{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Pseudospectral methods tutorial, part 1\n", "## UNCW, March 2018\n", "\n", "\n", "A gentle stroll through pseudospectral methods: differentiating functions using finite differences and spectral methods (the Fast Fourier Transform).\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1D domain - periodic functions $f(x)$ for $x\\in[0,L_x]$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First load the package for plotting." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ "using Pkg\n", "Pkg.activate(\"../../.\")\n", "\n", "using PyPlot, FFTW" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create the physical grid $x$. For a domain of length $L_x$ with $n_x$ grid points the grid spacing is $\\delta=L_x/n_x$. Our grid points then are: $x = 0,\\delta, 2\\delta,\\dots,L_x-\\delta$. Notice, that the final grid point *does not* correspond to $x=L_x$ but to $x=L_x-\\delta$. This is because of periodicity: $f(L_x)=f(0)$ and, therefore, the grid point $x=L_x$ is the same as $x=0$.|\n", "\n", "Thus, our grid points for an array with elements $x_j = (j-1)\\delta$, where $j=1,\\dots,n_x$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [], "source": [ "nx = 32\n", "Lx = 2.0*pi\n", "\n", "dx = Lx/nx\n", " x = 0:dx:Lx-dx;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's define a function, e.g., $f(x) = \\sin(2x)+\\frac1{2}\\cos(5x)$. The approximation of this function on our $x$-grid is the array with elements\n", "$$f_j \\equiv f(x_j),\\text{ for }j=1,\\dots,n_x.$$\n", "\n", "Let us see how well the array $f_j$ approximates function $f(x)$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = @. sin(2*x) + 0.5*cos(5*x) # a test function f(x)\n", "\n", "\n", "x_cont = range(0, Lx, length=1001) # a much finer x-grid used for plotting the \"actual\" f(x)\n", "f_cont = @. sin(2*x_cont) + 0.5*cos(5*x_cont) # the same function f(x) defined on the finer grid\n", "\n", "\n", "# plot f(x) and f_j; for f(x) we just plot f on the finer grid, f_cont\n", "\n", "figure(1, figsize=(8, 3) )\n", "plot(x_cont, f_cont, linestyle=\"solid\", label=L\"f(x)\") # plots the abs value of fft of f(x)\n", "plot(x, f, marker=\"*\", color=\"r\", linestyle=\"none\", label=L\"f_j\") # plots the abs value of fft of f(x)\n", "legend()\n", "xlim(0, Lx)\n", "xlabel(L\"x\")\n", "ylabel(L\"f(x)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Remark**: Do $n_x=32$ grid points capture the behavior of $f(x)$ good enough? How would a grid with $16$ points look? A rule-of-thumb is that we need about $4$ grid points per wavelength of the highest harmonic. In our case $f(x)$ includes a $\\sin(5x)$ term, oscillates 5 times within our domain. Therefore our rule-of-thumb would argue that we capture the behavior of $f(x)$ if we use at least $20$ grid points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The derivative of the above function is $df/dx = 2\\cos(2x)-\\frac5{2}\\sin(5x)$. Let us pretend that we do not know the derivative and instead try to compute it numerically. \n", "\n", "(When we are coding something new we should *always* try to start with something we know what the answer should be so we can compare our numerical results. This step may seem obvious, but, nonetheless, it is often overlooked by most people...)\n", "\n", "The simplest approximation for the array of the derivative $(df/dx)_j$ is the, so called, second-order centered finite differences:\n", "$$\\left(\\frac{df}{dx}\\right)_j = \\frac{f_{j+1}-f_{j-1}}{2\\delta},\\text{ for }j=1,\\dots,n_x,$$\n", "where it is understood that $f_{0}=f_{n_x}$ and $f_{n_x+1}=f_1$ due to periodic boundary conditions.\n", "\n", "Let's see how this approximation compares with the actual derivative." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# the analytical expression for df/dx\n", "dfdx_an = 2*cos.(2*x) - 2.5*sin.(5*x)\n", "\n", "# the analytical expression for df/dx computed on the finer grid (for plotting purposes)\n", "dfdx_an_cont = 2*cos.(2*x_cont) - 2.5*sin.(5*x_cont) \n", "\n", "# the finite differences approximation\n", "dfdx_fd = zeros(nx)\n", "for j in 2:nx-1\n", " dfdx_fd[j] = (f[j+1]- f[j-1])/(2*dx)\n", "end\n", "# for the j=1 and j=nx grid points we use the fact that f(x) is periodic!\n", "dfdx_fd[1] = (f[2] - f[nx]) /(2*dx)\n", "dfdx_fd[nx] = (f[1] - f[nx-1])/(2*dx)\n", "\n", "\n", "\n", "# Plot (df/dx)_j and compare with the actual df/dx\n", "\n", "fig, axs = subplots(nrows=2, ncols=1, figsize=(8, 6) )\n", "\n", "sca(axs[1])\n", "plot(x_cont, dfdx_an_cont, label=\"analytical\")\n", "plot(x, dfdx_fd, marker=\"d\", color=\"g\", linestyle=\"none\", label=\"numerical\")\n", "\n", "xlabel(L\"x\")\n", "ylabel(L\"df / dx\")\n", "legend(loc=\"upper right\", fancybox=\"true\")\n", "xlim(0, Lx-dx)\n", "\n", "sca(axs[2])\n", "plot(x, abs.(dfdx_an - dfdx_fd), marker=\"d\", label=\"|numerical-analytical|\")\n", "legend(loc=\"upper left\", fancybox=\"true\")\n", "xlabel(L\"x\")\n", "ylabel(\"absolute error\")\n", "xlim(0, Lx-dx);\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the error at each grid-point is of order $10^{-1}$. If we increase the number of grid-points, of course, the error will decrease.\n", "\n", "For second-order finite differences the error should decrease as $n_x^2$. This means that if we increase the numbers of grid-points by a factor of $10$ then the error should decrease by a factor of $10^2$. This is OK, but we can do _much better_ using **spectral methods**.\n", "\n", "**Exercise**: Confirm the above assertion. Show (merely by plotting) that the error for the finite-difference approximation of the derivative decreases as $n_x^2$?\n", "\n", "To use spectral methods we need to remind ourselves what a Fourier series is.\n", "\n", "Any periodic and square-integrable function defined on the domain $0\\le x\\le L_x$ can be expanded as a Fourier series:\n", "$$ f(x) = \\sum_{k} \\hat{\\;f}_{k}\\,e^{i k x},$$\n", "where the wavenumbers $k = \\frac{2\\pi}{L_x}[0,\\pm1,\\pm2,\\dots]$. The coefficents $\\hat{\\;f}_{k}$ are\n", "$$\\hat{\\;f}_{k} = \\frac1{L_x}\\int_{0}^{L_x} f(x)\\,e^{-i k x}\\,dx.$$\n", "\n", "By \"square-integrable\" we mean that $\\int_0^{L_x} \\left|f(x)\\right|^2 dx <\\infty$. Note that $f$ does not have to be differentiable. In fact, it can even be discontinuous within our domain. However, in this tutorial we will only use differentiable functions for our examples.\n", "\n", "The derivative is trivially expressed as a Fourier series as:\n", "$$ \\frac{df}{dx} = \\sum_{k} i k \\hat{\\;f}_{k}\\,e^{i k x}.$$\n", "(Just differentiate the right-hand-side of the Fourier series for $f(x)$.)\n", "\n", "\n", "Our function $f$ is, conveniently, already expanded as a Fourier series so we can read off the coefficients $\\hat{\\;f}_{k}$:\n", "$$\\hat{\\;f}_{k}=\\begin{cases}\n", " \\frac1{2i} \\quad\\text{if $k=4\\pi/L_x$,} \\\\\n", " -\\frac1{2i} \\quad\\text{if $k=-4\\pi/L_x$,} \\\\\n", " \\frac1{4} \\quad\\text{if $k=10\\pi/L_x$,} \\\\\n", " \\frac1{4} \\quad\\text{if $k=-10\\pi/L_x$,} \\\\\n", " 0 \\quad\\text{otherwise.} \\\\\n", " \\end{cases}$$\n", "This mean that for our example the Fourier series is not an infinite sum but rather it terminates since after some wavenumber all coefficients are zero.\n", "\n", "**Exercise**: Use the coefficients above and compute the Fourier series for $\\sum_{k} i k \\hat{\\;f}_{k}\\,e^{i k x}$ (i.e. sum all the terms). Do you recover the analytical expression for $df/dx$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The wavenumbers that take part in the sum for the Fourier series of a function $f(x)$ form an array: $k_m = (2\\pi/L_x) m$, with $m=0,\\pm1,\\pm2,\\dots$. However, if our function $f(x)$ is restricted only on the values of the $x$-grid, $x_j=(j-1)\\delta=(j-1)L_x/n_x$, $j=1,\\dots,n_x$, then _only_ $n_x$ of all wavenumbers are independent. Thus the Fourier series truncates from an _infinite_ sum to a _finite_ sum. To see first that consider:\n", "$$ f(x_j) = \\sum_{m=-\\infty}^{+\\infty} \\hat{\\;f}_{k} \\exp{\\Big[ i \\underbrace{\\frac{2\\pi}{L_x} m}_{= k_m} \\; \\underbrace{(j-1)\\frac{L_x}{n_x}}_{=x_j}\\Big]}$$\n", "But the exponential inside the sum above remains unchanged if we replace $m\\mapsto m+n_x$, i.e.,\n", "$$ \\exp{\\left[ 2\\pi i \\frac{(m+n_x) (j-1)}{n_x}\\right]} = \\underbrace{\\exp{\\left[ 2\\pi i (j-1)\\right]}}_{=1\\text{ since }j\\in\\mathbb{Z}}\\exp{\\left[ 2\\pi i\\frac{m (j-1)}{n_x}\\right]} = \\exp{\\left[ 2\\pi i \\frac{m (j-1)}{n_x}\\right]}. $$\n", "\n", "Therefore we only need to take $n_x$ different wavenumbers in the sum. It does not really matter which ones we choose to have, given that we include $k_x=0$. Conventionally, we take $n_x$ to be even and choose:\n", "$$k = \\frac{2\\pi}{n_x}\\left[0,1,2,\\dots,\\frac{n_x}{2},-\\frac{n_x}{2}+1,-\\frac{n_x}{2}+2,\\dots,-2,-1\\right].$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If our example function $f$ was not as simple we couldn't not just read off the values of the coefficients $\\hat{\\;f}_{k}$ from $f$. In that case we could go back to the definition and compute the coefficients $\\hat{\\;f}_{k}$ through the integral above (or by approximating the integral numerically). Fortunately though, even in those cases we don't have to do that. There exist the Fast Fourier Transform (`fft`) algorithm (which is included in Matlab, Python, Julia, etc). This algorithm is very well optimized, i.e., it is much faster than actually approximating the integral numerically. We can obtain the coefficents $\\hat{\\;f}_{k}$ using `fft` as:\n", "$$\n", "\\mathtt{fft}(f) = \\hat{\\;f}_{k}\\,n_x.\n", "$$\n", "Above by $\\mathtt{fft}(f)$ we mean performing `fft` on the array with elements $f_j$. The multiplication with $n_x$ on the right-hand-side above is due to the normalization that `fft` algorithm uses. Furthermore, with the inverse, `ifft` we can compute $f$ from $\\hat{\\;f}_{k}$.\n", "$$\n", "\\mathtt{ifft}(\\hat{\\;f}_{k}) = f\\big/n_x.\n", "$$\n", "\n", "\n", "\n", "With the coefficients $\\hat{\\;f}_{k}$ in hand we compute $df/dx$ as\n", "$$\\frac{df}{dx} = \\mathtt{ifft}\\left[ i k \\mathtt{fft}(f)\\right] .$$\n", "\n", "Let us see how well the numerical approximation of the derivative using spectral methods compares with the actual analytical expression for $df/dx$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [], "source": [ "# the k_x wavenumbers in the order that the FFT algorithm assumes\n", "k = 2.0*pi/Lx * cat(0:nx/2, -nx/2+1:-1, dims=1);\n", "\n", " fh = fft(f)/nx # the FFT of f(x)\n", "dfdx_num = real(ifft(im*k.*fh)*nx); # the numerical approximation for df/dx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that after we used `ifft` we also took the real part. We do that to remove any imaginary parts that the algoritm might introduce (which should be of order $10^{-16}$).\n", "\n", "First we plot the coefficients $\\hat{\\;f}_{k}$ obtained using the `fft` algorithm. Do we see power at the wavenumbers we were expecting?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(1, figsize=(8, 3) )\n", "plot(k, abs.(fh), marker=\"d\", markersize=10, linestyle=\":\", linewidth=0.5) # plots the abs value of fft of f(x)\n", "xlim(-12, 12)\n", "xlabel(L\"k_x\")\n", "ylabel(L\"|\\hat{f}_{k_x}|\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's compare the numerical approximation of $df/dx$ with the analytical one." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = subplots(nrows=2, ncols=1, figsize=(8, 6) )\n", "\n", "sca(axs[1])\n", "plot(x_cont, dfdx_an_cont, label=\"analytical\")\n", "plot(x, dfdx_num, marker=\"*\", color=\"r\", linestyle=\"none\", label=\"numerical\")\n", "\n", "xlabel(L\"x\")\n", "ylabel(L\"df / dx\")\n", "legend(loc=\"upper right\", fancybox=\"true\")\n", "xlim(0, Lx-dx)\n", "\n", "sca(axs[2])\n", "plot(x, abs.(dfdx_an - dfdx_num), marker=\"d\", label=\"|numerical-analytical|\")\n", "legend(loc=\"upper left\", fancybox=\"true\")\n", "xlabel(L\"x\")\n", "ylabel(\"absolute error\")\n", "xlim(0, Lx-dx);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wow!\n", "\n", "See how much better accuracy we got now? We got an error of (nearly) machine precission. And we obtained this just with only $n_x=32$ points. Try doing that with finite differences...\n", "\n", "(The error with finite differences using $n_x=10^{20}\\approx 1000000$ points is still about $10^{-10}$, i.e., $10^4$ larger compared to spectral methods!)\n", "\n", "**Exercise**: Can we perhaps push spectral methods even further? What about if we had $n_x=16$ points? How far can we decreasee the resolution and still evaluate $df/dx$ with such good accuracy?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2D domain - periodic functions $f(x,y)$ for $(x,y)\\in[0,L_x]\\times[0,L_y]$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's apply the same principles on a two-dimensional domain for periodic functions $f(x,y)$, i.e., function with the property $f(x+L_x,y)=f(x,y+L_y)=f(x,y)$. Same principle apply; now the Fourier series is:\n", "$$ f(x,y) = \\sum_k\\sum_l \\hat{\\;f}_{k,l} \\, e^{i(k x+l y)},$$\n", "with $k=(2\\pi/L_x)[0,\\pm 1,\\pm2,\\dots]$ and $l=(2\\pi/L_y)[0,\\pm 1,\\pm2,\\dots]$.\n", "\n", "First, we create the physical grid $x$, $y$. It is instructive to take different domain lengths, $L_x$ and $L_y$ and different grid points in each direction, $n_x$, $n_y$. This way make sure that we treat each dimension correctly." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false }, "outputs": [], "source": [ "nx, ny = 64, 32 # number of grid points\n", "Lx, Ly = 2.0*pi, 1.0*pi # size of the domain in each direction\n", "\n", "# constructing the physical grid (x,y)\n", "dx, dy = Lx/nx, Ly/ny\n", " x = 0:dx:Lx-dx\n", " y = 0:dy:Ly-dy\n", "\n", "X = zeros(nx,ny)\n", "Y = zeros(nx,ny)\n", "for j in 1:ny, i in 1:nx\n", " X[i,j], Y[i, j] = x[i], y[j]\n", "end\n", "\n", "# constructing the wavenumber grid (k,l)\n", "k = 2.0*pi/Lx * cat(0:nx/2, -nx/2+1:-1, dims=1);\n", "l = 2.0*pi/Ly * cat(0:ny/2, -ny/2+1:-1, dims=1);\n", "\n", "K = zeros(nx, ny)\n", "L = zeros(nx, ny)\n", "for j in 1:ny, i in 1:nx\n", " K[i, j] = k[i]\n", " L[i, j] = l[j]\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's define a two-dimensional function:\n", "$$f(x,y) = \\cos\\left(3\\frac{2\\pi}{L_x} x\\right)\\sin\\left(2\\frac{2\\pi}{L_y} y\\right).$$\n", "Let's compute $\\partial f/\\partial y$ numerically and compare with the analytical expression." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [], "source": [ "k0 = 2.0*pi/Lx # the fundamental x-wavenumber\n", "l0 = 2.0*pi/Ly # the fundamental y-wavenumber\n", "\n", "mx, my = 3, 2\n", "f = cos.(mx*k0*X).*sin.(my*l0*Y)\n", "fh = fft(f)\n", "\n", "dfdy_an = my*l0*cos.(mx*k0*X).*cos.(my*l0*Y)\n", "dfdy_num = real(ifft(im*L.*fh));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Plot the two-dimensional power spectra of $f$: $|\\hat{\\;f}_{k,l}|$. Is it how you expexted it to be?\n", "(Regarding normalization, the coefficients $\\hat{\\;f}_{k,l} = \\mathtt{fft}(f)\\big/(n_x n_y)$.)\n", "\n", "Now, as we did before, let's plot the numerical and analytical $\\partial f/\\partial y$ and compare. If all is good, we should expect machine precision error..." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "levs = -4:1:4 # the contour levels for the plots of \\partial f/\\partial y\n", "\n", "# contour plot of the analytical \\partial f/\\partial y\n", "figure(figsize=(8, 3))\n", "\n", "contourf(X, Y, dfdy_an, levs) # notice that contour levels are prescribed\n", "xlabel(L\"$x$\")\n", "ylabel(L\"$y$\")\n", "title(L\"analytical $\\partial f/\\partial y$\")\n", "xlim(0, Lx-dx)\n", "ylim(0, Ly-dy)\n", "clim(-4,4)\n", "colorbar(ticks=-4:2:4)\n", "\n", "# contour plot of the numerical approcimation to \\partial f/\\partial y\n", "figure(figsize=(8, 3))\n", "contourf(X, Y, dfdy_num, levs)\n", "\n", "xlabel(L\"$x$\")\n", "ylabel(L\"$y$\")\n", "title(L\"numerical $\\partial f/\\partial y$\")\n", "xlim(0, Lx-dx)\n", "ylim(0, Ly-dy)\n", "clim(-4,4)\n", "colorbar(ticks=-4:2:4)\n", "\n", "# contour plot of the absolute error\n", "figure(figsize=(8, 3))\n", "contourf(X, Y, abs.(dfdy_an - dfdy_num))\n", "\n", "xlabel(L\"$x$\")\n", "ylabel(L\"$y$\")\n", "title(\"absolute error = |analytical - numerical|\")\n", "xlim(0, Lx-dx)\n", "ylim(0, Ly-dy)\n", "colorbar();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What's your favorite number? Mine is $10^{-16}$; this is the machine precision with 64-bit arithmetic. When I see that probably I know I did everything correct. (Often if I see just plain $0$ the usually something's going wrong.)\n", "\n", "Do we get machine precision if we calculate the relative error that we made with our approximation?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "1.1102230246251565e-15" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rel_error = abs.(maximum(abs.(dfdy_an)) - maximum(abs.(dfdy_num)))/maximum(abs.(dfdy_an))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sure we do..." ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.1.0", "language": "julia", "name": "julia-1.1" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.1.0" } }, "nbformat": 4, "nbformat_minor": 1 }