{ "cells": [ { "cell_type": "markdown", "id": "e5a6a661", "metadata": {}, "source": [ "# Stiff Problem" ] }, { "cell_type": "markdown", "id": "45479852", "metadata": {}, "source": [ "**강좌**: *수치해석*" ] }, { "cell_type": "code", "execution_count": 1, "id": "c0109141", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "markdown", "id": "3e0f0172", "metadata": {}, "source": [ "## Stiff System\n", "### 예제\n", "Mass Spring Damper 로 구성된 운동방정식을 생각하자\n", "\n", ":::{figure-md} markdown-fig\n", "\"spring-damper-fig\"\n", "\n", "Spring-Damper System (From Wikimedia)\n", ":::\n", "\n", "$$\n", "m \\ddot{x} + c \\dot{x} + k x = 0, ~~~x(0) = x_0, ~\\dot{x} = 0\n", "$$\n", "\n", "이때 질량, Damper 계수 및 스프링 계수를 $m=1, c=1001, k=1000$로 하자.\n", "이를 1계 미분방정식을 만들면 다음과 같다.\n", "\n", "$$\n", "\\frac{d}{dt}{\\left [\n", "\\begin{matrix}\n", "x \\\\ \\dot{x}\n", "\\end{matrix}\n", "\\right ]}\n", "=\n", "\\left [\n", "\\begin{matrix}\n", "0 & 1 \\\\\n", "-k/m & -c/m\n", "\\end{matrix}\n", "\\right ]\n", "\\left [\n", "\\begin{matrix}\n", "x \\\\ \\dot{x}\n", "\\end{matrix}\n", "\\right ]\n", "$$\n", "\n", "이 System의 고유치 (Eigenvalue) 는" ] }, { "cell_type": "code", "execution_count": 2, "id": "1cdd3c3e", "metadata": {}, "outputs": [], "source": [ "from scipy import linalg" ] }, { "cell_type": "code", "execution_count": 3, "id": "efdf3f4c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([ -1.+0.j, -1000.+0.j]),\n", " array([[ 7.07106781e-01, -9.99999500e-04],\n", " [-7.07106781e-01, 9.99999500e-01]]))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.array([[0, 1], [-1000, -1001]])\n", "linalg.eig(a)" ] }, { "cell_type": "markdown", "id": "fe7fb028", "metadata": {}, "source": [ "고유치가 1000배 차이가 나는 System이다.\n", "이 방정식을 `solve_ivp` 로 해석해보면 다음과 같다." ] }, { "cell_type": "code", "execution_count": 4, "id": "8c9832b0", "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import solve_ivp" ] }, { "cell_type": "code", "execution_count": 5, "id": "convinced-seafood", "metadata": {}, "outputs": [], "source": [ "solve_ivp?" ] }, { "cell_type": "code", "execution_count": 6, "id": "374242f1", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(t, y):\n", " return np.array([y[1], -1000*y[0] - 1001*y[1]])\n", "\n", "# Solve IVP with RK45 and BDF\n", "sol1 = solve_ivp(f, [0, 30], [1, 0])\n", "sol2 = solve_ivp(f, [0, 30], [1, 0], method='BDF')\n", "\n", "# Plot with Marker\n", "plt.plot(sol1.t, sol1.y[0], marker='o')\n", "plt.plot(sol2.t, sol2.y[0], marker='x')\n", "plt.legend(['RK45 ({} evaluations)'.format(sol1.nfev), 'BDF ({} evaluations)'.format(sol2.nfev)])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5bf88490", "metadata": {}, "source": [ "Runge Kutta (RK45) 기법과 Backward Diffrence Formula (BDF)으로 해석한 결과 다음과 같은 차이가 있다.\n", "- 두 기법 모두 Adaptive step size를 조절했음에도 RK45는 매우 작은 시간간격으로 계산한다.\n", "- BDF 기법은 변화가 적은 영역에서 매우 큰 시간간격을 가져도 수치 안정성이 유지된다.\n", "\n", "`solve_ivp` 도움말을 확인해보면 일반적인 문제에 대해서는 Runge-Kutta 기법을 사용하지만, Stiff system에서는 ``Radau``, ``BDF``, ``LSODA`` 를 사용할 것을 권장한다. 후자는 Implicit 기법이다.\n", "\n", "### Stiff System 정의\n", "이렇게 System의 전파 속도 (고유치)의 차이가 큰 문제를 Stiff System이라 한다. 대표적인 문제는 다음과 같다.\n", "\n", "- 반응속도가 매우 다른 화학반응\n", "- 공기역학에서 점성에 의한 경계층 유동" ] }, { "cell_type": "markdown", "id": "0e0c426b", "metadata": {}, "source": [ "## Implicit Methods\n", "\n", "Implicit 기법은 미분값을 현재 시간의 값이 아닌 미래 시간의 값으로 가정한 후 계산하는 방식이다. 대표적인 방법들은 다음과 같다.\n", "\n", "- Implicit Euler Method \n", "- Crank Nicolson Method (Trapezoidal Method)\n", "- Backward Difference Formula\n", "- Diagonally Implicit Runge-Kutta Method\n", "\n", "### Implicit Euler Method\n", "Euler Explicit과 달리 미분항을 $t^{n+1}$ 에서 생각하자.\n", "\n", "$$\n", "\\frac{y_{n+1} - y_n}{h} = f(t_{n+1}, y_{n+1})\n", "$$\n", "\n", "Model 방정식에 대해서는 다음과 같이 생각할 수 있다.\n", "\n", "$$\n", "y_{n+1} - y_n = h \\lambda y_{n+1}\n", "$$\n", "$$\n", "y_{n+1} = \\frac{1}{1 - h \\lambda} y_n = \\sigma y_n\n", "$$\n", "\n", "여기서 $|\\sigma| < 1$ 이므로, 항상 안정적이다.\n", "\n", "$\\lambda=0.5$ 이고 $y_0 = 1.0$ 일 때 $[0, 20]$ 까지 Explict Euler 와 Implicit Euler를 비교하자." ] }, { "cell_type": "code", "execution_count": 7, "id": "e2de34e1", "metadata": {}, "outputs": [], "source": [ "def f(t, y):\n", " return -0.5*y" ] }, { "cell_type": "code", "execution_count": 8, "id": "6dcfb38f", "metadata": {}, "outputs": [], "source": [ "def expliciteuler_v1(f, tspan, y0, dt=0.1):\n", " \"\"\"\n", " Explicit Euler Method (ODE), High-order variant\n", " \n", " Parameters\n", " ----------\n", " f : function\n", " Derivative\n", " tpan : tuple\n", " initial and final time\n", " y0 : array\n", " initial guess\n", " dt : float\n", " Time step size\n", " \n", " Return\n", " ------\n", " t : array\n", " Time series\n", " y : array\n", " solutions\n", " \"\"\" \n", " # 시간 Array\n", " t0, te = tspan\n", " t = np.arange(t0, te+1e-10, dt)\n", " \n", " # Solution array\n", " y = np.empty((len(y0), len(t)))\n", " y[:, 0] = y0\n", " \n", " # Euler Explicit\n", " for i, ti in enumerate(t):\n", " if i > 0:\n", " y[:, i] = y[:, i-1] + dt*f(ti, y[:, i-1])\n", " \n", " return t, y" ] }, { "cell_type": "code", "execution_count": 9, "id": "24a4e12b", "metadata": {}, "outputs": [], "source": [ "def impliciteuler_model(lam, tspan, y0, dt=0.1):\n", " \"\"\"\n", " Implicit Euler Method (ODE)\n", " \n", " Parameters\n", " ----------\n", " lam : float\n", " Lambda for model equation\n", " tpan : tuple\n", " initial and final time\n", " y0 : array\n", " initial guess\n", " dt : float\n", " Time step size\n", " \n", " Return\n", " ------\n", " t : array\n", " Time series\n", " y : array\n", " solutions\n", " \"\"\" \n", " # 시간 Array\n", " t0, te = tspan\n", " t = np.arange(t0, te+1e-10, dt)\n", " \n", " # Solution array\n", " y = np.empty((len(y0), len(t)))\n", " y[:, 0] = y0\n", " \n", " # Implicit Euler model\n", " for i, ti in enumerate(t):\n", " if i > 0:\n", " y[:, i] = y[:, i-1] / (1 + lam*dt)\n", " \n", " return t, y" ] }, { "cell_type": "code", "execution_count": 10, "id": "ba90b042", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t, y = expliciteuler_v1(f, [0, 20], [1], dt=0.5)\n", "plt.plot(t, np.exp(-0.5*t))\n", "plt.plot(t, y[0])\n", "\n", "t, y = expliciteuler_v1(f, [0, 20], [1], dt=5.0)\n", "plt.plot(t, y[0])\n", "\n", "t, y = impliciteuler_model(0.5, [0, 20], [1], dt=0.5)\n", "plt.plot(t, y[0])\n", "\n", "t, y = impliciteuler_model(0.5, [0, 20], [1], dt=5.0)\n", "plt.plot(t, y[0])\n", "plt.ylim(-0.1, 1.1)\n", "\n", "plt.legend([\n", " 'Exact', r'Explicit Euler $\\Delta t=0.5$', r'Explicit Euler $\\Delta t=5.0$',\n", " r'Implicit Euler $\\Delta t=0.5$', r'Implicit Euler $\\Delta t=5.0$'\n", "])" ] }, { "cell_type": "markdown", "id": "afe71850", "metadata": {}, "source": [ "### Linearization\n", "일방적인 비선형 미분방정식에 대해 Implicit 방법을 적용하기 위해서는 선형화 (Linearization)이 필요하다.\n", "\n", "$$\n", "\\frac{y_{n+1} - y_n}{h} = f(t_{n+1}, y_{n+1}) \\approx f(t_{n+1}, y_n) + \\frac{\\partial f}{\\partial y} \n", "\\Delta y+ O((\\Delta y)^2)\n", ",~~~ \\Delta y = y_{n+1} - y_n\n", "$$\n", "\n", "즉\n", "\n", "$$\n", "\\left (\\frac{1}{h} - \\frac{\\partial f}{\\partial y} \\right) \\Delta y = f(t_{n+1}, y_n)\n", "$$\n", "\n", "- $\\frac{\\partial f}{\\partial y}$ 를 모르는 경우 간단한 Finite Difference 공식으로 근사화 한다.\n", "\n", "$$\n", "\\frac{\\partial f}{\\partial y} = \\frac{f(t_{n+1}, y_n + \\epsilon) - f(t_{n+1}, y_n)}{\\epsilon}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "id": "3afc7e60", "metadata": {}, "outputs": [], "source": [ "def impliciteuler_v1(f, tspan, y0, dt=0.1, dfdy=None):\n", " \"\"\"\n", " Implicit Euler Method (Non-linear variant)\n", " \n", " Parameters\n", " ----------\n", " f : function\n", " Derivative\n", " tpan : tuple\n", " initial and final time\n", " y0 : array\n", " initial guess\n", " dt : float\n", " Time step size\n", " dfdy : function\n", " Jacobian\n", " \n", " Return\n", " ------\n", " t : array\n", " Time series\n", " y : array\n", " solutions\n", " \"\"\" \n", " # 시간 Array\n", " t0, te = tspan\n", " t = np.arange(t0, te+1e-10, dt)\n", " \n", " # Solution array\n", " y = np.empty((len(y0), len(t)))\n", " y[:, 0] = y0\n", " \n", " if dfdy:\n", " need_jacobian = False\n", " else:\n", " need_jacobian = True\n", " \n", " # Implicit Euler model\n", " for i, ti in enumerate(t):\n", " # \n", " if need_jacobian:\n", " yi = y[:, i-1]\n", " eps = 1e-6\n", " dfdy = (f(ti, yi + eps) - f(ti, yi)) / eps\n", " \n", " if i > 0:\n", " dy = f(ti, y[:, i-1]) / (1/dt - dfdy)\n", " \n", " y[:, i] = y[:, i-1] +dy\n", " \n", " return t, y" ] }, { "cell_type": "code", "execution_count": 12, "id": "a6eec7cd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t, y = expliciteuler_v1(f, [0, 20], [1, 0], dt=0.5)\n", "plt.plot(t, np.exp(-0.5*t))\n", "plt.plot(t, y[0])\n", "\n", "t, y = impliciteuler_model(0.5, [0, 20], [1, 0], dt=0.5)\n", "plt.plot(t, y[0])\n", "\n", "t, y = impliciteuler_v1(f, [0, 20], [1, 0], dt=0.5)\n", "plt.plot(t, y[0])\n", "\n", "plt.legend([\n", " 'Exact', r'Explicit Euler $\\Delta t=0.5$',\n", " r'Implicit Euler $\\Delta t=0.5$', \n", " r'Implicit Euler (Linearized) $\\Delta t=0.5$', \n", "])" ] }, { "cell_type": "markdown", "id": "5b4f2801", "metadata": {}, "source": [ "Sytem에 대해서는 $\\frac{\\partial f}{\\partial y}$는 Jacboain Matrix로 계산한다.\n", "\n", "$$\n", "\\Delta f = \n", "\\left [\n", "\\begin{matrix}\n", "\\frac{\\partial f_1}{\\partial y_1} & \\frac{\\partial f_1}{\\partial y_2} & ... & \\frac{\\partial f_1}{\\partial y_n} \\\\\n", "\\frac{\\partial f_2}{\\partial y_1} & \\frac{\\partial f_2}{\\partial y_2} & ... & \\frac{\\partial f_2}{\\partial y_n} \\\\\n", "... & ... & ... & ... \\\\\n", "\\frac{\\partial f_n}{\\partial y_1} & \\frac{\\partial f_n}{\\partial y_2} & ... & \\frac{\\partial f_n}{\\partial y_n} \\\\\n", "\\end{matrix}\n", "\\right ]\n", "$$\n", "\n", "Jacobian Matrix는 그냥 구하거나 각 항을 Finite difference method로 구할 수 있다.\n", "\n", "#### 예제\n", "\n", "Mass, Spring, Damper System에서 Jacobian Matrix는 다음과 같다.\n", "\n", "$$\n", "\\frac{\\partial f}{\\partial y} =\n", "\\left [\n", "\\begin{matrix}\n", "0 & 1 \\\\\n", "-k/m & -c/m\n", "\\end{matrix}\n", "\\right ]\n", "\\left [\n", "\\begin{matrix}\n", "x \\\\ \\dot{x}\n", "\\end{matrix}\n", "\\right ]\n", "$$" ] }, { "cell_type": "code", "execution_count": 13, "id": "82c1708b", "metadata": {}, "outputs": [], "source": [ "def impliciteuler_v2(f, dfdy, tspan, y0, dt=0.1):\n", " \"\"\"\n", " Implicit Euler Method (Linear system)\n", " \n", " Parameters\n", " ----------\n", " f : function\n", " Derivative\n", " dfdy : function\n", " Jacobian\n", " tpan : tuple\n", " initial and final time\n", " y0 : array\n", " initial guess\n", " dt : float\n", " Time step size\n", " \n", " Return\n", " ------\n", " t : array\n", " Time series\n", " y : array\n", " solutions\n", " \"\"\"\n", " # 시간 Array\n", " t0, te = tspan\n", " t = np.arange(t0, te+1e-10, dt)\n", " \n", " # Solution array\n", " y = np.empty((len(y0), len(t)))\n", " y[:, 0] = y0\n", " \n", " # Implicit Euler model\n", " for i, ti in enumerate(t):\n", " if i > 0:\n", " a = np.identity(len(y0))/dt - dfdy\n", " dy = np.linalg.solve(a, f(ti, y[:, i-1]))\n", " \n", " y[:, i] = y[:, i-1] +dy\n", " \n", " return t, y" ] }, { "cell_type": "code", "execution_count": 14, "id": "4f95693f", "metadata": {}, "outputs": [], "source": [ "def impliciteuler_v3(f, tspan, y0, dt=0.1, dfdy='none'):\n", " \"\"\"\n", " Implicit Euler Method (Non-linear system)\n", " \n", " Parameters\n", " ----------\n", " f : function\n", " Derivative\n", " tpan : tuple\n", " initial and final time\n", " y0 : array\n", " initial guess\n", " dt : float\n", " Time step size\n", " dfdy : function\n", " Jacobian\n", " \n", " Return\n", " ------\n", " t : array\n", " Time series\n", " y : array\n", " solutions\n", " \"\"\"\n", " # 시간 Array\n", " t0, te = tspan\n", " t = np.arange(t0, te+1e-10, dt)\n", " \n", " # Solution array\n", " ny = len(y0)\n", " y = np.empty((ny, len(t))) \n", " y[:, 0] = y0\n", " \n", " if dfdy == 'none':\n", " need_jacobian = True\n", " eye = np.identity(len(y0))\n", " else:\n", " need_jacobian = False\n", " \n", " # Implicit Euler model\n", " for i, ti in enumerate(t):\n", " if i > 0:\n", " if need_jacobian:\n", " # Compute Jacobian\n", " yi = y[:, i-1]\n", " eps = 1e-6\n", " dfdy = np.array([\n", " (f(ti, yi + e*eps) - f(ti, yi))/eps \n", " for e in eye\n", " ]).T\n", " \n", " a = np.identity(len(y0))/dt - dfdy\n", " dy = np.linalg.solve(a, f(ti, y[:, i-1]))\n", " \n", " y[:, i] = y[:, i-1] +dy\n", " \n", " return t, y" ] }, { "cell_type": "code", "execution_count": 15, "id": "15ceb20d", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_11543/2654520036.py:2: RuntimeWarning: overflow encountered in scalar multiply\n", " return np.array([y[1], -1000*y[0] - 1001*y[1]])\n", "/tmp/ipykernel_11543/1411676160.py:34: RuntimeWarning: invalid value encountered in add\n", " y[:, i] = y[:, i-1] + dt*f(ti, y[:, i-1])\n" ] }, { "data": { "text/plain": [ "(-0.1, 1.1)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(t, y):\n", " return np.array([y[1], -1000*y[0] - 1001*y[1]])\n", "\n", "jac = np.array([[0, 1], [-1000, -1001]])\n", "\n", "plt.plot(sol2.t, sol2.y[0], marker='x')\n", "t, y = expliciteuler_v1(f, [0, 30], [1, 0], dt=0.001)\n", "plt.plot(t, y[0])\n", "\n", "t, y = expliciteuler_v1(f, [0, 30], [1, 0], dt=0.01)\n", "plt.plot(t, y[0])\n", "\n", "#t, y = impliciteuler_v2(f, jac, [0, 30], [1, 0], dt=0.1)\n", "t, y = impliciteuler_v3(f, [0, 30], [1, 0], dt=0.1)\n", "plt.plot(t, y[0])\n", "\n", "plt.legend([\n", " r'BDF', r'Explicit Euler $\\Delta t=0.001$', r'Explicit Euler $\\Delta t=0.01$',\n", " r'Implicit Euler $\\Delta t=0.1$'\n", "])\n", "\n", "plt.ylim(-0.1, 1.1)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }