diff --git a/docs/examples/edtrk_from_the_ground_up.ipynb b/docs/examples/edtrk_from_the_ground_up.ipynb index be1921e..d80c839 100644 --- a/docs/examples/edtrk_from_the_ground_up.ipynb +++ b/docs/examples/edtrk_from_the_ground_up.ipynb @@ -2,25 +2,1216 @@ "cells": [ { "cell_type": "markdown", + "id": "cell-0", "metadata": {}, "source": [ - "Placeholder for a tutorial I want to write, explaining Fourier pseudo-spectral\n", - "ETDRK methods from the ground up." + "# ETDRK from the Ground Up\n", + "\n", + "This tutorial explains **Fourier pseudo-spectral Exponential Time Differencing\n", + "Runge-Kutta (ETDRK) methods** from first principles. These methods are the\n", + "backbone of every timestepper in `Exponax`. We will build up from scalar ODEs\n", + "to spectral methods, implement ETDRK0 through ETDRK4, discuss dealiasing, and\n", + "extend to higher spatial dimensions.\n", + "\n", + "**Outline:**\n", + "\n", + "1. Linear ODEs and the matrix exponential\n", + "2. Spectral derivatives (turning a PDE into decoupled ODEs)\n", + "3. ETDRK0 — exact integration of linear PDEs\n", + "4. Semi-linear PDEs and ETDRK1/2\n", + "5. The contour integral trick for numerically stable coefficients\n", + "6. Convergence comparison of ETDRK orders\n", + "7. Dealiasing (Orszag's 2/3 rule)\n", + "8. Higher dimensions and limitations\n", + "\n", + "**Key references:**\n", + "\n", + "- Cox & Matthews (2002), *Exponential Time Differencing for Stiff Systems*,\n", + " J. Comput. Phys. 176.\n", + "- Kassam & Trefethen (2005), *Fourth-Order Time-Stepping for Stiff PDEs*,\n", + " SIAM J. Sci. Comput. 26." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cell-1", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:48.707759Z", + "iopub.status.busy": "2026-02-11T15:31:48.707601Z", + "iopub.status.idle": "2026-02-11T15:31:49.487222Z", + "shell.execute_reply": "2026-02-11T15:31:49.486887Z" + } + }, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import exponax as ex\n", + "from exponax._spectral import (\n", + " build_derivative_operator,\n", + " build_laplace_operator,\n", + " build_wavenumbers,\n", + " low_pass_filter_mask,\n", + ")\n", + "from exponax.etdrk import ETDRK0, roots_of_unity\n", + "\n", + "jax.config.update(\"jax_enable_x64\", True)" + ] + }, + { + "cell_type": "markdown", + "id": "cell-2", + "metadata": {}, + "source": [ + "## Linear ODEs and the Matrix Exponential\n", + "\n", + "Consider the scalar ODE\n", + "\n", + "$$ \\frac{du}{dt} = \\lambda u, \\qquad u(0) = u_0. $$\n", + "\n", + "Its exact solution is $u(t) = e^{\\lambda t}\\, u_0$. A classical explicit Euler\n", + "step $u^{[t+1]} = u^{[t]} + \\Delta t\\, \\lambda\\, u^{[t]} = (1 + \\lambda \\Delta t)\\, u^{[t]}$\n", + "approximates this, but the **exponential integrator** $u^{[t+1]} = e^{\\lambda\n", + "\\Delta t}\\, u^{[t]}$ is *exact* — no time-discretization error at all.\n", + "\n", + "For systems $\\frac{d\\mathbf{u}}{dt} = A\\, \\mathbf{u}$, the solution involves\n", + "the **matrix exponential**: $\\mathbf{u}(t) = e^{At}\\, \\mathbf{u}_0$. This is\n", + "generally $\\mathcal{O}(N^3)$ to compute via `expm`. However, when $A$ is\n", + "**diagonal**, the matrix exponential reduces to element-wise exponentiation of\n", + "the eigenvalues — only $\\mathcal{O}(N)$ work. As we will see, Fourier\n", + "transforms diagonalize constant-coefficient differential operators, giving us\n", + "exactly this structure." ] }, { "cell_type": "code", "execution_count": null, + "id": "cell-3", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:49.488508Z", + "iopub.status.busy": "2026-02-11T15:31:49.488358Z", + "iopub.status.idle": "2026-02-11T15:31:49.885373Z", + "shell.execute_reply": "2026-02-11T15:31:49.885083Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING:2026-02-11 16:31:49,508:jax._src.xla_bridge:876: An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Scalar ODE: du/dt = lambda * u, u(0) = u_0\n", + "LAMBDA = -1.5\n", + "U_0 = 2.0\n", + "T_FINAL = 4.0\n", + "DT_EULER = 0.2\n", + "\n", + "# Exact solution\n", + "t_exact = jnp.linspace(0, T_FINAL, 200)\n", + "u_exact = U_0 * jnp.exp(LAMBDA * t_exact)\n", + "\n", + "# Euler forward\n", + "n_steps = int(T_FINAL / DT_EULER)\n", + "t_euler = jnp.arange(n_steps + 1) * DT_EULER\n", + "u_euler = [U_0]\n", + "for _ in range(n_steps):\n", + " u_euler.append(u_euler[-1] + DT_EULER * LAMBDA * u_euler[-1])\n", + "u_euler = jnp.array(u_euler)\n", + "\n", + "# Exponential integrator (exact for linear ODE)\n", + "exp_factor = jnp.exp(LAMBDA * DT_EULER)\n", + "u_exp = [U_0]\n", + "for _ in range(n_steps):\n", + " u_exp.append(exp_factor * u_exp[-1])\n", + "u_exp = jnp.array(u_exp)\n", + "\n", + "fig, ax = plt.subplots(figsize=(6, 3.5))\n", + "ax.plot(t_exact, u_exact, \"k-\", label=\"Exact\", linewidth=2)\n", + "ax.plot(t_euler, u_euler, \"o--\", label=f\"Euler (\\u0394t={DT_EULER})\", markersize=4)\n", + "ax.plot(t_euler, u_exp, \"s-\", label=f\"Exponential (\\u0394t={DT_EULER})\", markersize=4)\n", + "ax.set_xlabel(\"t\")\n", + "ax.set_ylabel(\"u(t)\")\n", + "ax.legend()\n", + "ax.set_title(\"Scalar ODE: exact exponential vs Euler forward\")\n", + "ax.grid(True, alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "cell-4", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:49.886590Z", + "iopub.status.busy": "2026-02-11T15:31:49.886483Z", + "iopub.status.idle": "2026-02-11T15:31:50.321700Z", + "shell.execute_reply": "2026-02-11T15:31:50.321382Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Via expm: [0.60653066 0.06766764 1.80967484]\n", + "Via element-wise exp: [0.60653066 0.06766764 1.80967484]\n", + "Max difference: 1.39e-17\n" + ] + } + ], + "source": [ + "# System du/dt = A u with diagonal A\n", + "eigenvalues = jnp.array([-0.5, -2.0, -0.1])\n", + "A = jnp.diag(eigenvalues)\n", + "u0_sys = jnp.array([1.0, 0.5, 2.0])\n", + "DT_SYS = 1.0\n", + "\n", + "# Matrix exponential via jax.scipy\n", + "exp_A_dt = jax.scipy.linalg.expm(A * DT_SYS)\n", + "u1_expm = exp_A_dt @ u0_sys\n", + "\n", + "# For a diagonal matrix, this equals element-wise exp\n", + "u1_diag = jnp.exp(eigenvalues * DT_SYS) * u0_sys\n", + "\n", + "print(f\"Via expm: {u1_expm}\")\n", + "print(f\"Via element-wise exp: {u1_diag}\")\n", + "print(f\"Max difference: {jnp.max(jnp.abs(u1_expm - u1_diag)):.2e}\")" + ] + }, + { + "cell_type": "markdown", + "id": "cell-5", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "## From PDEs to ODEs: Spectral Derivatives\n", + "\n", + "To solve a PDE numerically, we use the **method of lines**: discretize space\n", + "into $N$ degrees of freedom, keeping time continuous. This turns the PDE into\n", + "a system of $N$ coupled ODEs.\n", + "\n", + "For **periodic domains** $[0, L)$, the Discrete Fourier Transform (DFT)\n", + "diagonalizes constant-coefficient differential operators. A spatial derivative\n", + "becomes a pointwise multiplication in Fourier space:\n", + "\n", + "$$ \\widehat{\\frac{\\partial u}{\\partial x}} = i k \\, \\hat{u}_k, \\qquad\n", + "k = \\frac{2\\pi}{L} n, \\quad n = 0, 1, \\dots, N/2. $$\n", + "\n", + "The second derivative (Laplacian in 1D) becomes:\n", + "\n", + "$$ \\widehat{\\frac{\\partial^2 u}{\\partial x^2}} = -k^2 \\, \\hat{u}_k. $$\n", + "\n", + "This turns a linear PDE like $u_t = \\nu\\, u_{xx}$ into $N/2+1$ **decoupled**\n", + "scalar ODEs: $\\frac{d\\hat{u}_k}{dt} = -\\nu k^2 \\hat{u}_k$. Each can be\n", + "solved exactly with an exponential!" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "cell-6", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:50.322955Z", + "iopub.status.busy": "2026-02-11T15:31:50.322807Z", + "iopub.status.idle": "2026-02-11T15:31:51.044388Z", + "shell.execute_reply": "2026-02-11T15:31:51.044069Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Max error of spectral derivative: 5.33e-14\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "NUM_POINTS = 128\n", + "DOMAIN_EXTENT = 2 * jnp.pi\n", + "\n", + "grid = ex.make_grid(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "x = grid[0]\n", + "\n", + "# Function and its exact derivative\n", + "u = jnp.sin(x) + 0.5 * jnp.sin(3 * x)\n", + "u_x_exact = jnp.cos(x) + 1.5 * jnp.cos(3 * x)\n", + "\n", + "# Spectral derivative: multiply Fourier coefficients by ik\n", + "u_with_channel = u[jnp.newaxis, :] # shape (1, N)\n", + "derivative_op = build_derivative_operator(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "u_hat = jnp.fft.rfftn(u_with_channel, axes=(-1,))\n", + "u_x_hat = derivative_op * u_hat\n", + "u_x_spectral = jnp.fft.irfftn(u_x_hat, s=(NUM_POINTS,), axes=(-1,))[0]\n", + "\n", + "error = jnp.max(jnp.abs(u_x_spectral - u_x_exact))\n", + "print(f\"Max error of spectral derivative: {error:.2e}\")\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))\n", + "axes[0].plot(x, u, label=r\"$\\sin(x) + 0.5\\sin(3x)$\")\n", + "axes[0].set_title(\"Function\")\n", + "axes[0].legend()\n", + "axes[0].grid(True, alpha=0.3)\n", + "\n", + "axes[1].plot(x, u_x_exact, \"k-\", label=\"Exact derivative\", linewidth=2)\n", + "axes[1].plot(x, u_x_spectral, \"r--\", label=\"Spectral derivative\")\n", + "axes[1].set_title(\"Derivative\")\n", + "axes[1].legend()\n", + "axes[1].grid(True, alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "cell-7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:51.045558Z", + "iopub.status.busy": "2026-02-11T15:31:51.045446Z", + "iopub.status.idle": "2026-02-11T15:31:51.155706Z", + "shell.execute_reply": "2026-02-11T15:31:51.155406Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Wavenumbers shape: (1, 65)\n", + "Derivative operator shape: (1, 65)\n", + "Laplace operator shape: (1, 65)\n", + "\n", + "First 8 wavenumbers: [0. 1. 2. 3. 4. 5. 6. 7.]\n", + "First 8 derivative op (imag part): [0. 1. 2. 3. 4. 5. 6. 7.]\n", + "First 8 Laplace op (real part): [ 0. -1. -4. -9. -16. -25. -36. -49.]\n" + ] + } + ], + "source": [ + "wavenumbers = build_wavenumbers(1, NUM_POINTS)\n", + "derivative_op = build_derivative_operator(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "laplace_op = build_laplace_operator(derivative_op)\n", + "\n", + "print(f\"Wavenumbers shape: {wavenumbers.shape}\")\n", + "print(f\"Derivative operator shape: {derivative_op.shape}\")\n", + "print(f\"Laplace operator shape: {laplace_op.shape}\")\n", + "print()\n", + "print(f\"First 8 wavenumbers: {wavenumbers[0, :8]}\")\n", + "print(f\"First 8 derivative op (imag part): {derivative_op[0, :8].imag}\")\n", + "print(f\"First 8 Laplace op (real part): {laplace_op[0, :8].real}\")" + ] + }, + { + "cell_type": "markdown", + "id": "cell-8", + "metadata": {}, + "source": [ + "## ETDRK0: Exact Integration of Linear PDEs\n", + "\n", + "Since the spectral linear operator $\\hat{\\mathcal{L}}$ is diagonal (one value\n", + "per wavenumber), the matrix exponential reduces to an element-wise exponential.\n", + "One time step reads:\n", + "\n", + "$$ \\hat{u}_k^{[t+1]} = \\exp\\bigl(\\hat{\\mathcal{L}}_k \\cdot \\Delta t\\bigr)\n", + "\\;\\hat{u}_k^{[t]}. $$\n", + "\n", + "This is **ETDRK0** — it solves linear PDEs exactly (up to machine precision)\n", + "with no time-discretization error, as long as the initial condition is\n", + "bandlimited.\n", + "\n", + "**Running example: the heat equation** $u_t = \\nu\\, u_{xx}$. The linear\n", + "operator in Fourier space is $\\hat{\\mathcal{L}}_k = \\nu \\cdot (-k^2) = \\nu\n", + "\\cdot \\hat{\\Delta}_k$, and the analytical solution is\n", + "$\\hat{u}_k(t) = e^{-\\nu k^2 t}\\, \\hat{u}_k(0)$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "cell-9", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:51.156809Z", + "iopub.status.busy": "2026-02-11T15:31:51.156704Z", + "iopub.status.idle": "2026-02-11T15:31:51.469956Z", + "shell.execute_reply": "2026-02-11T15:31:51.469638Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Manual ETDRK0 vs analytical: 2.55e-15\n", + "ETDRK0 class vs analytical: 2.55e-15\n", + "Diffusion stp vs analytical: 6.99e-15\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "NUM_POINTS = 128\n", + "DOMAIN_EXTENT = 1.0\n", + "DT = 0.001\n", + "NU = 0.01\n", + "NUM_STEPS = 50\n", + "\n", + "grid = ex.make_grid(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "x = grid[0]\n", + "\n", + "# Initial condition: single sine mode\n", + "u_0 = jnp.sin(2 * jnp.pi * x / DOMAIN_EXTENT)[jnp.newaxis, :] # shape (1, N)\n", + "\n", + "# --- Method 1: Manual ETDRK0 ---\n", + "derivative_op = build_derivative_operator(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "linear_op = NU * build_laplace_operator(derivative_op) # shape (1, N//2+1)\n", + "exp_term = jnp.exp(DT * linear_op)\n", + "\n", + "u_hat = jnp.fft.rfftn(u_0, axes=(-1,))\n", + "for _ in range(NUM_STEPS):\n", + " u_hat = exp_term * u_hat\n", + "u_manual = jnp.fft.irfftn(u_hat, s=(NUM_POINTS,), axes=(-1,))\n", + "\n", + "# --- Method 2: ETDRK0 class ---\n", + "etdrk0 = ETDRK0(DT, linear_op)\n", + "u_hat = jnp.fft.rfftn(u_0, axes=(-1,))\n", + "for _ in range(NUM_STEPS):\n", + " u_hat = etdrk0.step_fourier(u_hat)\n", + "u_etdrk0 = jnp.fft.irfftn(u_hat, s=(NUM_POINTS,), axes=(-1,))\n", + "\n", + "# --- Method 3: Exponax Diffusion stepper ---\n", + "diffusion_stepper = ex.stepper.Diffusion(\n", + " 1, DOMAIN_EXTENT, NUM_POINTS, DT, diffusivity=NU\n", + ")\n", + "u_stepper = u_0\n", + "for _ in range(NUM_STEPS):\n", + " u_stepper = diffusion_stepper(u_stepper)\n", + "\n", + "# --- Method 4: Analytical solution ---\n", + "k = 2 * jnp.pi / DOMAIN_EXTENT\n", + "t = NUM_STEPS * DT\n", + "u_analytical = (jnp.exp(-NU * k**2 * t) * jnp.sin(2 * jnp.pi * x / DOMAIN_EXTENT))[\n", + " jnp.newaxis, :\n", + "]\n", + "\n", + "print(f\"Manual ETDRK0 vs analytical: {jnp.max(jnp.abs(u_manual - u_analytical)):.2e}\")\n", + "print(f\"ETDRK0 class vs analytical: {jnp.max(jnp.abs(u_etdrk0 - u_analytical)):.2e}\")\n", + "print(f\"Diffusion stp vs analytical: {jnp.max(jnp.abs(u_stepper - u_analytical)):.2e}\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(6, 3.5))\n", + "ax.plot(x, u_0[0], label=\"Initial condition\", linewidth=2)\n", + "ax.plot(x, u_analytical[0], \"k--\", label=\"Analytical\", linewidth=2)\n", + "ax.plot(x, u_manual[0], \"r:\", label=\"Manual ETDRK0\", linewidth=3)\n", + "ax.set_xlabel(\"x\")\n", + "ax.set_ylabel(\"u\")\n", + "ax.legend()\n", + "ax.set_title(f\"Heat equation: {NUM_STEPS} steps (t = {t:.3f})\")\n", + "ax.grid(True, alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-10", + "metadata": {}, + "source": [ + "## Semi-Linear PDEs: The ETDRK Approach\n", + "\n", + "Many interesting PDEs have both a linear and a nonlinear part:\n", + "\n", + "$$ u_t = \\underbrace{\\mathcal{L}\\, u}_{\\text{linear}} +\n", + "\\underbrace{\\mathcal{N}(u)}_{\\text{nonlinear}}. $$\n", + "\n", + "**Example: Burgers equation** (conservative form)\n", + "\n", + "$$ u_t + \\tfrac{1}{2}(u^2)_x = \\nu\\, u_{xx} $$\n", + "\n", + "Here $\\mathcal{L} = \\nu\\, \\partial_{xx}$ (diffusion) and\n", + "$\\mathcal{N}(u) = -\\tfrac{1}{2}(u^2)_x$ (nonlinear advection).\n", + "\n", + "The **variation-of-constants** formula integrates the linear part exactly and\n", + "leaves an integral over the nonlinear forcing:\n", + "\n", + "$$ \\hat{u}_k(t + \\Delta t) = e^{\\hat{\\mathcal{L}}_k \\Delta t}\\,\n", + "\\hat{u}_k(t) + \\int_0^{\\Delta t} e^{\\hat{\\mathcal{L}}_k(\\Delta t - \\tau)}\\,\n", + "\\hat{\\mathcal{N}}_k\\bigl(u(t+\\tau)\\bigr)\\, d\\tau. $$\n", + "\n", + "**ETDRK1** approximates this integral with a rectangle rule, replacing\n", + "$\\hat{\\mathcal{N}}_k$ by its value at $t$. This yields the coefficient\n", + "$\\varphi_1(z) = (e^z - 1)/z$ where $z = \\hat{\\mathcal{L}}_k \\Delta t$:\n", + "\n", + "$$ \\hat{u}_k^{[t+1]} = e^{\\hat{\\mathcal{L}}_k \\Delta t}\\, \\hat{u}_k^{[t]}\n", + "+ \\Delta t\\, \\varphi_1(\\hat{\\mathcal{L}}_k \\Delta t) \\;\n", + "\\hat{\\mathcal{N}}_k(\\hat{u}^{[t]}). $$\n", + "\n", + "**ETDRK2** adds a corrector stage for second-order accuracy.\n", + "\n", + "The nonlinear term is evaluated **pseudo-spectrally**: dealias $\\to$ IFFT\n", + "$\\to$ compute $u^2$ pointwise $\\to$ FFT $\\to$ multiply by $ik$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "cell-11", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:51.471010Z", + "iopub.status.busy": "2026-02-11T15:31:51.470907Z", + "iopub.status.idle": "2026-02-11T15:31:51.730275Z", + "shell.execute_reply": "2026-02-11T15:31:51.729981Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "NUM_POINTS = 128\n", + "DOMAIN_EXTENT = 1.0\n", + "NU = 0.02\n", + "CONVECTION_SCALE = 1.0\n", + "\n", + "grid = ex.make_grid(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "x = grid[0]\n", + "\n", + "# Smooth initial condition\n", + "u_0 = jnp.sin(2 * jnp.pi * x / DOMAIN_EXTENT)[jnp.newaxis, :] # shape (1, N)\n", + "\n", + "# Build operators\n", + "derivative_op = build_derivative_operator(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "sum_derivative_op = jnp.sum(derivative_op, axis=0, keepdims=True) # shape (1, N//2+1)\n", + "\n", + "# Dealiasing mask (Orszag's 2/3 rule) — matches BaseNonlinearFun\n", + "nyquist_mode = NUM_POINTS // 2 + 1\n", + "highest_resolved = nyquist_mode - 1\n", + "cutoff = 2 / 3 * highest_resolved - 1\n", + "dealiasing_mask = low_pass_filter_mask(1, NUM_POINTS, cutoff=cutoff)\n", + "\n", + "# Pseudo-spectral evaluation of N(u) = -1/2 * convection_scale * (u^2)_x\n", + "u_hat = jnp.fft.rfftn(u_0, axes=(-1,))\n", + "u_hat_dealiased = dealiasing_mask * u_hat\n", + "u_phys = jnp.fft.irfftn(u_hat_dealiased, s=(NUM_POINTS,), axes=(-1,))\n", + "u_squared_hat = jnp.fft.rfftn(u_phys**2, axes=(-1,))\n", + "N_hat = -CONVECTION_SCALE * 0.5 * sum_derivative_op * u_squared_hat\n", + "\n", + "# Transform back to physical space for visualization\n", + "N_physical = jnp.fft.irfftn(N_hat, s=(NUM_POINTS,), axes=(-1,))\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))\n", + "axes[0].plot(x, u_0[0], label=\"u(x)\")\n", + "axes[0].set_title(\"State u\")\n", + "axes[0].legend()\n", + "axes[0].grid(True, alpha=0.3)\n", + "\n", + "axes[1].plot(\n", + " x,\n", + " N_physical[0],\n", + " color=\"tab:orange\",\n", + " label=r\"$\\mathcal{N}(u) = -\\frac{1}{2}(u^2)_x$\",\n", + ")\n", + "axes[1].set_title(\"Nonlinear term (conservative Burgers)\")\n", + "axes[1].legend()\n", + "axes[1].grid(True, alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "cell-12", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:51.731398Z", + "iopub.status.busy": "2026-02-11T15:31:51.731290Z", + "iopub.status.idle": "2026-02-11T15:31:52.249510Z", + "shell.execute_reply": "2026-02-11T15:31:52.249234Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Manual ETDRK1 vs Exponax Burgers: 0.00e+00\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "DT = 0.01\n", + "\n", + "# Build linear operator (diffusion)\n", + "linear_op = NU * build_laplace_operator(derivative_op)\n", + "\n", + "# Compute ETDRK1 coefficients via contour integral\n", + "NUM_CIRCLE_POINTS = 16\n", + "CIRCLE_RADIUS = 1.0\n", + "roots = roots_of_unity(NUM_CIRCLE_POINTS)\n", + "LR = CIRCLE_RADIUS * roots + linear_op[..., jnp.newaxis] * DT # (..., N//2+1, M)\n", + "exp_term = jnp.exp(DT * linear_op)\n", + "coef_1 = DT * jnp.mean((jnp.exp(LR) - 1) / LR, axis=-1).real\n", + "\n", + "# Nonlinear term at current state\n", + "u_hat = jnp.fft.rfftn(u_0, axes=(-1,))\n", + "u_hat_dealiased = dealiasing_mask * u_hat\n", + "u_phys = jnp.fft.irfftn(u_hat_dealiased, s=(NUM_POINTS,), axes=(-1,))\n", + "u_sq_hat = jnp.fft.rfftn(u_phys**2, axes=(-1,))\n", + "N_hat = -CONVECTION_SCALE * 0.5 * sum_derivative_op * u_sq_hat\n", + "\n", + "# ETDRK1 step: u_next = exp_term * u_hat + coef_1 * N_hat\n", + "u_next_hat = exp_term * u_hat + coef_1 * N_hat\n", + "u_next_manual = jnp.fft.irfftn(u_next_hat, s=(NUM_POINTS,), axes=(-1,))\n", + "\n", + "# Compare with Exponax Burgers stepper (order=1, conservative=True)\n", + "burgers_stepper = ex.stepper.Burgers(\n", + " 1,\n", + " DOMAIN_EXTENT,\n", + " NUM_POINTS,\n", + " DT,\n", + " diffusivity=NU,\n", + " convection_scale=CONVECTION_SCALE,\n", + " order=1,\n", + " conservative=True,\n", + ")\n", + "u_next_exponax = burgers_stepper(u_0)\n", + "\n", + "error = jnp.max(jnp.abs(u_next_manual - u_next_exponax))\n", + "print(f\"Manual ETDRK1 vs Exponax Burgers: {error:.2e}\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(6, 3.5))\n", + "ax.plot(x, u_0[0], label=\"Initial condition\")\n", + "ax.plot(x, u_next_manual[0], \"r--\", label=\"Manual ETDRK1\", linewidth=2)\n", + "ax.plot(x, u_next_exponax[0], \"k:\", label=\"Exponax Burgers (order=1)\", linewidth=2)\n", + "ax.set_xlabel(\"x\")\n", + "ax.set_ylabel(\"u\")\n", + "ax.legend()\n", + "ax.set_title(\"One ETDRK1 step for Burgers equation\")\n", + "ax.grid(True, alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-13", + "metadata": {}, + "source": [ + "## Numerically Stable Coefficients: The Contour Integral Trick\n", + "\n", + "The ETDRK1 coefficient $\\varphi_1(z) = (e^z - 1)/z$ has a **removable\n", + "singularity** at $z = 0$ (the limit is 1). However, naive floating-point\n", + "evaluation suffers from catastrophic cancellation near $z = 0$: the numerator\n", + "$e^z - 1 \\approx 0$ and the denominator $z \\approx 0$, producing `nan`.\n", + "\n", + "**Kassam & Trefethen (2005)** proposed using **Cauchy's integral formula**:\n", + "evaluate $\\varphi_1$ on a circle of radius $r$ centered at each\n", + "$z_k = \\hat{\\mathcal{L}}_k \\Delta t$ in the complex plane, then average\n", + "over $M$ equispaced points:\n", + "\n", + "$$ \\varphi_1(z_k) \\approx \\frac{1}{M} \\sum_{m=1}^{M}\n", + "\\frac{e^{z_k + r\\, \\omega_m} - 1}{z_k + r\\, \\omega_m}, $$\n", + "\n", + "where $\\omega_m$ are the $M$-th roots of unity. The key insight is that the\n", + "evaluation points $z_k + r\\, \\omega_m$ are *never* exactly zero (they sit on\n", + "a circle around $z_k$), so no cancellation occurs.\n", + "\n", + "Exponax uses $M = 16$ and $r = 1.0$ by default." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "cell-14", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:52.250583Z", + "iopub.status.busy": "2026-02-11T15:31:52.250480Z", + "iopub.status.idle": "2026-02-11T15:31:52.536017Z", + "shell.execute_reply": "2026-02-11T15:31:52.535719Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " z naive contour\n", + "--------------------------------------------------------\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 1.0e+00 1.718281828459046 1.718281828459038\n", + " 1.0e-01 1.051709180756477 1.051709180756473\n", + " 1.0e-02 1.005016708416795 1.005016708416803\n", + " 1.0e-04 1.000050001667141 1.000050001666706\n", + " 1.0e-08 0.999999993922529 1.000000004999997\n", + " 1.0e-15 1.110223024625157 0.999999999999998\n", + " 0.0e+00 nan 0.999999999999997\n", + " -1.0e+00 0.632120558828558 0.632120558828557\n", + " -1.0e-02 0.995016625083189 0.995016625083192\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Compare naive vs contour evaluation of phi_1(z) = (exp(z) - 1) / z\n", + "\n", + "\n", + "def phi_1_naive(z):\n", + " return (jnp.exp(z) - 1) / z\n", + "\n", + "\n", + "def phi_1_contour(z, M=16, r=1.0):\n", + " \"\"\"Evaluate phi_1 using contour integral with M points.\"\"\"\n", + " w = roots_of_unity(M)\n", + " zr = z + r * w\n", + " return jnp.mean((jnp.exp(zr) - 1) / zr).real\n", + "\n", + "\n", + "test_z = [1.0, 0.1, 0.01, 1e-4, 1e-8, 1e-15, 0.0, -1.0, -0.01]\n", + "\n", + "print(f\"{'z':>12s} {'naive':>20s} {'contour':>20s}\")\n", + "print(\"-\" * 56)\n", + "for z_val in test_z:\n", + " naive_val = float(phi_1_naive(z_val))\n", + " contour_val = float(phi_1_contour(z_val))\n", + " print(f\"{z_val:12.1e} {naive_val:20.15f} {contour_val:20.15f}\")\n", + "\n", + "# Visualize the 16 roots of unity\n", + "fig, ax = plt.subplots(figsize=(4, 4))\n", + "M = 16\n", + "w = roots_of_unity(M)\n", + "ax.plot(jnp.real(w), jnp.imag(w), \"o\", markersize=6, label=\"Evaluation points\")\n", + "theta = jnp.linspace(0, 2 * jnp.pi, 200)\n", + "ax.plot(jnp.cos(theta), jnp.sin(theta), \"k--\", alpha=0.3)\n", + "ax.plot(0, 0, \"rx\", markersize=10, markeredgewidth=2, label=\"z = 0 (singularity)\")\n", + "ax.set_aspect(\"equal\")\n", + "ax.set_xlabel(\"Re\")\n", + "ax.set_ylabel(\"Im\")\n", + "ax.set_title(f\"{M} roots of unity on the unit circle\")\n", + "ax.legend(fontsize=8)\n", + "ax.grid(True, alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-15", + "metadata": {}, + "source": [ + "## ETDRK Orders 0--4: Convergence Comparison\n", + "\n", + "The ETDRK family provides methods of different temporal orders. Each higher\n", + "order requires more nonlinear function evaluations per step but achieves\n", + "higher accuracy:\n", + "\n", + "| Method | Nonlinear evals/step | Temporal order | Notes |\n", + "|---------|---------------------|----------------|-------|\n", + "| ETDRK0 | 0 | exact (linear) | Linear PDEs only |\n", + "| ETDRK1 | 1 | 1 | Rectangle rule |\n", + "| ETDRK2 | 2 | 2 | Predictor-corrector, **Exponax default** |\n", + "| ETDRK4 | 4 | 4 | RK4-like with half-steps |\n", + "\n", + "ETDRK2 (the default in Exponax) is a good compromise for single precision.\n", + "For highest accuracy, use ETDRK4 with double precision\n", + "(`jax_enable_x64=True`).\n", + "\n", + "Below we compare all four on Burgers equation — first qualitatively\n", + "(space-time plots), then quantitatively (convergence rates)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "cell-16", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:52.537226Z", + "iopub.status.busy": "2026-02-11T15:31:52.537120Z", + "iopub.status.idle": "2026-02-11T15:31:53.277583Z", + "shell.execute_reply": "2026-02-11T15:31:53.277305Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "NUM_POINTS = 128\n", + "DOMAIN_EXTENT = 1.0\n", + "DT = 0.01\n", + "NU = 0.02\n", + "NUM_STEPS = 200\n", + "\n", + "grid = ex.make_grid(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "x = grid[0]\n", + "u_0 = jnp.sin(2 * jnp.pi * x / DOMAIN_EXTENT)[jnp.newaxis, :]\n", + "\n", + "fig, axes = plt.subplots(1, 4, figsize=(14, 3.5), sharey=True)\n", + "\n", + "for i, (order, title) in enumerate(\n", + " [(0, \"ETDRK0\"), (1, \"ETDRK1\"), (2, \"ETDRK2\"), (4, \"ETDRK4\")]\n", + "):\n", + " stepper = ex.stepper.Burgers(\n", + " 1,\n", + " DOMAIN_EXTENT,\n", + " NUM_POINTS,\n", + " DT,\n", + " diffusivity=NU,\n", + " order=order,\n", + " conservative=True,\n", + " )\n", + " rollout_fn = ex.rollout(stepper, NUM_STEPS, include_init=True)\n", + " trajectory = rollout_fn(u_0)\n", + "\n", + " axes[i].imshow(\n", + " trajectory[:, 0, :].T,\n", + " aspect=\"auto\",\n", + " origin=\"lower\",\n", + " cmap=\"RdBu_r\",\n", + " vmin=-1,\n", + " vmax=1,\n", + " extent=[0, NUM_STEPS * DT, 0, DOMAIN_EXTENT],\n", + " )\n", + " axes[i].set_title(title)\n", + " axes[i].set_xlabel(\"Time\")\n", + " if i == 0:\n", + " axes[i].set_ylabel(\"Space\")\n", + "\n", + "plt.suptitle(\"Burgers equation with different ETDRK orders\", y=1.02)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "cell-17", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:53.278829Z", + "iopub.status.busy": "2026-02-11T15:31:53.278728Z", + "iopub.status.idle": "2026-02-11T15:31:55.773399Z", + "shell.execute_reply": "2026-02-11T15:31:55.773110Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ETDRK1: slopes = ['2.35', '1.24', '1.08', '1.04']\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ETDRK2: slopes = ['1.98', '1.97', '2.00', '2.00']\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ETDRK4: slopes = ['3.65', '3.69', '3.74', '3.85']\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Temporal convergence test\n", + "NUM_POINTS = 256\n", + "DOMAIN_EXTENT = 1.0\n", + "NU = 0.02\n", + "T_FINAL = 0.5\n", + "\n", + "grid = ex.make_grid(1, DOMAIN_EXTENT, NUM_POINTS)\n", + "x = grid[0]\n", + "u_0 = jnp.sin(2 * jnp.pi * x / DOMAIN_EXTENT)[jnp.newaxis, :]\n", + "\n", + "# Reference solution: ETDRK4 with very small dt\n", + "DT_REF = 1e-4\n", + "n_ref = int(T_FINAL / DT_REF)\n", + "ref_stepper = ex.stepper.Burgers(\n", + " 1,\n", + " DOMAIN_EXTENT,\n", + " NUM_POINTS,\n", + " DT_REF,\n", + " diffusivity=NU,\n", + " order=4,\n", + " conservative=True,\n", + ")\n", + "u_ref = ex.repeat(ref_stepper, n_ref)(u_0)\n", + "\n", + "# Test various dt values\n", + "dt_values = [0.1, 0.05, 0.025, 0.0125, 0.00625]\n", + "\n", + "fig, ax = plt.subplots(figsize=(6, 4.5))\n", + "\n", + "for order, label, marker in [\n", + " (1, \"ETDRK1\", \"o\"),\n", + " (2, \"ETDRK2\", \"s\"),\n", + " (4, \"ETDRK4\", \"D\"),\n", + "]:\n", + " errors = []\n", + " for dt in dt_values:\n", + " n_steps = int(T_FINAL / dt)\n", + " stepper = ex.stepper.Burgers(\n", + " 1,\n", + " DOMAIN_EXTENT,\n", + " NUM_POINTS,\n", + " dt,\n", + " diffusivity=NU,\n", + " order=order,\n", + " conservative=True,\n", + " )\n", + " u_final = ex.repeat(stepper, n_steps)(u_0)\n", + " l2_err = float(jnp.sqrt(jnp.mean((u_final - u_ref) ** 2)))\n", + " errors.append(l2_err)\n", + "\n", + " ax.loglog(dt_values, errors, f\"{marker}-\", label=label, markersize=6)\n", + "\n", + " # Print measured slopes\n", + " log_dt = jnp.log(jnp.array(dt_values))\n", + " log_err = jnp.log(jnp.array(errors))\n", + " slopes = jnp.diff(log_err) / jnp.diff(log_dt)\n", + " print(f\"{label}: slopes = {[f'{s:.2f}' for s in slopes]}\")\n", + "\n", + "# Reference slope triangles\n", + "dt_arr = jnp.array(dt_values)\n", + "for slope, ls in [(1, \":\"), (2, \"--\"), (4, \"-.\")]:\n", + " # Anchor at the midpoint of the dt range\n", + " anchor_dt = dt_arr[2]\n", + " anchor_err = float(anchor_dt) ** slope * 0.3\n", + " ref_line = anchor_err * (dt_arr / anchor_dt) ** slope\n", + " ax.loglog(dt_arr, ref_line, \"gray\", ls=ls, alpha=0.4, label=f\"slope {slope}\")\n", + "\n", + "ax.set_xlabel(r\"$\\Delta t$\")\n", + "ax.set_ylabel(r\"$L^2$ error\")\n", + "ax.set_title(\"Temporal convergence of ETDRK methods\")\n", + "ax.legend(fontsize=8)\n", + "ax.grid(True, alpha=0.3, which=\"both\")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-18", + "metadata": {}, + "source": [ + "## Dealiasing: Orszag's 2/3 Rule\n", + "\n", + "When we evaluate a **quadratic** nonlinearity like $u^2$ pseudo-spectrally,\n", + "multiplying two signals in physical space corresponds to convolving their\n", + "Fourier coefficients. If modes $k_1$ and $k_2$ are both populated, the product\n", + "creates energy at $k_1 + k_2$. When $k_1 + k_2$ exceeds the Nyquist\n", + "frequency $N/2$, this energy is **aliased** back into the resolved range,\n", + "creating spurious content.\n", + "\n", + "**Orszag's 2/3 rule**: before evaluating the nonlinearity, zero out the\n", + "top 1/3 of Fourier modes. Then the maximum sum\n", + "$k_1 + k_2 \\le 2 \\cdot \\tfrac{2}{3} \\cdot \\tfrac{N}{2}\n", + "= \\tfrac{2N}{3}$ stays below $N/2 + N/3 = \\tfrac{5N}{6}$,\n", + "meaning any aliases only land in the already-zeroed modes and will be\n", + "removed at the next dealiasing step.\n", + "\n", + "In Exponax, the `dealiasing_fraction=2/3` parameter controls this." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "cell-19", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:55.774559Z", + "iopub.status.busy": "2026-02-11T15:31:55.774443Z", + "iopub.status.idle": "2026-02-11T15:31:56.702174Z", + "shell.execute_reply": "2026-02-11T15:31:56.701887Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(12, 3.5))\n", + "\n", + "for ax, N in zip(axes, [32, 64], strict=False):\n", + " wn = build_wavenumbers(1, N)[0] # shape (N//2+1,)\n", + " # Match the cutoff computation from BaseNonlinearFun\n", + " nyquist = N // 2 + 1\n", + " highest = nyquist - 1\n", + " cutoff = 2 / 3 * highest - 1\n", + " mask = low_pass_filter_mask(1, N, cutoff=cutoff)[0] # shape (N//2+1,)\n", + "\n", + " colors = [\"tab:blue\" if m else \"tab:red\" for m in mask]\n", + " ax.bar(wn, jnp.ones_like(wn), color=colors, width=0.8)\n", + " ax.set_xlabel(\"Wavenumber k\")\n", + " ax.set_title(f\"Dealiasing mask (N={N}): blue=kept, red=zeroed\")\n", + " ax.axvline(\n", + " x=float(cutoff + 1),\n", + " color=\"k\",\n", + " linestyle=\"--\",\n", + " alpha=0.5,\n", + " label=f\"cutoff={cutoff:.1f}\",\n", + " )\n", + " ax.legend(fontsize=8)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-20", + "metadata": {}, + "source": [ + "## Higher Dimensions\n", + "\n", + "The Fourier basis naturally extends to higher dimensions via tensor products.\n", + "In 2D, the derivative operator has shape `(D, N, N//2+1)` and the Laplacian\n", + "sums over spatial dimensions:\n", + "\n", + "$$ \\hat{\\Delta}_\\mathbf{k} = \\sum_{d=1}^{D} (i k_d)^2 = -|\\mathbf{k}|^2. $$\n", + "\n", + "Everything — ETDRK coefficients, dealiasing masks, the exponential term — is\n", + "computed element-wise per wavenumber vector, so the generalization is\n", + "straightforward." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "cell-21", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-11T15:31:56.703383Z", + "iopub.status.busy": "2026-02-11T15:31:56.703279Z", + "iopub.status.idle": "2026-02-11T15:31:57.519258Z", + "shell.execute_reply": "2026-02-11T15:31:57.518944Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_1060111/3804100045.py:33: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", + " plt.tight_layout()\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "NUM_POINTS_2D = 64\n", + "DOMAIN_EXTENT_2D = 1.0\n", + "DT_2D = 0.0005\n", + "NU_2D = 0.01\n", + "NUM_STEPS_2D = 50\n", + "\n", + "grid_2d = ex.make_grid(2, DOMAIN_EXTENT_2D, NUM_POINTS_2D)\n", + "\n", + "# Sinusoidal IC: sin(2*pi*x) * sin(2*pi*y)\n", + "u_0_2d = jnp.sin(2 * jnp.pi * grid_2d[0:1] / DOMAIN_EXTENT_2D) * jnp.sin(\n", + " 2 * jnp.pi * grid_2d[1:2] / DOMAIN_EXTENT_2D\n", + ")\n", + "\n", + "diffusion_2d = ex.stepper.Diffusion(\n", + " 2,\n", + " DOMAIN_EXTENT_2D,\n", + " NUM_POINTS_2D,\n", + " DT_2D,\n", + " diffusivity=NU_2D,\n", + ")\n", + "u_final_2d = ex.repeat(diffusion_2d, NUM_STEPS_2D)(u_0_2d)\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n", + "for ax, (u, title) in zip(\n", + " axes,\n", + " [(u_0_2d, \"Initial\"), (u_final_2d, f\"After {NUM_STEPS_2D} steps\")],\n", + " strict=False,\n", + "):\n", + " im = ax.imshow(\n", + " u[0].T,\n", + " origin=\"lower\",\n", + " cmap=\"RdBu_r\",\n", + " vmin=-1,\n", + " vmax=1,\n", + " extent=[0, DOMAIN_EXTENT_2D, 0, DOMAIN_EXTENT_2D],\n", + " )\n", + " ax.set_title(title)\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + "plt.colorbar(im, ax=axes, shrink=0.8)\n", + "plt.suptitle(f\"2D Diffusion (\\u03bd={NU_2D})\")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-22", + "metadata": {}, + "source": [ + "## Limitations\n", + "\n", + "**Theoretical limitations of Fourier pseudo-spectral ETDRK:**\n", + "\n", + "1. **Periodic boundary conditions only** — the DFT assumes periodicity.\n", + "2. **No channel mixing in the linear operator** — $\\hat{\\mathcal{L}}$ acts\n", + " independently per channel (no coupled systems like the wave equation in\n", + " first-order form).\n", + "3. **First-order in time** — the PDE must be of the form $u_t = \\dots$\n", + " (no $u_{tt}$).\n", + "4. **Smooth solutions required** — Fourier methods produce Gibbs ringing near\n", + " discontinuities. Solutions must remain sufficiently smooth.\n", + "5. **CFL-like constraint on the nonlinear part** — while the linear part is\n", + " integrated exactly, the nonlinear term is treated explicitly, imposing a\n", + " practical time-step limit.\n", + "6. **Cartesian domains only** — the uniform grid and FFT require\n", + " rectangular/cuboid domains.\n", + "\n", + "**Exponax-specific limitations:**\n", + "\n", + "1. Same domain extent in every spatial dimension (scaled hypercube).\n", + "2. Same number of grid points $N$ in every dimension.\n", + "3. Real-valued states only (uses `rfftn`).\n", + "4. Constant time step $\\Delta t$ (no adaptive stepping).\n", + "5. Available orders: 0, 1, 2, 3, 4." + ] } ], "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, "language_info": { - "name": "python" + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 5 } diff --git a/mkdocs.yml b/mkdocs.yml index 175fc1a..f087871 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -104,6 +104,7 @@ nav: - Advanced: - 1D Burgers Emulator Training: 'examples/learning_burgers_autoregressive_neural_operator.ipynb' - More on Metrics: 'examples/on_metrics_advanced.ipynb' + - ETDRK from the Ground Up: 'examples/edtrk_from_the_ground_up.ipynb' - Additional: - Nice Features: 'examples/additional_features.ipynb' - Performance Hints: 'examples/performance_hints.ipynb'