{ "cells": [ { "cell_type": "markdown", "metadata": { "tags": [ "remove_cell" ] }, "source": [ "
\n", "
\n", "

Ingenieurinformatik – Übung

\n", " Lehrstuhl Computational Civil Engineering
\n", " Kontakt: Email senden | Individuelle Kontakte siehe Webseite des Lehrstuhls
\n", " Links: \n", " Vorlesungsskript | \n", " Webseite des Lehrstuhls\n", "
\n", "
\n", " \n", "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ableitungsfunktion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In dieser Aufgabe wird die numerische Berechnung der Ableitungsfunktion vorgestellt. Insbesondere wird die Berechnung der Werte am Rand und der Berechnungsfehler betrachtet. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gegeben ist die Funktion $\\sf y(x)$ mit\n", "\n", "$$ \\sf y(x) = e^{-(x-2)^2} $$\n", "\n", "Stellen Sie die Funktion $\\sf y$ und deren Ableitung $\\sf y'$ graphisch im Intervall $\\sf x \\in [0,4]$ dar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil1.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "Die analytische Ableitung der Funktion $\\sf y(x)$ lautet\n", "\n", "$$ \\sf y'(x) = - 2(x-2)e^{-(x-2)^2} $$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "x = np.linspace(0, 4, 100)\n", "y = np.exp(-(x-2)**2)\n", "yp = -2*(x-2)*np.exp(-(x-2)**2)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x, y, label='y(x)')\n", "plt.plot(x, yp, label='y\\'(x)')\n", "\n", "plt.legend()\n", "plt.grid()\n", "plt.xlabel('x')\n", "\n", "# Ausgabe für den Lösungshinweis\n", "# plt.savefig('teil1.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil B\n", "\n", "Diskretisieren Sie die das obige Intervall, z.B. mit 20 Stützstellen, und bestimmen sie numerisch die Ableitungsfunktion. Für Stützstellen, welche nicht am Rand liegen, verwenden Sie die zentrale Differenzenformel zweiter Ordnung. Die Randwerte werden mit den Vorwärtsdifferenzenquotienten\n", "\n", "$$ \\sf y'_i = \\frac{y_{i+1} - y_i}{\\Delta x} $$\n", "bzw. mit dem Rückwärtsdifferenzentquotienten \n", "\n", "$$ \\sf y'_i = \\frac{y_{i} - y_{i-1}}{\\Delta x} $$\n", "jeweils erster Ordnung berechnet. Stellen Sie die analytisch und numerisch bestimmten Ableitungsfunktionen zusammen dar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil2.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Definition der Anzahl der Stützstellen für die Diskretisierung\n", "nx = 20\n", "\n", "# Diskretisierung des betrachteten Intervalls\n", "xi = np.linspace(0, 4, nx)\n", "dx = xi[1] - xi[0]\n", "\n", "# Funktionswerte an den Stützstellen xi\n", "yi = np.exp(-(xi-2)**2)\n", "\n", "# Graphische Ausgabe, nur zur visuellen Kontrolle\n", "plt.scatter(xi, yi, c='C1', label='diskretisiert')\n", "plt.plot(x, y, label='analytisch')\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('y(x)')\n", "plt.legend()\n", "plt.grid();" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Erstellung eines Arrays für die numerische Ableitung\n", "yip = np.zeros_like(yi)\n", "\n", "# Berechnung der Ableitung im inneren Bereich, d.h.\n", "# ohne die Randwerte, mit der zentralen Differenzenformel\n", "yip[1:-1] = (yi[2:] - yi[:-2]) / (2*dx)\n", "\n", "# Berechnung der Ableitung an den Randpunkten\n", "# mit der Vorwärtsdifferenzenformel\n", "yip[0] = (yi[1] - yi[0]) / dx\n", "# mit der Rückwärtsdifferenzenformel\n", "yip[-1] = (yi[-1] - yi[-2]) / dx\n", "\n", "# yip[0] = (-3*yi[0] + 4*yi[1] - yi[2]) / (2*dx)\n", "# yip[-1] = (3*yi[-1] - 4*yi[-2] + yi[-3]) / (2*dx)\n", "\n", "# Graphische Ausgabe\n", "plt.plot(x, yp, label='analytisch')\n", "plt.scatter(xi, yip, c='C1', label='numerisch')\n", "\n", "plt.legend()\n", "plt.ylabel('y\\'(x)')\n", "plt.xlabel('x')\n", "plt.grid()\n", "\n", "# Ausgabe für den Lösungshinweis \n", "# plt.savefig('teil2.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil C\n", "\n", "Berechnen Sie die Abweichung zwischen der analytischen und numerischen Ableitung an jedem Stützpunkt und stellen Sie diese graphisch dar. Verkleinern Sie den Gitterabstand $\\sf \\Delta x$, z.B. um einen Faktor 4. Was fällt Ihnen auf?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgaben könnten wie folgt aussehen.\n", "\n", "![](teil3a.png)\n", "\n", "![](teil3b.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "# Definition einer Hilfsfunktion\n", "def ableitung_f1(nx):\n", " # Diskretisierung des betrachteten Intervalls\n", " xi = np.linspace(0, 4, nx)\n", " dx = xi[1] - xi[0]\n", "\n", " # Funktionswerte an den Stützstellen xi\n", " yi = np.exp(-(xi-2)**2)\n", " \n", " # Erstellung eines Arrays für die numerische Ableitung\n", " yip = np.zeros_like(yi)\n", "\n", " # Berechnung der Ableitung im inneren Bereich, d.h.\n", " # ohne die Randwerte, mit der zentralen Differenzenformel\n", " yip[1:-1] = (yi[2:] - yi[:-2]) / (2*dx)\n", "\n", " # Berechnung der Ableitung an den Randpunkten\n", " # mit der Vorwärtsdifferenzenformel\n", " yip[0] = (yi[1] - yi[0]) / dx\n", " # mit der Rückwärtsdifferenzenformel\n", " yip[-1] = (yi[-1] - yi[-2]) / dx\n", " \n", " return xi, yip" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "# Analytische Ableitung als Funktion\n", "def ableitung_analytisch(x):\n", " return -2*(x-2)*np.exp(-(x-2)**2)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Ausgabe für den Lösungshinweis nx = 20\n", "xi, yip = ableitung_f1(20)\n", "yip_analytisch = ableitung_analytisch(xi)\n", " \n", "diff = yip - yip_analytisch\n", "plt.plot(xi, diff, marker='.')\n", "plt.grid()\n", "plt.xlabel('x')\n", "plt.ylabel('numerisch - analytisch')\n", "# plt.savefig('teil3a.png')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Ausgabe für den Lösungshinweis nx = 80\n", "xi, yip = ableitung_f1(80)\n", "yip_analytisch = ableitung_analytisch(xi)\n", " \n", "diff = yip - yip_analytisch\n", "plt.plot(xi, diff, marker='.')\n", "plt.grid()\n", "plt.xlabel('x')\n", "plt.ylabel('numerisch - analytisch')\n", "# plt.savefig('teil3b.png')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for nx in [20, 40, 80]:\n", " xi, yip = ableitung_f1(nx)\n", " yip_analytisch = ableitung_analytisch(xi)\n", " \n", " diff = yip - yip_analytisch\n", " plt.plot(xi, diff, marker='.', label=f'nx={nx}')\n", "\n", "plt.legend()\n", "plt.grid()\n", "plt.xlabel('x')\n", "plt.ylabel('numerisch - analytisch');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil D\n", "\n", "Bestimmen Sie die Formel für den Vorwärtsdifferenzenquotienten zweiter Ordnung zur Berechnung der ersten Ableitung. Verwenden Sie dafür die Taylor-Entwicklung an zwei vorwärtsgerichteten Punkten, d.h. $\\sf i+1, i+2$. \n", "\n", "Die Rückwärtsformel lautet\n", "\n", "$$ \\sf y'_i = \\frac{3y_{i} - 4y_{i-1} + y_{i-2}}{2\\Delta x} + \\mathcal{O}\\left(\\Delta x^2\\right)$$" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "Die Taylor-Entwicklungen an den Stellen $\\sf x_i + \\Delta x = x_{i+1}$ bzw. $\\sf x_i + \\Delta x = x_{i+1}$ lauten bis zur Ordnung $\\sf \\mathcal{O}\\left(\\Delta x^3\\right)$:\n", "\n", "$$\\sf y(x_i + \\Delta x) = y_{i+1} = y_i + y'_i\\Delta x + \\frac{1}{2}y''_i\\Delta x^2 + \\mathcal{O}\\left(\\Delta x^3\\right) $$\n", "$$\\sf y(x_i + 2\\Delta x) = y_{i+2} = y_i + y'_i(2\\Delta x) + \\frac{1}{2}y''_i(2\\Delta x)^2 + \\mathcal{O}\\left(\\Delta x^3\\right) $$\n", "\n", "Das Ziel ist die Bestimmung des Terms $\\sf y'$ nur mit Hilfe von den Funktionswerten, d.h. $\\sf y$. Das bedeutet, dass die Terme der zweiten Ableitungen $\\sf y''$ eliminiert werden müssen. Dies kann errreicht werden indem die erste Gleichung mit vier multipliziert wird und dann die zweite Gleichung davon substrahiert wird.\n", "\n", "$$\\sf 4y_{i+1} = 4y_i + 4y'_i\\Delta x + 2y''_i\\Delta x^2 + \\mathcal{O}\\left(\\Delta x^3\\right) $$\n", "$$\\sf y_{i+2} = y_i + 2y'_i\\Delta x + 2y''_i\\Delta x^2 + \\mathcal{O}\\left(\\Delta x^3\\right) $$\n", "\n", "$$\\sf \\Rightarrow 4y_{i+1} - y_{i+2} = 3y_i + 2y'_i\\Delta x + \\mathcal{O}\\left(\\Delta x^3\\right) $$\n", "\n", "Die Auflösung nach $\\sf y'_i$ führt zu\n", "\n", "$$ \\sf y'_i = \\frac{-3y_i + 4y_{i+1} - y_{i+2}}{2\\Delta x} + \\mathcal{O}\\left(\\Delta x^2\\right) $$\n", "\n", "Dies ist die Vorwärtsdifferenzenformel für die erste Ableitung zweiter Ordnung." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil E\n", "\n", "Verwenden Sie die Formeln zweiter Ordnung für die Berechnung der Ableitung am Rand. Wie sieht nun die Abweichung zwischen der analytischen und numerischen Ableitung aus? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil5.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "# Definition einer Hilfsfunktion, jetzt mit der Randberechnung \n", "# zweiter Ordnung\n", "def ableitung_f2(nx):\n", " # Diskretisierung des betrachteten Intervalls\n", " xi = np.linspace(0, 4, nx)\n", " dx = xi[1] - xi[0]\n", "\n", " # Funktionswerte an den Stützstellen xi\n", " yi = np.exp(-(xi-2)**2)\n", " \n", " # Erstellung eines Arrays für die numerische Ableitung\n", " yip = np.zeros_like(yi)\n", "\n", " # Berechnung der Ableitung im inneren Bereich, d.h.\n", " # ohne die Randwerte, mit der zentralen Differenzenformel\n", " yip[1:-1] = (yi[2:] - yi[:-2]) / (2*dx)\n", "\n", " # Berechnung der Ableitung an den Randpunkten\n", " # mit der Vorwärtsdifferenzenformel\n", " yip[0] = (-3*yi[0] + 4*yi[1] - yi[2]) / (2*dx)\n", " # mit der Rückwärtsdifferenzenformel\n", " yip[-1] = (3*yi[-1] - 4*yi[-2] + yi[-3]) / (2*dx)\n", " \n", " return xi, yip" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Ausgabe für den Lösungshinweis nx = 80\n", "xi, yip = ableitung_f2(80)\n", "yip_analytisch = ableitung_analytisch(xi)\n", " \n", "diff = yip - yip_analytisch\n", "plt.plot(xi, diff, marker='.')\n", "plt.grid()\n", "plt.title('nx=80')\n", "plt.xlabel('x')\n", "plt.ylabel('numerisch - analytisch')\n", "plt.savefig('teil5.png')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Vergleichende Ausgabe\n", "xi, yip_f1 = ableitung_f1(80)\n", "xi, yip_f2 = ableitung_f2(80)\n", "\n", "yip_analytisch = ableitung_analytisch(xi)\n", " \n", "diff_f1 = yip_f1 - yip_analytisch\n", "diff_f2 = yip_f2 - yip_analytisch\n", "\n", "plt.plot(xi, diff_f1, marker='.', label='erste Ordnung')\n", "plt.plot(xi, diff_f2, marker='.', label='zweite Ordnung')\n", "\n", "plt.legend()\n", "plt.grid()\n", "plt.title('nx=80')\n", "plt.xlabel('x')\n", "plt.ylabel('numerisch - analytisch');" ] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }