From 6977606961200e090f70f3d4589c2c45992577da Mon Sep 17 00:00:00 2001 From: Felix Koehler Date: Mon, 23 Sep 2024 12:50:20 +0200 Subject: [PATCH] Add temporal convergence notebook --- validation/etdrk_convergence.ipynb | 324 +++++++++++++++++++++++++++++ 1 file changed, 324 insertions(+) create mode 100644 validation/etdrk_convergence.ipynb diff --git a/validation/etdrk_convergence.ipynb b/validation/etdrk_convergence.ipynb new file mode 100644 index 0000000..fb01c45 --- /dev/null +++ b/validation/etdrk_convergence.ipynb @@ -0,0 +1,324 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Temporal Convergence of ETDRK schemes\n", + "\n", + "Inspired by figure 4.2 (a) in\n", + "\n", + "Montanelli, H. and Bootland, N., 2020. Solving periodic semilinear stiff PDEs in\n", + "1D, 2D and 3D with exponential integrators. Mathematics and Computers in\n", + "Simulation, 178, pp.307-327.\n", + "\n", + "this notebook assesses the convergence of all available ETDRK schemes in\n", + "`Exponax`. It does so by having four different steppers (same constitutive\n", + "parameters to the conservative KS equation) integrate an initial condition to a\n", + "state after 10 time units with various different $\\Delta t$ (and hence also\n", + "increasingly many time steps the smaller $\\Delta t$ is). The error is then\n", + "calculated against the solution using the finest $\\Delta t$.\n", + "\n", + "In a loglog plot, we observe polynomially linear, quadratic, cubic, and quartic\n", + "convergence for the first, second, third, and fourth order ETDRK schemes,\n", + "respectively.\n", + "\n", + "We measure the error in terms of the relative $L^2$ norm of the difference\n", + "between the numerical solution at the current $\\Delta t$ and the reference\n", + "solution at the finest $\\Delta t$.\n", + "\n", + "$$\n", + "\\text{error} = \\frac{\\|u_{\\Delta t} - u_{\\Delta t_{\\text{ref}}}\\|_{L^2(\\Omega)}}{\\|u_{\\Delta t_{\\text{ref}}}\\|_{L^2(\\Omega)}}\n", + "$$\n", + "\n", + "In discrete terms, this can be realized by the normalized root mean square error\n", + "(nRMSE)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Switch to double precision\n", + "jax.config.update(\"jax_enable_x64\", True)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "import exponax as ex" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Choosing a reasonably high number of points (with domain_extent=60.0, the KS\n", + "# in single precision has populated modes up to wavenumber ~80. Hence using >160\n", + "# points gives essentially no spatial discretization error. Hence, we can fully\n", + "# focus on the error due to integration in time.)\n", + "N = 256" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "2024-09-23 12:49:32.974648: W external/xla/xla/service/gpu/nvptx_compiler.cc:836] The NVIDIA driver's CUDA version is 12.2 which is older than the PTX compiler version (12.6.68). Because the driver is older than the PTX compiler version, XLA is disabling parallel compilation, which may slow down compilation. You should update your NVIDIA driver or use the NVIDIA-provided CUDA forward compatibility packages.\n" + ] + } + ], + "source": [ + "u_0 = ex.ic.RandomTruncatedFourierSeries(1)(N, key=jax.random.PRNGKey(0))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "dt_range = 2.0 ** (-jnp.arange(2, 12))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Array([0.25 , 0.125 , 0.0625 , 0.03125 , 0.015625 ,\n", + " 0.0078125 , 0.00390625, 0.00195312, 0.00097656, 0.00048828], dtype=float64)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dt_range" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_state_at_10(dt, order):\n", + " num_steps = int(10.0 / dt)\n", + " repeated_stepper = ex.RepeatedStepper(\n", + " ex.stepper.KuramotoSivashinskyConservative(1, 60.0, N, dt, order=order),\n", + " num_steps,\n", + " )\n", + " returned = repeated_stepper(u_0)\n", + " return returned" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "result_states_1 = jnp.array([compute_state_at_10(dt, 1) for dt in dt_range])\n", + "result_states_2 = jnp.array([compute_state_at_10(dt, 2) for dt in dt_range])\n", + "result_states_3 = jnp.array([compute_state_at_10(dt, 3) for dt in dt_range])\n", + "result_states_4 = jnp.array([compute_state_at_10(dt, 4) for dt in dt_range])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "rel_errors_1 = jnp.array(\n", + " [ex.metrics.nRMSE(u, result_states_1[-1]) for u in result_states_1][:-1]\n", + ")\n", + "rel_errors_2 = jnp.array(\n", + " [ex.metrics.nRMSE(u, result_states_2[-1]) for u in result_states_2][:-1]\n", + ")\n", + "rel_errors_3 = jnp.array(\n", + " [ex.metrics.nRMSE(u, result_states_3[-1]) for u in result_states_3][:-1]\n", + ")\n", + "rel_errors_4 = jnp.array(\n", + " [ex.metrics.nRMSE(u, result_states_4[-1]) for u in result_states_4][:-1]\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "dt_range_reduced = dt_range[:-1]" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.loglog(dt_range_reduced, rel_errors_1, \"o-\", label=\"First order\")\n", + "plt.loglog(dt_range_reduced, rel_errors_2, \"o-\", label=\"Second order\")\n", + "plt.loglog(dt_range_reduced, rel_errors_3, \"o-\", label=\"Third order\")\n", + "plt.loglog(dt_range_reduced, rel_errors_4, \"o-\", label=\"Fourth order\")\n", + "plt.xlabel(\"Time step size\")\n", + "plt.ylabel(\"Relative error\")\n", + "plt.legend()\n", + "plt.yticks(\n", + " [1e0, 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9, 1e-10, 1e-11],\n", + ")\n", + "plt.grid()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_convergence_rate(errors):\n", + " finest = errors[2:]\n", + " fine = errors[1:-1]\n", + " coarse = errors[:-2]\n", + " factor = (coarse - fine) / (fine - finest)\n", + " return jnp.log(factor) / jnp.log(2.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "convergence_rates_1 = compute_convergence_rate(rel_errors_1)\n", + "convergence_rates_2 = compute_convergence_rate(rel_errors_2)\n", + "convergence_rates_3 = compute_convergence_rate(rel_errors_3)\n", + "convergence_rates_4 = compute_convergence_rate(rel_errors_4)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(Array([1.48017438, 1.20098716, 1.09633277, 1.04742766, 1.02355578,\n", + " 1.01174108, 1.00586162], dtype=float64),\n", + " Array([1.68338196, 1.79811745, 1.883822 , 1.93732912, 1.96757454,\n", + " 1.98358097, 1.99175836], dtype=float64),\n", + " Array([2.49810195, 2.60026756, 2.72694438, 2.83703527, 2.91111544,\n", + " 2.95391233, 2.97682663], dtype=float64),\n", + " Array([2.86942868, 3.19226336, 3.50906618, 3.72809117, 3.85845911,\n", + " 3.92865792, 4.38288168], dtype=float64))" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "convergence_rates_1, convergence_rates_2, convergence_rates_3, convergence_rates_4" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(convergence_rates_1, \"o-\", label=\"First order\")\n", + "plt.plot(convergence_rates_2, \"o-\", label=\"Second order\")\n", + "plt.plot(convergence_rates_3, \"o-\", label=\"Third order\")\n", + "plt.plot(convergence_rates_4, \"o-\", label=\"Fourth order\")\n", + "plt.xlabel(\"Refinement level\")\n", + "plt.ylabel(\"Convergence rate\")\n", + "plt.legend()\n", + "plt.grid()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "exponax_dev", + "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": "3.10.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}