{ "metadata": { "name": "", "signature": "sha256:de10c45d2c5ddf69d89d1a1d4c7a881f6f17b2e80facaadaee858290b204e048" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Z\u00e1klady po\u010d\u00edta\u010dov\u00e9 fyziky II - NEVF138\n", "## SYLABUS (p\u0159edb\u011b\u017en\u00fd)\n", "\n", "### ODR\n", "* Numerick\u00e1 derivace, Taylor, Richardsonova extrapolace\n", "* Integr\u00e1tory - explicitn\u00ed, implicitn\u00ed, prediktor/korektor, Runge Kutta, Tuh\u00e9 soustavy - aplikace na chemickou kinetiku\n", "* Geometrick\u00e9/symplektick\u00e9 integr\u00e1tory - aplikace na pohybov\u00e9 rovnice, HARHA\n", "* Po\u010d\u00e1te\u010dn\u00ed \u00faloha/okrajov\u00e1 \u00faloha\n", "\n", "### PDR\n", "* Metoda s\u00edt\u00ed\n", "* Metoda kone\u010dn\u00fdch prvk\u016f - Slab\u00e1 formulace, kone\u010dn\u00e9 prvky, generov\u00e1n\u00ed s\u00edt\u00ed, FEniCS, OpenFOAM\n", "* Aplikace - \u0159e\u0161en\u00ed Schr\u00f6dingerovy rovnice r\u016fzn\u00fdmi metodami, v\u00fdpo\u010dty elektrick\u00e9ho a magnetick\u00e9ho pole\n", "* Kombinace ODR + PDR - Particle-In-Cell\n", "\n", "### Line\u00e1rn\u00ed algebra\n", "* \u0158e\u0161en\u00ed soustav lin. rovnic, podm\u00edn\u011bnost matice\n", "* Itera\u010dn\u00ed metody (Jacobi, Gauss Seidel, SOR ), p\u0159\u00edm\u00e9 metody (LU, FA, CR, FACR\u2026 CG ?)\n", "* Hled\u00e1n\u00ed vlastn\u00edch \u010d\u00edsel\n", "\n", "### Dal\u0161\u00ed t\u00e9mata\n", "* Aplikace na experiment\u00e1n\u00ed data? - \n", "* Tichonovova regularizace, dekonvoluce, optimalizace, Newtonova metoda\u2026\n", "* __N\u00e1vrhy student\u016f jsou v\u00edt\u00e1ny__\n", "\n", "# \u00davodn\u00ed pozn\u00e1mky\n", "* Pozn\u00e1mky k p\u0159edn\u00e1\u0161ce jsou na http://nbviewer.ipython.org/github/rouckas/NEVF138\n", "* Ilustra\u010dn\u00ed p\u0159\u00edklady v jazyce Python, knihovny numpy, scipy...\n", "* Z\u00e1klady Pythonu - m\u011bly by b\u00fdt z\u0159ejm\u00e9, vysv\u011btl\u00edm za b\u011bhu.\n", "\n", "## Druhy chyb\n", "* Fyzik\u00e1ln\u00ed aproximace - Newton/OTR...\n", "* Chyba vstupn\u00edch parametr\u016f - po\u010d. podm., fyzik\u00e1ln\u00ed konstanty...\n", "* Chyba metody - v d\u016fsledku diskretizace. T\u00edm se budeme hlavn\u011b zab\u00fdvat\n", "* Zaokrouhlovac\u00ed chyba - v d\u016fsledku kone\u010dn\u00e9 p\u0159esnosti po\u010d\u00edta\u010de\n", "\n", "# Numerick\u00e9 derivov\u00e1n\u00ed\n", "\n", "Jak vyhodnocov\u00e1n\u00edm $f(x)$ v r\u016fzn\u00fdch bodech zjistit $f'(x)$. Vyjdeme z definice\n", "$$\n", "f'(x) = \\lim_{h\\to 0}\\frac{f(x+h)-f(x)}{h}\n", "$$\n", "\n", "Diskretizace, ot\u00e1zka p\u0159esnosti (chyba metody a zaokrouhlovac\u00ed chyba), dop\u0159edn\u00e9 diference, centr\u00e1ln\u00ed diference\n", "\n", "Asymptotick\u00e9 chov\u00e1n\u00ed chyby a jej\u00ed eliminace - Richardsonova extrapolace\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "%config InlineBackend.close_figures=False\n", "import pylab as P\n", "import numpy as N" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "#define function for calculating the forward differences:\n", "def diff_FD(f, x, dx): return (f(x+dx) - f(x))/dx" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "#the asymptotic error of the above functions obtained by Taylor expansion:\n", "def diff_FD_err(f, d2f, d3f, x, dx): return 0.5*d2f(x)*dx" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# use function sin(x) to test our implementation\n", "def f(x): return N.sin(x)\n", "def dfdx(x): return N.cos(x)\n", "def dfdx2(x): return -N.sin(x)\n", "def dfdx3(x): return -N.cos(x)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# calculate the derivative at x0=1. for the following values of dx\n", "x0 = 1.0\n", "dx = N.logspace(-17, 1, 500)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Chyba dop\u0159edn\u00fdch diferenc\u00ed" ] }, { "cell_type": "code", "collapsed": false, "input": [ "P.figure(figsize=(8,5))\n", "\n", "rel_err = N.abs((diff_FD(f, x0, dx) - dfdx(x0))/dfdx(x0))\n", "P.loglog(dx, rel_err)\n", " \n", "# some plotting setup to make it look nice\n", "%config InlineBackend.close_figures=False\n", "from matplotlib.ticker import LogLocator\n", "P.ylim([1e-13, 1e1])\n", "P.gca().xaxis.set_major_locator(LogLocator(base=100., numticks=20))\n", "P.xlabel(\"step size\")\n", "P.ylabel(\"rel. error\")\n", "P.grid(which=\"both\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAfkAAAFOCAYAAACFeWQpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "#compare with the asymptotic error value\n", "err = N.abs(diff_FD_err(f, dfdx2, dfdx3, x0, dx)/dfdx(x0))\n", "P.loglog(dx, err,\":k\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAFOCAYAAAD0N3VGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "#define functions for calculating the centered differences:\n", "def diff_CD(f, x, dx): return (f(x+dx) - f(x-dx))/(2*dx)\n", "\n", "#the asymptotic errors of the above functions obtained by Taylor expansion:\n", "def diff_CD_err(f, d2f, d3f, x, dx): return 1/6.*d3f(x)*dx**2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Chyba centr\u00e1ln\u00edch diferenc\u00ed" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rel_err = N.abs((diff_CD(f, x0, dx) - dfdx(x0))/dfdx(x0))\n", "P.loglog(dx, rel_err)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAFOCAYAAAD0N3VGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "#compare with the asymptotic error value\n", "err = N.abs(diff_CD_err(f, dfdx2, dfdx3, x0, dx)/dfdx(x0))\n", "P.loglog(dx, err,\":k\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAFOCAYAAAD0N3VGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Richardsonova extrapolace" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# try to apply the Richardson extrapolation to both methods once, and finally try to subtract first\n", "# 4 terms of the asymptotic error expansion\n", "def richardson(f, x0, dx, p):\n", " if len(p) > 1:\n", " return (2**p[0]*richardson(f, x0, dx, p[1:]) -\\\n", " richardson(f, x0, 2*dx, p[1:]))/(2**p[0]-1)\n", " return (2**p[0]*operator(f, x0, dx) - operator(f, x0, 2*dx))/(2**p[0]-1)\n", "\n", "for operator, p1 in [(diff_FD, [1]), (diff_CD, [2]), (diff_CD, [2, 4, 6, 8])]:\n", " rel_err = N.abs((richardson(f, x0, dx, p1) - dfdx(x0))/dfdx(x0))\n", " P.loglog(dx, rel_err,\"--\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAFOCAYAAAD0N3VGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nImBmZtbG/gfKOth6TaTMdAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed we can easily obtain a method of 10$^{\\rm th}$ order accuracy. Although maybe not the most efficient one." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerick\u00e9 integrov\u00e1n\u00ed\n", "Op\u011bt z definice: Riemann\u016fv integr\u00e1l $\\to$ obd\u00e9ln\u00edkov\u00e9 pravidlo" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }