize=(12.0, 4.2), ncols=2)\n", "\n", "ax = axes[0]\n", "ax_e = axes[1]\n", "\n", "t_max = 5.0\n", "omega = 3.0\n", "times = np.linspace(0, t_max, 100)\n", "\n", "u0 = [0.5, 0.5]\n", "\n", "analytical = np.array([u0[0] * np.cos(omega * times) + (u0[0]/omega) * np.sin(omega * times),\n", " -u0[0] * omega * np.sin(omega * times) + u0[0] * np.cos(omega * times)]).T\n", "\n", "\n", "\n", "times_fe1 = np.linspace(0, t_max, 100)\n", "dt1 = times_fe1[1] - times_fe1[0]\n", "sol_fe1 = forward_euler_generic(harmonic_rhs, u0, times_fe1, omega)\n", "\n", "times_fe2 = np.linspace(0, t_max, 400)\n", "dt2 = times_fe2[1] - times_fe2[0]\n", "sol_fe2 = forward_euler_generic(harmonic_rhs, u0, times_fe2, omega)\n", "\n", "times_ssprk2 = np.linspace(0, t_max, 80)\n", "dt3 = times_ssprk2[1] - times_ssprk2[0]\n", "sol_ssprk2 = ssprk22_generic(harmonic_rhs, u0, times_ssprk2, omega)\n", "\n", "times_rk2 = np.linspace(0, t_max, 80)\n", "dt4 = times_rk2[1] - times_rk2[0]\n", "sol_rk2 = rk2_generic(harmonic_rhs, u0, times_rk2, omega)\n", "\n", "\n", "ax.plot(sol_fe1[:,0], sol_fe1[:,1],\n", " color='tab:red', label=f\"F.E. dt = {dt1:.3f}\")\n", "\n", "ax.plot(sol_fe2[:,0], sol_fe2[:,1],\n", " color='tab:purple', label=f\"F.E. dt = {dt2:.3f}\")\n", "\n", "ax.plot(sol_ssprk2[:,0], sol_ssprk2[:,1],\n", " color='tab:blue', label=f\"SSPRK2 dt = {dt3:.3f}\")\n", "\n", "ax.plot(sol_rk2[:,0], sol_rk2[:,1],\n", " color='tab:green', label=f\"RK2 dt = {dt4:.3f}\")\n", "\n", "\n", "ax.plot(analytical[:,0], analytical[:,1],\n", " 'k-', label=f\"Analytical\")\n", "\n", "ax_e.plot(times, energy(analytical, omega), 'k')\n", "ax_e.plot(times_fe1, energy(sol_fe1, omega), 'tab:red')\n", "ax_e.plot(times_fe2, energy(sol_fe2, omega), 'tab:purple')\n", "ax_e.plot(times_ssprk2, energy(sol_ssprk2, omega), 'tab:blue')\n", "ax_e.plot(times_rk2, energy(sol_rk2, omega), 'tab:green')\n", "\n", "ax.legend(fontsize=12)\n", "ax.set_xlabel(\"x(t)\", fontsize=10)\n", "ax.set_ylabel(\"v(t)\", fontsize=10)\n", "ax.tick_params(axis='both', labelsize=8)\n", "\n", "\n", "print(f\"dE F.E. (dt={dt1:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_fe1, omega)[-1]):.3e}\")\n", "print(f\"dE F.E. (dt={dt2:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_fe2, omega)[-1]):.3e}\")\n", "print(f\"dE SSPRK2 (dt={dt3:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_ssprk2, omega)[-1]):.3e}\")\n", "print(f\"dE RK2 (dt={dt4:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_rk2, omega)[-1]):.3e}\")\n", "\n", "ax_e.set_yscale(\"log\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5f45e264", "metadata": {}, "source": [ "::: {.callout-tip}\n", "## Question\n", "Why does SSPRK2 still cause a growth of energy?\n", ":::" ] }, { "cell_type": "markdown", "id": "aa06ebe1", "metadata": {}, "source": [ "## Stiffness\n", "\n", "We don't go into detail about stiff ODEs in this lecture, but still mention some definitions.\n", "\n", "- **Definition 1** Step size required for stability is much smaller than the step size required for accuracy\n", "- **Definition 2** Computational cost of an explicit method becomes larger than that of an implicit one\n", "\n", "Arise in biology, chemistry, low-Mach number compressible flows." ] }, { "cell_type": "markdown", "id": "29a71aeb", "metadata": {}, "source": [ "## Symplectic integrators\n", "\n", "Consider ODE system given by\n", "\n", "$$\n", "\\frac{d q_i}{d t} = -\\frac{\\partial H}{\\partial p_i}, \\quad \\frac{d p_i}{d t} = \\frac{\\partial H}{\\partial q_i},\n", "$$\n", "where $H$ is the **Hamiltonian** of the system.\n", "\n", "* Why do are we interested in specific methods for such systems?\n", "* What can these systems describe?\n", "\n", "::: {.callout-note}\n", "## Naming\n", "$q_i$ are called \"generalized coordinates\", $p_i$ - \"generalized momenta\"\n", ":::" ] }, { "cell_type": "markdown", "id": "4a8a7dee", "metadata": {}, "source": [ "\n", "### Example: interacting particles\n", "\n", "$$\n", "H(p,q) = \\frac{1}{2} \\frac{1}{m}\\sum_i p_i^2 + \\sum_{i" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| code-line-numbers: true\n", "#| code-fold: true\n", "#| fig-cap: \"Harmonic oscillator phase space (left) and energy (right), omega=3\"\n", "\n", "def verlet_generic(rhs, u0, times, omega):\n", " u = np.zeros((len(times), len(u0)))\n", " u[0,:] = u0\n", " for (i, t) in enumerate(times[1:]):\n", " dt = (times[i+1] - times[i])\n", " p_hs = u[i,1] + 0.5 * dt * rhs(u[i,:], omega)[1]\n", " u[i+1,0] = u[i,0] + dt * p_hs\n", " u[i+1,1] = p_hs + 0.5 * dt * rhs(u[i+1,:], omega)[1]\n", " return u\n", "\n", "fig, axes = plt.subplots(figsize=(12.0, 4.2), ncols=2)\n", "\n", "ax = axes[0]\n", "ax_e = axes[1]\n", "\n", "\n", "times_verlet = np.linspace(0, t_max, 20)\n", "dt5 = times_verlet[1] - times_verlet[0]\n", "sol_verlet = verlet_generic(harmonic_rhs, u0, times_verlet, omega)\n", "sol_ssprk2_new = ssprk22_generic(harmonic_rhs, u0, times_verlet, omega)\n", "\n", "ax.plot(sol_fe2[:,0], sol_fe2[:,1],\n", " color='tab:purple', label=f\"F.E. dt = {dt2:.3f}\")\n", "\n", "ax.plot(sol_ssprk2[:,0], sol_ssprk2[:,1],\n", " color='tab:blue', label=f\"SSPRK2 dt = {dt3:.3f}\")\n", "\n", "# ax.plot(sol_ssprk2_new[:,0], sol_ssprk2_new[:,1],\n", "# color='tab:orange', label=f\"SSPRK2 dt = {dt5:.3f}\")\n", "\n", "ax.plot(sol_verlet[:,0], sol_verlet[:,1],\n", " color='tab:red', label=f\"Verlet dt = {dt5:.3f}; 2/omega={2/omega:.3f}\")\n", "\n", "ax.plot(analytical[:,0], analytical[:,1],\n", " 'k-', label=f\"Analytical\")\n", "\n", "ax_e.plot(times, energy(analytical, omega), 'k')\n", "ax_e.plot(times_fe2, energy(sol_fe2, omega), 'tab:purple')\n", "ax_e.plot(times_ssprk2, energy(sol_ssprk2, omega), 'tab:blue')\n", "# ax_e.plot(times_verlet, energy(sol_ssprk2_new, omega), 'tab:orange')\n", "ax_e.plot(times_verlet, energy(sol_verlet, omega), 'tab:red')\n", "\n", "ax.legend(fontsize=12, loc=\"upper right\")\n", "ax.set_xlabel(\"x(t)\", fontsize=10)\n", "ax.set_ylabel(\"v(t)\", fontsize=10)\n", "ax.tick_params(axis='both', labelsize=8)\n", "\n", "\n", "print(f\"dE F.E. (dt={dt2:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_fe2, omega)[-1]):.3e}\")\n", "print(f\"dE SSPRK2 (dt={dt3:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_ssprk2, omega)[-1]):.3e}\")\n", "print(f\"dE SSPRK2 (dt={dt5:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_ssprk2_new, omega)[-1]):.3e}\")\n", "print(f\"dE Verlet (dt={dt5:.3f}) at t={t_max}: {(energy(analytical, omega)[-1] - energy(sol_verlet, omega)[-1]):.3e}\")\n", "\n", "# ax_e.set_yscale(\"log\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c6abcac6", "metadata": {}, "source": [ "## Code\n", "- [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/) - huge amount of methods available\n", "- [Comparison of various methods (2019!!!)](https://www.stochasticlifestyle.com/comparison-differential-equation-solver-suites-matlab-r-julia-python-c-fortran) (see also [summary table](https://www.stochasticlifestyle.com/wp-content/uploads/2019/11/de_solver_software_comparsion.pdf))" ] }, { "cell_type": "markdown", "id": "0158ab28", "metadata": {}, "source": [ "## Summary\n", "\n", "Methods not covered in this lecture but also useful/actively developed:\n", "\n", "- IMEX (IMplicit/EXplicit): separate RHS into stiff and non-stiff parts, treat them implicitly and explicitly, respectively.\n", " - [\"Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations\", Ascher, Ruth et al.](https://doi.org/10.1016/S0168-9274(97)00056-1)\n", " - [\"Additive Runge–Kutta schemes for convection–diffusion–reaction equations\", Kennedy & Carpenter](https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf)\n", "- MPRK (Modified Patankar Runge–Kutta) for production-destruction systems. Ensure non-negativity of densities.\n", " - [\"On order conditions for modified Patankar–Runge–Kutta schemes\", Kopecz & Meister](https://doi.org/10.1016/j.apnum.2017.09.004)\n", " - Implementation available in [PositiveIntegrators.jl](https://doi.org/10.21105/joss.08130)\n", "- Explicit integrators for particles with velocity-dependent force terms (for example, Lorentz force)\n", " - [\"On the Boris solver in particle-in-cell simulation\", Zenitani & Umeda](https://doi.org/10.1063/1.5051077)" ] }, { "cell_type": "markdown", "id": "28ccd829", "metadata": {}, "source": [ "### Exercises\n", "\n", "1. Derive the stability polynomial $R(z)$ for the RK4 method\n", "1. Prove the SSP property of a method in Shu-Osher form (hint: use the TVD property of forward Euler, the triangle inequality and look at the definition of $c_{SSP}$)\n", "1. Derive energy growth rate for SSPRK2 for the harmonic oscillator\n", "1. Show that forward Euler is **always** unstable for the harmonic oscillator via growth factor analysis\n", "1. Show that the forward Euler method is not a symplectic method\n", "\n", "### Questions\n", "1. What is the difference between monotonicity and stability of a method?\n", "1. Why are implicit methods oftentimes more computationally expensive?\n", "1. What is the difference between a symplectic and a phase space volume-preserving integrator? Which condition is stronger? Why?\n", "1. What two formulations of explicit symplectic integrators do you know and what is the difference between them?" ] }, { "cell_type": "markdown", "id": "0a08d417", "metadata": {}, "source": [ "## References\n", "\n", "1. S. Gottlieb, On High Order Strong Stability Preserving Runge–Kutta and Multi Step Time Discretizations\n", "1. Kubatko, Yeager et al., Optimal Strong-Stability-Preserving Runge–Kutta Time Discretizations for Discontinuous Galerkin Methods\n", "1. A. Giorgilli, Notes on Hamiltonian Dynamical Systems" ] }, { "cell_type": "markdown", "id": "ed614a73", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "py310", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 5 }