{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"\n",
"\n",
"# Exploratory Computing with Python\n",
"*Developed by Mark Bakker*\n",
"## Notebook 6: Systems of linear equations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this Notebook, we learn how to build and solve systems of linear equations, and apply these techniques to solve practical problems."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building and solving a system of linear equations\n",
"A parabola is defined by three points (provided they are not on a straight line). \n",
"The equation for a parabola is $y=ax^2+bx+c$, where $a$, $b$, and $c$ are constants.\n",
"Given three points $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$, the following system of three linear equations may be compiled\n",
"\n",
"$$\n",
"\\begin{split}\n",
"x_1^2a+x_1b+c&=y_1 \\\\\n",
"x_2^2a+x_2b+c&=y_2 \\\\\n",
"x_3^2a+x_3b+c&=y_3 \\\\\n",
"\\end{split}\n",
"$$\n",
"\n",
"Or in matrix form\n",
"\n",
"$$\n",
"\\left(\n",
"\\begin{array}{ccc}\n",
"x_1^2 & x_1 & 1 \\\\\n",
"x_2^2 & x_2 & 1 \\\\\n",
"x_3^2 & x_3 & 1 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"\\left(\n",
"\\begin{array}{c}\n",
"a \\\\b \\\\c \\\\\n",
"\\end{array}\n",
"\\right)\n",
"=\n",
"\\left(\n",
"\\begin{array}{c}\n",
"y_1 \\\\\n",
"y_2 \\\\\n",
"y_3 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"$$\n",
"\n",
"To solve this problem, we build a two-dimensional array containing the matrix (called `A`) and a one-dimensional array containing the right-hand side (called `rhs`).\n",
"Let's do that for the three points $(x_1,y_1)=(-2,2)$, $(x_2,y_2)=(1,-1)$, $(x_3,y_3)=(4,4)$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Array A:\n",
"[[ 4. -2. 1.]\n",
" [ 1. 1. 1.]\n",
" [16. 4. 1.]]\n",
"rhs: [ 2. -1. 4.]\n"
]
}
],
"source": [
"xp = np.array([-2, 1, 4])\n",
"yp = np.array([2, -1, 4])\n",
"A = np.zeros((3, 3))\n",
"rhs = np.zeros(3)\n",
"for i in range(3):\n",
" A[i] = xp[i] ** 2, xp[i], 1 # Store one row at a time\n",
" rhs[i] = yp[i]\n",
"print('Array A:')\n",
"print(A)\n",
"print('rhs:',rhs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The system may be solved with the `solve` method, which is part of the `linalg` subpackage of `numpy`. The `solve` method takes as input a two-dimensional array (the matrix) and a one-dimensional array (the right-hand side) and returns the solution. To check whether the solution is correct, we need to do a matrix multiply of the matrix stored in the array `A` and the obtained solution, which we call `sol`. As we learned the line\n",
"\n",
"`A * sol`\n",
"\n",
"does a term-by-term multiply. For a matrix multiply, the `@` symbol needs to be used (alternatively, the `np.dot` function can be used; the `@` symbol does not work in Python 2)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"solution is: [ 0.44444444 -0.55555556 -0.88888889]\n",
"specified values of y: [ 2 -1 4]\n",
"A @ sol: [ 2. -1. 4.]\n"
]
}
],
"source": [
"sol = np.linalg.solve(A, rhs)\n",
"print('solution is:', sol)\n",
"print('specified values of y:', yp)\n",
"print('A @ sol:', A @ sol)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also visually check whether we solved the problem correctly by drawing the three points and the parabola. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(xp, yp, 'ro')\n",
"x = np.linspace(-3, 5, 100)\n",
"y = sol[0] * x ** 2 + sol[1] * x + sol[2]\n",
"plt.plot(x, y, 'b');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 1. Fitting a wave\n",
"Consider the following four measurements of the quantity $y$ at time $t$: $(t_0,y_0)=(0,3)$, $(t_1,y_1)=(0.25,1)$, $(t_2,y_2)=(0.5,-3)$, $(t_3,y_3)=(0.75,1)$. The measurements are part of a wave that may be written as\n",
"\n",
"$y = a\\cos(\\pi t) + b\\cos(2\\pi t) + c\\cos(3\\pi t) + d\\cos(4\\pi t)$\n",
"\n",
"where $a$, $b$, $c$, and $d$ are parameters. Build a system of four linear equations and solve for the four parameters. Creates a plot of the wave for $t$ going from 0 to 1 and show the four measurements with dots."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fitting an arbitrary polynomial\n",
"In the next three exerises, we are going to fit a polynomial of arbitary degree $N$ to a set of $N+1$ data points. The function we are going to fit is \n",
"\n",
"$$f(x) = a_0 + a_1x + a_2x^2 + ... + a_Nx^N = \\sum\\limits_{n=0}^{N}a_nx^n$$\n",
"\n",
"Note that there are $N+1$ parameters $a_n$, while the degree of the polynomial is called $N$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 2. The `fpoly` function\n",
"First, write a function called `fpoly` that returns an array where item $n$ is equal to $x^n$. The input arguments of the function are the value of $x$ and the degree of the polynomial $N$. The output of the function is an array of length $N+1$. Test your function for $x=2$ and $N=4$ by executing\n",
"\n",
"`print fpoly(2, 4)`\n",
"\n",
"which should return `[ 1. 2. 4. 8. 16.]`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 3. The `solvepoly` function\n",
"Next, write a function that computes the parameters $a_n$ to fit a polynomial of degree $N$ through $N+1$ data points. Call the function `solvepoly`. The input arguments of the function are an array $x$ of length $N+1$ and an array $y$ of length $N+1$. The output is an array of parameters $a_n$ such that a polynomial of degree $N$ goes exactly through the $N+1$ data points $x$ and $y$. Inside the function, you need to compute a matrix of $N+1$ equations for the $N+1$ unknown parameters. For each of the rows of the matrix, call the function `fpoly`. Test your function by executing the following four commands. If your code is correct, the parameter array `a` is [ 3. 2.33333333 -6. 1.66666667].\n",
"\n",
" xp = np.array([0, 1, 2, 3])\n",
" yp = np.array([3, 1, -3, 1])\n",
" a = solvepoly(xp, yp)\n",
" print(a)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 4. The `fpolyeval` function\n",
"Finally, write a function called `fpolyeval` to evaluate the function $f(x) = \\sum\\limits_{n=0}^{N}a_nx^n$ for given parameters $a$ and an array of $x$ values. The `fpolyeval` function takes as input argument an array of arbitrary length $x$ and an array of parameters $a$ of length $N+1$. The function returns an array of $f(x)$ values with a length equal to the length of $x$. First test your function by executing\n",
"\n",
"`fpolyeval(xp, a)`\n",
"\n",
"where `xp` is the array with the values entered in Exercise 3 and `a` are the parameters computed in Exercise 3. When you programmed everything correctly, the function should return the four values of `yp` specified in Exercise 3. Test your function further by running the following commands, which should plot the four data points of Exercise 3 as markers and the 3$^\\text{rd}$ degree polynomial that goes exactly through the four points.\n",
"\n",
" x = np.linspace(-1,4,100)\n",
" y = fpolyeval(x, a)\n",
" plt.plot(xp, yp, 'ko', label='data')\n",
" plt.plot(x, y, label='fitted poly')\n",
" plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### One-dimensional groundwater flow\n",
"Consider a sand layer covered by a clay layer. The sand layer is bounded on each side by a canal with fixed water level $h_1^*$ (left) and $h_2^*$ (right); the distance between the two canals is $L$. Water leaks through the clay layer at a constant rate $P$ (see Figure). The groundwater head in the sand layer is governed by the second-order ordinary differential equation\n",
"\n",
"$$\\frac{\\text{d}^2h}{\\text{d}x^2} = -\\frac{P}{kD}$$\n",
"\n",
"where $h$ is the head, $k$ is the hydraulic conductivity of the sand layer, and $D$ is the thickness of the sand layer. The boundary conditions are that $h=h_1^*$ at $x=0$ and $h=h_2^*$ at $x=L$. \n",
"\n",
"\n",
"\n",
"Although it is easy to solve this problem exactly, we will solve it here numerically using the finite difference method (which allows for $P$ to be a function of $x$, for example). The head is computed at $N+1$ equally spaced points from $x=0$ to $x=L$. The points are labeled $x_0$ through $x_{N}$, where $x_n=n\\Delta x$, and $\\Delta x$ is the horizontal distance between the points. The head at point $x_n$ is called $h_n$. The second order derivative can be approximated as (see, e.g., Verrujt (2012) Soil Mechanics, Eq. 17.4; a link to a pdf of the full text of this book may be found under Software [here](http://geo.verruijt.net/).\n",
"\n",
"$$\\frac{\\text{d}^2h}{\\text{d}x^2} \\approx \\frac{1}{\\Delta x} \\left[ \\frac{h_{n+1}-h_n}{\\Delta x} - \\frac{h_{n}-h_{n-1}}{\\Delta x} \\right]= \\frac{h_{n-1}-2h_n+h_{n+1}}{(\\Delta x)^2}$$\n",
"\n",
"Substitution of this approximation of the derivative in the differential equation and rearranging terms gives\n",
"\n",
"$$h_{n-1}-2h_n+h_{n+1} = -P\\frac{(\\Delta x)^2}{kD}$$\n",
"\n",
"An equation like this may be written for every point $n$, except for the first and last point where we need to apply the boundary conditions:\n",
"\n",
"$$h_0=h_1^* \\qquad h_N=h_2^*$$\n",
"\n",
"When $N=4$, we need to solve a system of $N+1=5$ linear equations in the unknowns $h_0$ through $h_4$:\n",
"\n",
"$$\\begin{split}\n",
"h_0 &= h_1^* \\\\\n",
"h_{0}-2h_1+h_{2} &= -P(\\Delta x)^2/(kD) \\\\\n",
"h_{1}-2h_2+h_{3} &= -P(\\Delta x)^2/(kD) \\\\\n",
"h_{2}-2h_3+h_{4} &= -P(\\Delta x)^2/(kD) \\\\\n",
"h_4 &= h_2^* \n",
"\\end{split}$$\n",
"\n",
"or in matrix form\n",
"\n",
"$$\n",
"\\left(\n",
"\\begin{array}{ccccc}\n",
"1 & 0 & 0 & 0 & 0 \\\\\n",
"1 & -2 & 1 & 0 & 0 \\\\\n",
"0 & 1 & -2 & 1 & 0 \\\\\n",
"0 & 0 & 1 & -2 & 1 \\\\\n",
"0 & 0 & 0 & 0 & 1 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"\\left(\n",
"\\begin{array}{c}\n",
"h_0 \\\\\n",
"h_1 \\\\\n",
"h_2 \\\\\n",
"h_3 \\\\\n",
"h_4 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"=\n",
"\\left(\n",
"\\begin{array}{c}\n",
"h_1^* \\\\\n",
"-P(\\Delta x)^2/(kD) \\\\\n",
"-P(\\Delta x)^2/(kD) \\\\\n",
"-P(\\Delta x)^2/(kD) \\\\\n",
"h_2^* \\\\\n",
"\\end{array}\n",
"\\right)\n",
"$$\n",
"\n",
"Note that the matrix consists of mostly zeros. The matrix is referred to as a tri-diagonal matrix, as there are only values along three diagonals of the matrix. The matrix may be constructed by specifying the values and positions of the diagonals. The main diagonal has position number zero and has length $N+1$. The diagonal right above the main diagonal has position number $+1$ and length $N$, while the diagonal below the main diagonal has position number $-1$ and also length $N$. The `np.diag` function creates a matrix consisting of one diagonal. The input arguments are an array of the correct length with the values along the diagonal and the position of the diagonal. The matrix may be constructed as follows:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 1. 0. 0. 0. 0.]\n",
" [ 1. -2. 1. 0. 0.]\n",
" [ 0. 1. -2. 1. 0.]\n",
" [ 0. 0. 1. -2. 1.]\n",
" [ 0. 0. 0. 0. 1.]]\n"
]
}
],
"source": [
"N = 4\n",
"d0 = -2 * np.ones(N + 1) # main diagonal\n",
"d0[0] = 1 # first value of main diagonal is 1\n",
"d0[-1] = 1 # last value of main diagonal is 1\n",
"dplus1 = np.ones(N) # diagonal right above main diagonal, position 1\n",
"dplus1[0] = 0 # first value of diagonal is 0\n",
"dmin1 = np.ones(N) # diagonal right below main diagonal, position -1\n",
"dmin1[-1] = 0 # last value of diagonal is 0\n",
"A = np.diag(d0, 0) + np.diag(dplus1, 1) + np.diag(dmin1, -1)\n",
"print(A)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the finite-difference method described above is accurate when you use a reasonable number of points. Four points won't cut it. You may figure out whether you used enough points by, for example, doubling the number of points and compare the two solutions. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 5. The head between two canals\n",
"Compute the head distribution in a sand layer bounded on each side by a canal. Given: $k=10$ m/day, $D=10$ m, $h_1^*=20$ m, $h_2^*=22$ m, $L=1000$ m, $P=0.001$ m/d. Use $N=40$. Write Python code to:\n",
"\n",
"* Solve for the heads in all $N+1$ points\n",
"* Print the maximum value of the head between the two canals to the screen (this should be around 22.5)\n",
"* Create a plot of the head vs. $x$. Label the axes."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Consolidation\n",
"The deformation of saturated clay soils is a slow process, referred to as consolidation. In the compression of a soil, the porosity decreases, and as a result there is less space available for pore water. Hence, some pore water needs to be pushed out of the soil during compression. This may take considerable time in clays, as the permeability of clays is small. An extensive description of the consolidation process may be found in, e.g., Chapters 15-17 of Verruijt, 2012, Soil Mechanics, see this [link](http://geo.verruijt.net/)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider one-dimensional consolidation in a soil of height $h$. The water pressure $p$ in the soil sample is governed by the differential equation\n",
"\n",
"$$\\frac{\\partial p}{\\partial t} = c_v \\frac{\\partial^2 p}{\\partial z^2}$$\n",
"\n",
"where $z$ is the vertical coordinate (positive upward), and $c_v$ is the consolidation coefficient. We consider the problem where water can drain out at the top, but not at the bottom, so that the boundary condition at the bottom is\n",
"\n",
"$$z=0 \\qquad \\frac{\\partial p}{\\partial z} = 0$$\n",
"\n",
"and the boundary condition at the top is\n",
"\n",
"$$z=h \\qquad p = 0$$\n",
"\n",
"A constant load is applied at the top at time $t=0$ resulting, initially, in a uniform pressure $q$ throughout the soil sample (except for at $z=0$, where the pressure is always zero).\n",
"\n",
"$$t=0 \\qquad p = q$$\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The change of pressure with time in the soil is simulated with a numerical method (fully implicit finite differences, to be exact). The pressure is computed at $N+1$ points, equally distributed from $z=0$ to $z=h$. The points are labeled $z_0$ through $z_{N}$, where $z_n=n\\Delta z$ and $\\Delta z$ is the vertical distance between the points. The pressure at point $z_n$ is called $p_n$. A separate solution is computed for every time step $\\Delta t$. The time derivative is approximated as\n",
"\n",
"$$\\frac{\\partial p}{\\partial t} \\approx \\frac{p_n(t) - p_n(t-\\Delta t)}{\\Delta t}$$\n",
"\n",
"while the spatial derivative is approximated as\n",
"\n",
"$$\\frac{\\partial^2 p}{\\partial z^2} \\approx \\frac{p_{n-1}(t) -2p_n(t) + p_{n+1}(t)}{\\Delta z)^2} $$\n",
"\n",
"Subsitution of the approximations of these derivatives and gathering terms gives the following equation:\n",
"\n",
"$$p_{n-1}(t) - (2+\\mu)p_n(t) + p_{n+1}(t) = -\\mu p_n(t-\\Delta t)$$\n",
"\n",
"where \n",
"\n",
"$$\\mu = (\\Delta z)^2/(c_v\\Delta t)$$\n",
"\n",
"This is an equation for the pressure in points $(n-1)$, $n$, and $(n+1)$ at time $t$, where it is assumed that the pressure at time $t-\\Delta t$ is known.\n",
"\n",
"The equations for $n=0$ and $n=N$ are different. \n",
"At the bottom of the sample ($n=0$) the boundary condition is $\\partial p/\\partial z = 0$. The derivative may be approximated at $z_0=0$ as \n",
"\n",
"$$\\left(\\frac{\\partial p}{\\partial z}\\right)_{z=0} \\approx (p_1-p_{-1})/(2\\Delta z)=0$$\n",
"\n",
"where $p_{-1}$ is the pressure at an imaginary point $\\Delta z$ below $z_0$. The derivative is zero when $p_{-1}=p_1$, and substitution in the equation for $n=0$ gives\n",
"\n",
"$$- (2+\\mu)p_n(t) + 2p_{n+1}(t) = -\\mu p_n(t-\\Delta t)$$\n",
"\n",
"The equation for $n=N$ is easier, as at the top of the sample ($n=N$) the pressure is fixed to $p_N=0$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As an example, the system of equations for $N=4$ is\n",
"\n",
"$$\n",
"\\left(\n",
"\\begin{array}{ccccc}\n",
"-(2+\\mu) & 2 & 0 & 0 & 0 \\\\\n",
"1 & -(2+\\mu) & 1 & 0 & 0 \\\\\n",
"0 & 1 & -(2+\\mu) & 1 & 0 \\\\\n",
"0 & 0 & 1 & -(2+\\mu) & 1 \\\\\n",
"0 & 0 & 0 & 0 & 1 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"\\left(\n",
"\\begin{array}{c}\n",
"p_0(t) \\\\\n",
"p_1(t) \\\\\n",
"p_2(t) \\\\\n",
"p_3(t) \\\\\n",
"p_4(t) \\\\\n",
"\\end{array}\n",
"\\right)\n",
"=\n",
"\\left(\n",
"\\begin{array}{c}\n",
"-\\mu p_0(t-\\Delta t)) \\\\\n",
"-\\mu p_1(t-\\Delta t)) \\\\\n",
"-\\mu p_2(t-\\Delta t)) \\\\\n",
"-\\mu p_3(t-\\Delta t) \\\\\n",
"0 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"$$\n",
"\n",
"A solution is obtained by stepping through time. The matrix needs to be computed only once, as it doesn't change through time. Every time step, a new right-hand-side needs to be computed and a linear system of $N+1$ equations needs to be solved. If the matrix is called $A$ and the right-hand-side (based on the pressures at $t-\\Delta t$) is called $\\vec{r}(t-\\Delta t)$, then the pressure at time $t$, $\\vec{p}(t)$, is obtained by solving the system\n",
"\n",
"$$A\\vec{p}(t) = \\vec{r}(t-\\Delta t)$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note again that the presented numerical solution procedure is approximate and only gives accurate solutions when the time step $\\Delta t$ and the spatial discretization $\\Delta z$ are chosen small enough."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 6. One-dimensional consolidation\n",
"Consider the consolidation process of a clay layer that is 2 m thick. A uniform load is applied at time $t=0$ causing a unit increase in the pressure, i.e., $p(t=0)=1$. The consolidation coefficient of the clay is $c_v=1\\cdot 10^{-6}$ m$^2$/s. Simulate the consolidation process using the numerical method described above. Use $N=40$ and a time step $\\Delta t=4\\cdot 10^4$ sec. Take 50 time steps and plot the pressure distribution in the clay every 10 time steps. Add labels along the axes and a legend. Compare your solution to the graph in Fig. 16.2 of Veruit (2012) (Note that Verruijt plots $p$ along the horizontal axis). The last line of your plot should approximate the line $c_v t / h^2=0.5$ in the graph of Verrujt. \n",
"\n",
"Make sure that your Python code:\n",
"\n",
"* Solves for the pressure in all $N+1$ points for all 50 time steps and plots the results after 10, 20, 30, 40, and 50 time steps.\n",
"* Prints the maximum value of the pressure to the screen after 10, 20, 30, 40, and 50 time steps."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The inverse of a matrix\n",
"As mentioned, the values of the matrix `A` don't change through time. Hence, it is more efficient to compute and store the inverse of the matrix rather than repeatedly calling the `np.linalg.solve` method. The inverse of a matrix may be computed with the `inv` function of the `linalg` package. If the inverse of matrix `A` is called `Ainv`, the solution for the pressure may be obtained through matrix multiplication of `Ainv` with the right-hand side. For example, for the first problem in this Notebook, fitting a parabola through three points, the inverse of the matrix can be computed to obtain a solution as follows: "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sol: [ 0.44444444 -0.55555556 -0.88888889]\n"
]
}
],
"source": [
"A = np.array([[ 4, -2, 1],\n",
" [ 1, 1, 1],\n",
" [16, 4, 1]])\n",
"rhs = np.array([2,-1, 4])\n",
"Ainv = np.linalg.inv(A)\n",
"sol = Ainv @ rhs\n",
"print('sol:', sol)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 7. One-dimensional consolidation revisited\n",
"Modify your solution to Exercise 6 by computing and storing the inverse of the matrix, and compute a solution through multiplication of the inverse of the matrix with the right-hand-side vector"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 7"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sparse matrices\n",
"The prodedure we have used so far to construct the matrix for a finite-difference solution is not very efficient, as a full matrix is created, which consists of mainly zeros. Non-zero values only appear on three diagonals. There are more efficient routines that store what are called *sparse matrices*. In a sparse matrix, only the value and location of non-zero values in a matrix are stored. Functionality for sparse matrices is available in the `scipy.sparse` package. A sparse matrix may be created from diagonals with the `diags` function, which takes a list of arrays for the diagonals and a list of the numbers of the diagonals. For example, the matrix\n",
"$$\\left(\n",
"\\begin{array}{cccc}\n",
"2 & 3 & 0 & 0 \\\\\n",
"1 & 2 & 3 & 0 \\\\\n",
"0 & 1 & 2 & 3 \\\\\n",
"0 & 0 & 1 & 2 \\\\\n",
"\\end{array}\n",
"\\right)$$\n",
"is created as"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sparse matrix A\n",
"\n",
" Coords\tValues\n",
" (1, 0)\t1.0\n",
" (0, 0)\t2.0\n",
" (2, 1)\t1.0\n",
" (1, 1)\t2.0\n",
" (0, 1)\t3.0\n",
" (3, 2)\t1.0\n",
" (2, 2)\t2.0\n",
" (1, 2)\t3.0\n",
" (3, 3)\t2.0\n",
" (2, 3)\t3.0\n",
"Full matrix A as an array\n",
"[[2. 3. 0. 0.]\n",
" [1. 2. 3. 0.]\n",
" [0. 1. 2. 3.]\n",
" [0. 0. 1. 2.]]\n"
]
}
],
"source": [
"import scipy.sparse as sp\n",
"A = sp.diags([1 * np.ones(3), \n",
" 2 * np.ones(4), \n",
" 3 * np.ones(3)], \n",
" [-1, 0, 1], format='csc')\n",
"print('Sparse matrix A')\n",
"print(A) # Gives the way A is stored: row, column, value\n",
"print('Full matrix A as an array')\n",
"print(A.toarray()) # Returns the equivalent full array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are many ways to store a sparse matrix. In the code above, the sparse matrix `A` is stored in *compressed sparse column* (specified as `'csc'`). The advantages and disadvantages of this format are given [here](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csc_matrix.html). `A` is now a sparse matrix object. (Note that the multiplication sign does not do term-by-term multiplication for sparse matrix objects.) The solution to the system of equations $Ax=b$ is obtained with the `spsolve` function of the `scipy.sparse.linalg` module. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"type of A: \n",
"right-hand-side defined as: [0 1 2 3]\n",
"verify A @ x gives same: [0. 1. 2. 3.]\n"
]
}
],
"source": [
"from scipy.sparse.linalg import spsolve\n",
"print('type of A:', type(A))\n",
"b = np.arange(4)\n",
"x = spsolve(A,b) # x is solution of Ax=b\n",
"print('right-hand-side defined as:', b)\n",
"print('verify A @ x gives same:', A @ x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The main advantage of sparse matrices is that you can solve *much* larger problems than with full matrices, as you only store the (few) points that are not zero. The solver `spsolve` also makes use of the sparsity of the matrix and will generally be faster. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 8 Sparse matrix\n",
"Redo Exercise 5 but now use a *sparse* matrix. Obtain a solution for the head using $h_1^*=42$, $h_2^*=40$, and $N=10000$. All other parameters are the same as for Exercise 2. Create a plot of the head between the two canals. **Warning**: When you try to solve the problem with a regular (full) matrix and $N=10000$, you may run out of computer memory or the solve may take a *very* long time, and/or your program may hang. Don't try this, but if you accidentally do this and your Notebook doesn't recover, try to click on 'Kernel' in the menu bar at the top and then on 'Restart'."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 8"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solutions to the exercises"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 1"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a,b,c,d: [ 1. 2. 1. -1.]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tp = np.array([0, 0.25, 0.5, 0.75])\n",
"yp = np.array([ 3, 1, -3, 1])\n",
"A = np.zeros((4, 4))\n",
"rhs = np.zeros(4)\n",
"for i in range(4):\n",
" A[i] = np.cos(1 * np.pi * tp[i]), np.cos(2 * np.pi * tp[i]), \\\n",
" np.cos(3 * np.pi * tp[i]), np.cos(4 * np.pi * tp[i]) # Store one row at a time\n",
" rhs[i] = yp[i]\n",
"sol = np.linalg.solve(A, rhs)\n",
"print('a,b,c,d: ',sol)\n",
"\n",
"t = np.linspace(0, 1, 100)\n",
"y = sol[0] * np.cos(1 * np.pi * t) + sol[1] * np.cos(2 * np.pi * t) + \\\n",
" sol[2] * np.cos(3 * np.pi * t) + sol[3] * np.cos(4 * np.pi * t)\n",
"plt.plot(t, y, 'b', label='wave')\n",
"plt.plot(tp, yp, 'ro', label='data')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 1\n",
"\n",
"Answers to Exercise 2"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 1. 2. 4. 8. 16.]\n"
]
}
],
"source": [
"def fpoly(x, N):\n",
" rv = np.zeros(N + 1)\n",
" for n in range(N + 1):\n",
" rv[n] = x ** n\n",
" return rv\n",
"\n",
"print(fpoly(2, 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 2\n",
"\n",
"Answers to Exercise 3"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 3. 2.33333333 -6. 1.66666667]\n"
]
}
],
"source": [
"def solvepoly(x, y):\n",
" N = len(x) - 1\n",
" mat = np.zeros((N+1, N+1))\n",
" for n in range(N+1):\n",
" mat[n] = fpoly(x[n], N)\n",
" par = np.linalg.solve(mat, y)\n",
" return par\n",
" \n",
"xp = np.array([0, 1, 2, 3])\n",
"yp = np.array([3, 1, -3, 1])\n",
"a = solvepoly(xp, yp)\n",
"print(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 3\n",
"\n",
"Answers to Exercise 4"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 3. 1. -3. 1.]\n"
]
}
],
"source": [
"def fpolyeval(x, a):\n",
" rv = np.zeros(len(x))\n",
" for n in range(len(a)):\n",
" rv += a[n] * x ** n\n",
" return rv\n",
"\n",
"print(fpolyeval(xp, a))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(-1,4,100)\n",
"y = fpolyeval(x, a)\n",
"plt.plot(xp, yp, 'ko', label='data')\n",
"plt.plot(x, y, label='fitted poly')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 4\n",
"\n",
"Answers to Exercise 5"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"maximum head 22.449999999999903\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k = 10\n",
"D = 10\n",
"h1star = 20\n",
"h2star = 22\n",
"L = 1000\n",
"P = 0.001\n",
"N = 40\n",
"\n",
"d0 = -2 * np.ones(N + 1) # main diagonal\n",
"d0[0] = 1 # first value of main diagonal is 1\n",
"d0[-1] = 1 # last value of main diagonal is 1\n",
"dplus1 = np.ones(N) # diagonal right above main diagonal, position 1\n",
"dplus1[0] = 0 # first value of diagonal is 0\n",
"dmin1 = np.ones(N) # diagonal right below main diagonal, position -1\n",
"dmin1[-1] = 0 # last value of diagonal is 0\n",
"A = np.diag(d0, 0) + np.diag(dplus1, 1) + np.diag(dmin1, -1)\n",
"# Right hand side\n",
"delx = L / N\n",
"rhs = -P * delx ** 2 / (k * D) * np.ones(N + 1)\n",
"rhs[0] = h1star\n",
"rhs[-1] = h2star\n",
"# Solve for the head and plot\n",
"h = np.linalg.solve(A, rhs)\n",
"x = np.linspace(0, L, N + 1)\n",
"plt.plot(x, h)\n",
"plt.xlabel('x (m)')\n",
"plt.ylabel('head (m)')\n",
"print('maximum head ', np.max(h))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 5\n",
"\n",
"Answers to Exercise 6"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"maximum value after 10 timesteps is: 0.9425826615266134\n",
"maximum value after 20 timesteps is: 0.7742325163427506\n",
"maximum value after 30 timesteps is: 0.6117657473484334\n",
"maximum value after 40 timesteps is: 0.4801227573807983\n",
"maximum value after 50 timesteps is: 0.37636878032217186\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cv = 1e-6 # m^2/s\n",
"h = 2 # m\n",
"N = 40\n",
"delt = 4e4 # seconds\n",
"#\n",
"delz = h / N\n",
"mu = delz ** 2 / (cv * delt)\n",
"\n",
"d0 = -(2 + mu) * np.ones(N + 1)\n",
"d0[-1] = 1\n",
"dp1 = np.ones(N)\n",
"dp1[0] = 2\n",
"dm1 = np.ones(N)\n",
"dm1[-1] = 0\n",
"A = np.diag(d0) + np.diag(dp1, 1) + np.diag(dm1, -1)\n",
"\n",
"p = np.ones(N + 1)\n",
"for i in range(5):\n",
" for j in range(10):\n",
" rhs = -mu * p\n",
" rhs[-1] = 0\n",
" p = np.linalg.solve(A, rhs)\n",
" plt.plot(np.arange(0, h + 0.01, delz), p, label=str((i + 1) * 10) + ' timesteps')\n",
" print('maximum value after', 10 * ( i + 1), 'timesteps is:', p[0])\n",
"plt.xlim(0, 2)\n",
"plt.legend(loc='best')\n",
"plt.xlabel('z')\n",
"plt.ylabel('p')\n",
"plt.yticks(np.linspace(0, 1, 11))\n",
"plt.title('Consolidation');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 6\n",
"\n",
"Answers to Exercise 7"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"maximum value after 10 timesteps is: 0.9425826615266134\n",
"maximum value after 20 timesteps is: 0.7742325163427506\n",
"maximum value after 30 timesteps is: 0.6117657473484331\n",
"maximum value after 40 timesteps is: 0.48012275738079757\n",
"maximum value after 50 timesteps is: 0.3763687803221713\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cv = 1e-6 # m^2/s\n",
"h = 2 # m\n",
"N = 40\n",
"delt = 4e4 # seconds\n",
"#\n",
"delz = h / N\n",
"mu = delz ** 2 / (cv * delt)\n",
"\n",
"d0 = -(2 + mu) * np.ones(N + 1)\n",
"d0[-1] = 1\n",
"dp1 = np.ones(N)\n",
"dp1[0] = 2\n",
"dm1 = np.ones(N)\n",
"dm1[-1] = 0\n",
"A = np.diag(d0) + np.diag(dp1, 1) + np.diag(dm1, -1)\n",
"Ainv = np.linalg.inv(A)\n",
"\n",
"p = np.ones(N + 1)\n",
"for i in range(5):\n",
" for j in range(10):\n",
" rhs = -mu * p\n",
" rhs[-1] = 0\n",
" p = Ainv @ rhs\n",
" plt.plot(np.arange(0, h + 0.01, delz), p, label=str((i + 1) * 10) + ' timesteps')\n",
" print('maximum value after', 10 * ( i + 1), 'timesteps is:', p[0])\n",
"plt.xlim(0, 2)\n",
"plt.legend(loc='best')\n",
"plt.xlabel('z')\n",
"plt.ylabel('p')\n",
"plt.yticks(np.linspace(0, 1, 11))\n",
"plt.title('Consolidation');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 7\n",
"\n",
"Answers to Exercise 8"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.sparse import diags\n",
"from scipy.sparse.linalg import spsolve \n",
"k = 10\n",
"D = 10\n",
"h1star = 42\n",
"h2star = 40\n",
"L = 1000\n",
"P = 0.001\n",
"N = 10000\n",
"d0 = -2 * np.ones(N + 1) # main diagonal\n",
"d0[0] = 1 # first value of main diagonal is 1\n",
"d0[-1] = 1 # last value of main diagonal is 1\n",
"dplus1 = np.ones(N) # diagonal right above main diagonal, position 1\n",
"dplus1[0] = 0 # first value of diagonal is 0\n",
"dmin1 = np.ones(N) # diagonal right below main diagonal, position -1\n",
"dmin1[-1] = 0 # last value of diagonal is 0\n",
"A = diags([dmin1, d0, dplus1], [-1, 0, 1], format='csc')\n",
"# Right hand side\n",
"delx = L / N\n",
"rhs = -P * delx ** 2 / (k * D) * np.ones(N + 1)\n",
"rhs[0] = h1star\n",
"rhs[-1] = h2star\n",
"h = spsolve(A, rhs)\n",
"plt.plot(h)\n",
"plt.xlabel('node number')\n",
"plt.ylabel('head (m)');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to Exercise 8"
]
}
],
"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": 4
}
![](\"https://raw.githubusercontent.com/mbakker7/exploratory_computing_with_python/master/tudelft_logo.png\"){kind=logo}
\n",
"![\"Consolidation\"](\"http://i.imgur.com/2DH0sxT.png\")
\n",
"\n",
"Although it is easy to solve this problem exactly, we will solve it here numerically using the finite difference method (which allows for $P$ to be a function of $x$, for example). The head is computed at $N+1$ equally spaced points from $x=0$ to $x=L$. The points are labeled $x_0$ through $x_{N}$, where $x_n=n\\Delta x$, and $\\Delta x$ is the horizontal distance between the points. The head at point $x_n$ is called $h_n$. The second order derivative can be approximated as (see, e.g., Verrujt (2012) Soil Mechanics, Eq. 17.4; a link to a pdf of the full text of this book may be found under Software [here](http://geo.verruijt.net/).\n",
"\n",
"$$\\frac{\\text{d}^2h}{\\text{d}x^2} \\approx \\frac{1}{\\Delta x} \\left[ \\frac{h_{n+1}-h_n}{\\Delta x} - \\frac{h_{n}-h_{n-1}}{\\Delta x} \\right]= \\frac{h_{n-1}-2h_n+h_{n+1}}{(\\Delta x)^2}$$\n",
"\n",
"Substitution of this approximation of the derivative in the differential equation and rearranging terms gives\n",
"\n",
"$$h_{n-1}-2h_n+h_{n+1} = -P\\frac{(\\Delta x)^2}{kD}$$\n",
"\n",
"An equation like this may be written for every point $n$, except for the first and last point where we need to apply the boundary conditions:\n",
"\n",
"$$h_0=h_1^* \\qquad h_N=h_2^*$$\n",
"\n",
"When $N=4$, we need to solve a system of $N+1=5$ linear equations in the unknowns $h_0$ through $h_4$:\n",
"\n",
"$$\\begin{split}\n",
"h_0 &= h_1^* \\\\\n",
"h_{0}-2h_1+h_{2} &= -P(\\Delta x)^2/(kD) \\\\\n",
"h_{1}-2h_2+h_{3} &= -P(\\Delta x)^2/(kD) \\\\\n",
"h_{2}-2h_3+h_{4} &= -P(\\Delta x)^2/(kD) \\\\\n",
"h_4 &= h_2^* \n",
"\\end{split}$$\n",
"\n",
"or in matrix form\n",
"\n",
"$$\n",
"\\left(\n",
"\\begin{array}{ccccc}\n",
"1 & 0 & 0 & 0 & 0 \\\\\n",
"1 & -2 & 1 & 0 & 0 \\\\\n",
"0 & 1 & -2 & 1 & 0 \\\\\n",
"0 & 0 & 1 & -2 & 1 \\\\\n",
"0 & 0 & 0 & 0 & 1 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"\\left(\n",
"\\begin{array}{c}\n",
"h_0 \\\\\n",
"h_1 \\\\\n",
"h_2 \\\\\n",
"h_3 \\\\\n",
"h_4 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"=\n",
"\\left(\n",
"\\begin{array}{c}\n",
"h_1^* \\\\\n",
"-P(\\Delta x)^2/(kD) \\\\\n",
"-P(\\Delta x)^2/(kD) \\\\\n",
"-P(\\Delta x)^2/(kD) \\\\\n",
"h_2^* \\\\\n",
"\\end{array}\n",
"\\right)\n",
"$$\n",
"\n",
"Note that the matrix consists of mostly zeros. The matrix is referred to as a tri-diagonal matrix, as there are only values along three diagonals of the matrix. The matrix may be constructed by specifying the values and positions of the diagonals. The main diagonal has position number zero and has length $N+1$. The diagonal right above the main diagonal has position number $+1$ and length $N$, while the diagonal below the main diagonal has position number $-1$ and also length $N$. The `np.diag` function creates a matrix consisting of one diagonal. The input arguments are an array of the correct length with the values along the diagonal and the position of the diagonal. The matrix may be constructed as follows:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 1. 0. 0. 0. 0.]\n",
" [ 1. -2. 1. 0. 0.]\n",
" [ 0. 1. -2. 1. 0.]\n",
" [ 0. 0. 1. -2. 1.]\n",
" [ 0. 0. 0. 0. 1.]]\n"
]
}
],
"source": [
"N = 4\n",
"d0 = -2 * np.ones(N + 1) # main diagonal\n",
"d0[0] = 1 # first value of main diagonal is 1\n",
"d0[-1] = 1 # last value of main diagonal is 1\n",
"dplus1 = np.ones(N) # diagonal right above main diagonal, position 1\n",
"dplus1[0] = 0 # first value of diagonal is 0\n",
"dmin1 = np.ones(N) # diagonal right below main diagonal, position -1\n",
"dmin1[-1] = 0 # last value of diagonal is 0\n",
"A = np.diag(d0, 0) + np.diag(dplus1, 1) + np.diag(dmin1, -1)\n",
"print(A)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the finite-difference method described above is accurate when you use a reasonable number of points. Four points won't cut it. You may figure out whether you used enough points by, for example, doubling the number of points and compare the two solutions. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 5. The head between two canals\n",
"Compute the head distribution in a sand layer bounded on each side by a canal. Given: $k=10$ m/day, $D=10$ m, $h_1^*=20$ m, $h_2^*=22$ m, $L=1000$ m, $P=0.001$ m/d. Use $N=40$. Write Python code to:\n",
"\n",
"* Solve for the heads in all $N+1$ points\n",
"* Print the maximum value of the head between the two canals to the screen (this should be around 22.5)\n",
"* Create a plot of the head vs. $x$. Label the axes."
]
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"source": [
"Answers to Exercise 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Consolidation\n",
"The deformation of saturated clay soils is a slow process, referred to as consolidation. In the compression of a soil, the porosity decreases, and as a result there is less space available for pore water. Hence, some pore water needs to be pushed out of the soil during compression. This may take considerable time in clays, as the permeability of clays is small. An extensive description of the consolidation process may be found in, e.g., Chapters 15-17 of Verruijt, 2012, Soil Mechanics, see this [link](http://geo.verruijt.net/)."
]
},
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"cell_type": "markdown",
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"Consider one-dimensional consolidation in a soil of height $h$. The water pressure $p$ in the soil sample is governed by the differential equation\n",
"\n",
"$$\\frac{\\partial p}{\\partial t} = c_v \\frac{\\partial^2 p}{\\partial z^2}$$\n",
"\n",
"where $z$ is the vertical coordinate (positive upward), and $c_v$ is the consolidation coefficient. We consider the problem where water can drain out at the top, but not at the bottom, so that the boundary condition at the bottom is\n",
"\n",
"$$z=0 \\qquad \\frac{\\partial p}{\\partial z} = 0$$\n",
"\n",
"and the boundary condition at the top is\n",
"\n",
"$$z=h \\qquad p = 0$$\n",
"\n",
"A constant load is applied at the top at time $t=0$ resulting, initially, in a uniform pressure $q$ throughout the soil sample (except for at $z=0$, where the pressure is always zero).\n",
"\n",
"$$t=0 \\qquad p = q$$\n",
"\n",
"![\"Consolidation\"](\"http://i.imgur.com/4xdeoxw.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The change of pressure with time in the soil is simulated with a numerical method (fully implicit finite differences, to be exact). The pressure is computed at $N+1$ points, equally distributed from $z=0$ to $z=h$. The points are labeled $z_0$ through $z_{N}$, where $z_n=n\\Delta z$ and $\\Delta z$ is the vertical distance between the points. The pressure at point $z_n$ is called $p_n$. A separate solution is computed for every time step $\\Delta t$. The time derivative is approximated as\n",
"\n",
"$$\\frac{\\partial p}{\\partial t} \\approx \\frac{p_n(t) - p_n(t-\\Delta t)}{\\Delta t}$$\n",
"\n",
"while the spatial derivative is approximated as\n",
"\n",
"$$\\frac{\\partial^2 p}{\\partial z^2} \\approx \\frac{p_{n-1}(t) -2p_n(t) + p_{n+1}(t)}{\\Delta z)^2} $$\n",
"\n",
"Subsitution of the approximations of these derivatives and gathering terms gives the following equation:\n",
"\n",
"$$p_{n-1}(t) - (2+\\mu)p_n(t) + p_{n+1}(t) = -\\mu p_n(t-\\Delta t)$$\n",
"\n",
"where \n",
"\n",
"$$\\mu = (\\Delta z)^2/(c_v\\Delta t)$$\n",
"\n",
"This is an equation for the pressure in points $(n-1)$, $n$, and $(n+1)$ at time $t$, where it is assumed that the pressure at time $t-\\Delta t$ is known.\n",
"\n",
"The equations for $n=0$ and $n=N$ are different. \n",
"At the bottom of the sample ($n=0$) the boundary condition is $\\partial p/\\partial z = 0$. The derivative may be approximated at $z_0=0$ as \n",
"\n",
"$$\\left(\\frac{\\partial p}{\\partial z}\\right)_{z=0} \\approx (p_1-p_{-1})/(2\\Delta z)=0$$\n",
"\n",
"where $p_{-1}$ is the pressure at an imaginary point $\\Delta z$ below $z_0$. The derivative is zero when $p_{-1}=p_1$, and substitution in the equation for $n=0$ gives\n",
"\n",
"$$- (2+\\mu)p_n(t) + 2p_{n+1}(t) = -\\mu p_n(t-\\Delta t)$$\n",
"\n",
"The equation for $n=N$ is easier, as at the top of the sample ($n=N$) the pressure is fixed to $p_N=0$."
]
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"As an example, the system of equations for $N=4$ is\n",
"\n",
"$$\n",
"\\left(\n",
"\\begin{array}{ccccc}\n",
"-(2+\\mu) & 2 & 0 & 0 & 0 \\\\\n",
"1 & -(2+\\mu) & 1 & 0 & 0 \\\\\n",
"0 & 1 & -(2+\\mu) & 1 & 0 \\\\\n",
"0 & 0 & 1 & -(2+\\mu) & 1 \\\\\n",
"0 & 0 & 0 & 0 & 1 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"\\left(\n",
"\\begin{array}{c}\n",
"p_0(t) \\\\\n",
"p_1(t) \\\\\n",
"p_2(t) \\\\\n",
"p_3(t) \\\\\n",
"p_4(t) \\\\\n",
"\\end{array}\n",
"\\right)\n",
"=\n",
"\\left(\n",
"\\begin{array}{c}\n",
"-\\mu p_0(t-\\Delta t)) \\\\\n",
"-\\mu p_1(t-\\Delta t)) \\\\\n",
"-\\mu p_2(t-\\Delta t)) \\\\\n",
"-\\mu p_3(t-\\Delta t) \\\\\n",
"0 \\\\\n",
"\\end{array}\n",
"\\right)\n",
"$$\n",
"\n",
"A solution is obtained by stepping through time. The matrix needs to be computed only once, as it doesn't change through time. Every time step, a new right-hand-side needs to be computed and a linear system of $N+1$ equations needs to be solved. If the matrix is called $A$ and the right-hand-side (based on the pressures at $t-\\Delta t$) is called $\\vec{r}(t-\\Delta t)$, then the pressure at time $t$, $\\vec{p}(t)$, is obtained by solving the system\n",
"\n",
"$$A\\vec{p}(t) = \\vec{r}(t-\\Delta t)$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note again that the presented numerical solution procedure is approximate and only gives accurate solutions when the time step $\\Delta t$ and the spatial discretization $\\Delta z$ are chosen small enough."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 6. One-dimensional consolidation\n",
"Consider the consolidation process of a clay layer that is 2 m thick. A uniform load is applied at time $t=0$ causing a unit increase in the pressure, i.e., $p(t=0)=1$. The consolidation coefficient of the clay is $c_v=1\\cdot 10^{-6}$ m$^2$/s. Simulate the consolidation process using the numerical method described above. Use $N=40$ and a time step $\\Delta t=4\\cdot 10^4$ sec. Take 50 time steps and plot the pressure distribution in the clay every 10 time steps. Add labels along the axes and a legend. Compare your solution to the graph in Fig. 16.2 of Veruit (2012) (Note that Verruijt plots $p$ along the horizontal axis). The last line of your plot should approximate the line $c_v t / h^2=0.5$ in the graph of Verrujt. \n",
"\n",
"Make sure that your Python code:\n",
"\n",
"* Solves for the pressure in all $N+1$ points for all 50 time steps and plots the results after 10, 20, 30, 40, and 50 time steps.\n",
"* Prints the maximum value of the pressure to the screen after 10, 20, 30, 40, and 50 time steps."
]
},
{
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"execution_count": null,
"metadata": {},
"outputs": [],
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"cell_type": "markdown",
"metadata": {},
"source": [
"Answers to Exercise 6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The inverse of a matrix\n",
"As mentioned, the values of the matrix `A` don't change through time. Hence, it is more efficient to compute and store the inverse of the matrix rather than repeatedly calling the `np.linalg.solve` method. The inverse of a matrix may be computed with the `inv` function of the `linalg` package. If the inverse of matrix `A` is called `Ainv`, the solution for the pressure may be obtained through matrix multiplication of `Ainv` with the right-hand side. For example, for the first problem in this Notebook, fitting a parabola through three points, the inverse of the matrix can be computed to obtain a solution as follows: "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sol: [ 0.44444444 -0.55555556 -0.88888889]\n"
]
}
],
"source": [
"A = np.array([[ 4, -2, 1],\n",
" [ 1, 1, 1],\n",
" [16, 4, 1]])\n",
"rhs = np.array([2,-1, 4])\n",
"Ainv = np.linalg.inv(A)\n",
"sol = Ainv @ rhs\n",
"print('sol:', sol)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 7. One-dimensional consolidation revisited\n",
"Modify your solution to Exercise 6 by computing and storing the inverse of the matrix, and compute a solution through multiplication of the inverse of the matrix with the right-hand-side vector"
]
},
{
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"cell_type": "markdown",
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"Answers to Exercise 7"
]
},
{
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"source": [
"### Sparse matrices\n",
"The prodedure we have used so far to construct the matrix for a finite-difference solution is not very efficient, as a full matrix is created, which consists of mainly zeros. Non-zero values only appear on three diagonals. There are more efficient routines that store what are called *sparse matrices*. In a sparse matrix, only the value and location of non-zero values in a matrix are stored. Functionality for sparse matrices is available in the `scipy.sparse` package. A sparse matrix may be created from diagonals with the `diags` function, which takes a list of arrays for the diagonals and a list of the numbers of the diagonals. For example, the matrix\n",
"$$\\left(\n",
"\\begin{array}{cccc}\n",
"2 & 3 & 0 & 0 \\\\\n",
"1 & 2 & 3 & 0 \\\\\n",
"0 & 1 & 2 & 3 \\\\\n",
"0 & 0 & 1 & 2 \\\\\n",
"\\end{array}\n",
"\\right)$$\n",
"is created as"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sparse matrix A\n",
"