{ "cells": [ { "cell_type": "markdown", "id": "0f11c341", "metadata": {}, "source": [ "# 7 · Time Integration: Forward Euler, Backward Euler, BDF2\n", "\n", "To animate motion we march Newton's law $M\\ddot x = -\\nabla V(x)$ forward in time with a step $h$.\n", "We compare three integrators on the same pinned cantilever beam: **Forward Euler** (explicit, order 1,\n", "cheap but explodes unless $h$ is tiny), **Backward Euler** (implicit, order 1, stable but damps) and\n", "**BDF2** (implicit, order 2, barely damps). Each implicit step minimizes the potential plus an inertia\n", "term that pulls $x$ toward where momentum alone would carry it ($\\tilde x$); the two implicit schemes\n", "differ only in $\\tilde x$ and the weight $c$:\n", "\n", "$$x_{n+1} = \\arg\\min_x \\; V(x) + \\frac{c}{2h^2}\\,\\lVert x - \\tilde x\\rVert_M^2 .$$" ] }, { "cell_type": "markdown", "id": "4c120e61", "metadata": {}, "source": [ "Imports, and every tunable parameter of this notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "49c8a076", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:29.140613Z", "iopub.status.busy": "2026-09-24T03:44:29.140538Z", "iopub.status.idle": "2026-09-24T03:44:29.716995Z", "shell.execute_reply": "2026-09-24T03:44:29.716444Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import os\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import igl\n", "import simkit\n", "import utils\n", "\n", "NOTEBOOK = \"007_time_integration\" # this file's name\n", "RESULTS_DIR = utils.notebook_results_path(NOTEBOOK) # results/007_time_integration/\n", "MEDIA_DIR = \"media\" # tracked copies for the website\n", "# mesh\n", "NX, NY = 14, 4 # grid resolution (vertices along x, y)\n", "WIDTH, HEIGHT = 2.0, 0.3 # beam size\n", "# material and loads\n", "MATERIAL = \"macklin-mueller-neo-hookean\" # elastic energy model passed to simkit.energies.elastic_*_x\n", "YM, PR = 500.0, 0.4 # Young's modulus, Poisson ratio\n", "RHO = 1.0 # density\n", "GRAVITY = -9.8 # vertical gravitational acceleration\n", "K_PIN = 1e7 # soft-pin stiffness on the left edge\n", "# implicit solves\n", "NEWTON_ITERS = 30 # max Newton iterations per implicit step\n", "NEWTON_TOL = 1e-6 # Newton stops when the step is shorter than this\n", "# validation\n", "H_CHECK = 0.01 # timestep of the sanity checks\n", "FD_STEP = 1e-6 # central-difference step of the gradient check\n", "FD_NOISE = 0.01 # size of the random pose / velocity perturbations of the checks\n", "SEED = 0 # random seed of that perturbation\n", "# order of accuracy\n", "T_ORDER = 0.5 # final time of the accuracy study\n", "H_REF = 0.0003125 # fine BDF2 reference timestep\n", "H_ORDER = [0.02, 0.01, 0.005, 0.0025] # timesteps whose error is measured\n", "H_ERROR_FIELD = 0.01 # timestep whose per-vertex error is drawn\n", "# forward vs backward Euler\n", "H_BLOW = 0.008 # timestep of the explicit/implicit race\n", "H_FE_SMALL = 0.0002 # a timestep small enough for Forward Euler to survive T_BLOW\n", "T_BLOW = 0.3 # its duration\n", "BLOW_LIMIT = 1e3 # a coordinate beyond this counts as \"exploded\"\n", "N_FRAMES_BLOW, FPS_BLOW = 40, 20 # its video\n", "# numerical damping\n", "T_DAMP = 3.0 # duration of the damping study\n", "DTS = [0.001, 0.01, 0.1] # timesteps compared\n", "N_FRAMES_DAMP, FPS_DAMP = 60, 30 # its videos" ] }, { "cell_type": "markdown", "id": "ce0f1fd8", "metadata": {}, "source": [ "## The beam\n", "\n", "A $2 \\times 0.3$ grid from libigl, with its left edge pinned. We also track the right-edge (\"tip\")\n", "vertices to measure the swing later. Blue squares mark the pinned vertices, orange dots the tip." ] }, { "cell_type": "code", "execution_count": 2, "id": "b070f736", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:29.718497Z", "iopub.status.busy": "2026-09-24T03:44:29.718397Z", "iopub.status.idle": "2026-09-24T03:44:29.792278Z", "shell.execute_reply": "2026-09-24T03:44:29.791817Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "V_grid, T = igl.triangulated_grid(NX, NY) # unit square, NX x NY vertices\n", "X = (V_grid - 0.5) * np.array([WIDTH, HEIGHT]) # centered WIDTH x HEIGHT beam\n", "n, dim = X.shape\n", "pin_idx = np.where(X[:, 0] <= X[:, 0].min() + 1e-6)[0]\n", "tip_idx = np.where(X[:, 0] >= X[:, 0].max() - 1e-6)[0]\n", "x_rest = X.reshape(-1, 1)\n", "\n", "fig, ax = plt.subplots(figsize=(9, 2.4))\n", "utils.plot_mesh(ax, X, T, pins=pin_idx, title=f\"rest beam: {n} vertices, {len(T)} triangles\")\n", "ax.scatter(X[tip_idx, 0], X[tip_idx, 1], s=34, color=utils.HANDLE_C, zorder=5, label=\"tip (tracked)\")\n", "ax.legend(loc=\"center left\", bbox_to_anchor=(1.01, 0.5), fontsize=9)\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"mesh.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_mesh.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "489793dc", "metadata": {}, "source": [ "## Constant operators\n", "\n", "Everything that does not change during a simulation is built once from simkit: the deformation\n", "Jacobian `J`, triangle areas `vol`, Lamé parameters, the (lumped, diagonal) mass matrix `M`, the gravity\n", "force `f_g`, and the soft-pin penalty `(Q_pin, b_pin)`. The scalar fields the dynamics rely on are\n", "drawn below: every triangle of this regular grid has the same area and the same Lamé parameters\n", "$\\mu, \\lambda$, and each vertex's mass is a share of its neighbouring triangles' area, so boundary\n", "vertices carry half the interior mass and the corners the least (darker colours)." ] }, { "cell_type": "code", "execution_count": 3, "id": "61df1f22", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:29.793529Z", "iopub.status.busy": "2026-09-24T03:44:29.793445Z", "iopub.status.idle": "2026-09-24T03:44:30.008858Z", "shell.execute_reply": "2026-09-24T03:44:30.008447Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "J = simkit.deformation_jacobian(X, T)\n", "vol = simkit.volume(X, T)\n", "mu_value, lam_value = simkit.ympr_to_lame(YM, PR)\n", "mu = np.full((len(T), 1), mu_value)\n", "lam = np.full((len(T), 1), lam_value)\n", "M_vertex = simkit.massmatrix(X, T, rho=RHO) # (n, n) lumped mass\n", "M = sp.sparse.kron(M_vertex, sp.sparse.eye(dim)).tocsc() # (n*dim, n*dim)\n", "f_g = simkit.gravity_force(X, T, a=GRAVITY, rho=RHO).reshape(-1, 1)\n", "Q_pin, b_pin = simkit.dirichlet_penalty(pin_idx, X[pin_idx], n, K_PIN)\n", "\n", "fig, axes = plt.subplots(3, 1, figsize=(8, 6.6))\n", "utils.plot_scalar_field(axes[0], X, T, vol, title=f\"triangle area vol (all {vol.mean():.2e})\",\n", " cmap=\"cividis\", vmin=0.0, vmax=1.2 * vol.max(), label=\"area\")\n", "utils.plot_scalar_field(axes[1], X, T, mu, cmap=\"cividis\", vmin=0.0, vmax=1.2 * mu_value, label=r\"$\\mu$\",\n", " title=rf\"Lamé $\\mu$ (all {mu_value:.0f}); $\\lambda$ = {lam_value:.0f} everywhere\")\n", "utils.plot_scalar_field(axes[2], X, T, M_vertex.diagonal(), title=\"lumped vertex mass diag(M)\",\n", " cmap=\"viridis\", label=\"mass\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"area_mass.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_area_mass.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "87abcfc7", "metadata": {}, "source": [ "## The potential $V(x)$\n", "\n", "`beam_potential_system` returns the static potential: elastic energy, the pinned left edge and gravity,\n", "one term per line. Gravity is linear in $x$, so it has no Hessian term. Forward Euler only needs its\n", "gradient (the force is $-\\nabla V$)." ] }, { "cell_type": "code", "execution_count": 4, "id": "47ab795a", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:30.010389Z", "iopub.status.busy": "2026-09-24T03:44:30.010290Z", "iopub.status.idle": "2026-09-24T03:44:30.012788Z", "shell.execute_reply": "2026-09-24T03:44:30.012305Z" } }, "outputs": [], "source": [ "def beam_potential_system():\n", " \"\"\"Potential V(x) of the beam: elastic + soft pin + gravity (no inertia).\"\"\"\n", "\n", " def energy_func(x):\n", " E_elastic = simkit.energies.elastic_energy_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL)\n", " E_pin = simkit.energies.quadratic_energy(x, Q_pin, b_pin)\n", " E_gravity = -(f_g.T @ x).item()\n", " E_total = E_elastic + E_pin + E_gravity\n", " return E_total\n", "\n", " def gradient_func(x):\n", " g_elastic = simkit.energies.elastic_gradient_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL)\n", " g_pin = simkit.energies.quadratic_gradient(x, Q_pin, b_pin)\n", " g_gravity = -f_g\n", " g_total = g_elastic + g_pin + g_gravity\n", " return g_total\n", "\n", " def hessian_func(x):\n", " H_elastic = simkit.energies.elastic_hessian_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL, psd=True)\n", " H_pin = simkit.energies.quadratic_hessian(Q_pin)\n", " H_total = H_elastic + H_pin\n", " return H_total\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "84b48078", "metadata": {}, "source": [ "## One implicit step\n", "\n", "`implicit_step_system(x_tilde, c, h)` is the incremental potential minimized by every implicit step: the\n", "potential plus the inertia term $\\tfrac{c}{2h^2}\\lVert x-\\tilde x\\rVert_M^2$\n", "(`simkit.energies.kinetic_energy` and friends, applied to $d = x - \\tilde x$). It is rebuilt at every\n", "step with that step's target." ] }, { "cell_type": "code", "execution_count": 5, "id": "03e76ca0", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:30.013895Z", "iopub.status.busy": "2026-09-24T03:44:30.013816Z", "iopub.status.idle": "2026-09-24T03:44:30.015954Z", "shell.execute_reply": "2026-09-24T03:44:30.015474Z" } }, "outputs": [], "source": [ "def implicit_step_system(x_tilde, c, h):\n", " \"\"\"Incremental potential of one implicit step: V(x) + c / (2 h^2) ||x - x_tilde||_M^2.\"\"\"\n", " V_energy, V_gradient, V_hessian = beam_potential_system()\n", "\n", " def energy_func(x):\n", " E_potential = V_energy(x)\n", " E_inertia = simkit.energies.kinetic_energy(x - x_tilde, M, h, c)\n", " E_total = E_potential + E_inertia\n", " return E_total\n", "\n", " def gradient_func(x):\n", " g_potential = V_gradient(x)\n", " g_inertia = simkit.energies.kinetic_gradient(x - x_tilde, M, h, c)\n", " g_total = g_potential + g_inertia\n", " return g_total\n", "\n", " def hessian_func(x):\n", " H_potential = V_hessian(x)\n", " H_inertia = simkit.energies.kinetic_hessian(M, h, c)\n", " H_total = H_potential + H_inertia\n", " return H_total\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "e547a2ce", "metadata": {}, "source": [ "## The three steppers\n", "\n", "Each maps the state (positions $x_n$, velocities $v_n$) to the next one. Only the target $\\tilde x$,\n", "the weight $c$ and the velocity update differ:\n", "\n", "* **Forward Euler**: $x_{n+1} = x_n + h v_n$, $\\;v_{n+1} = v_n - h M^{-1}\\nabla V(x_n)$ (`simkit.integrators.forward_euler`, lumped mass, no solve). Pins are clamped afterwards.\n", "* **Backward Euler**: $c = 1$, $\\;\\tilde x = x_n + h v_n$, $\\;v_{n+1} = (x_{n+1} - x_n)/h$.\n", "* **BDF2**: $c = \\tfrac94$, $\\;\\tilde x = \\tfrac43 x_n - \\tfrac13 x_{n-1} + \\tfrac{8h}{9} v_n - \\tfrac{2h}{9} v_{n-1}$, $\\;v_{n+1} = (3x_{n+1} - 4x_n + x_{n-1})/(2h)$." ] }, { "cell_type": "code", "execution_count": 6, "id": "74fce1c2", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:30.017338Z", "iopub.status.busy": "2026-09-24T03:44:30.017244Z", "iopub.status.idle": "2026-09-24T03:44:30.019943Z", "shell.execute_reply": "2026-09-24T03:44:30.019442Z" } }, "outputs": [], "source": [ "pin_dofs = (pin_idx[:, None] * dim + np.arange(dim)).ravel()\n", "\n", "def forward_euler_step(x, v, h):\n", " \"\"\"Explicit step: read the force at x_n, no solve.\"\"\"\n", " V_energy, V_gradient, V_hessian = beam_potential_system()\n", " x_next, v_next = simkit.integrators.forward_euler(x, v, V_gradient, M, h)\n", " x_next[pin_dofs] = x_rest[pin_dofs] # hard-clamp the pins\n", " v_next[pin_dofs] = 0.0\n", " return x_next, v_next\n", "\n", "def backward_euler_step(x, v, h):\n", " \"\"\"Implicit step with c = 1 and target x_n + h v_n.\"\"\"\n", " x_tilde = x + h * v\n", " energy_func, gradient_func, hessian_func = implicit_step_system(x_tilde, 1.0, h)\n", " x_next = simkit.solvers.newton_solver(x_tilde, energy_func, gradient_func, hessian_func,\n", " tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS, do_line_search=True)\n", " v_next = (x_next - x) / h\n", " return x_next, v_next\n", "\n", "def bdf2_step(x, v, x_prev, v_prev, h):\n", " \"\"\"Implicit step with c = 9/4 and the second-order BDF2 target.\"\"\"\n", " x_tilde = (4 / 3) * x - (1 / 3) * x_prev + (8 * h / 9) * v - (2 * h / 9) * v_prev\n", " energy_func, gradient_func, hessian_func = implicit_step_system(x_tilde, 9 / 4, h)\n", " x_next = simkit.solvers.newton_solver(x_tilde, energy_func, gradient_func, hessian_func,\n", " tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS, do_line_search=True)\n", " v_next = (3 * x_next - 4 * x + x_prev) / (2 * h)\n", " return x_next, v_next" ] }, { "cell_type": "markdown", "id": "49c2ee07", "metadata": {}, "source": [ "## Sanity checks\n", "\n", "Three cheap checks before simulating: the step gradient matches a central finite difference\n", "(`simkit.gradient_cfd`) at a random pose; our Backward Euler step from a random velocity matches the\n", "library's `simkit.integrators.backward_euler` (same Newton solve); and Newton converges on the first\n", "step from rest. Expect a gradient error near $10^{-7}$ and a difference at rounding level. The plot shows\n", "$\\lVert\\nabla E\\rVert$ after each Newton step; Newton stops once its step is shorter than `NEWTON_TOL`.\n", "At $h = 0.001$ and $0.1$ the gradient drops by 8 and 4 orders of magnitude. At $h = 0.01$ the line search\n", "stalls after one step at $\\approx 8\\cdot10^{-4}$ (the remaining decrease is below the rounding error of\n", "the total energy), still 1000 times below the start and ample for one timestep." ] }, { "cell_type": "code", "execution_count": 7, "id": "97f4b293", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:30.021008Z", "iopub.status.busy": "2026-09-24T03:44:30.020921Z", "iopub.status.idle": "2026-09-24T03:44:30.143473Z", "shell.execute_reply": "2026-09-24T03:44:30.143084Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradient check: relative error 6.45e-08\n", "our BE step vs simkit.integrators.backward_euler: max difference 1.1e-16 (the step itself moves vertices by up to 1.0e-03)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(SEED)\n", "x_test = x_rest + FD_NOISE * rng.standard_normal(x_rest.shape)\n", "energy_func, gradient_func, hessian_func = implicit_step_system(x_rest, 1.0, H_CHECK)\n", "g_fd = simkit.gradient_cfd(lambda y: np.array(energy_func(y.reshape(-1, 1))), x_test.ravel(), FD_STEP)\n", "g_an = gradient_func(x_test).ravel()\n", "print(f\"gradient check: relative error {np.linalg.norm(g_fd - g_an) / np.linalg.norm(g_an):.2e}\")\n", "\n", "v_test = FD_NOISE * rng.standard_normal(x_rest.shape)\n", "x_ours, _ = backward_euler_step(x_rest, v_test, H_CHECK)\n", "V_energy, V_gradient, V_hessian = beam_potential_system()\n", "x_lib = simkit.integrators.backward_euler(x_rest, x_rest - H_CHECK * v_test, V_energy, V_gradient,\n", " V_hessian, M, H_CHECK, tolerance=NEWTON_TOL,\n", " max_iter=NEWTON_ITERS, do_line_search=True)\n", "print(f\"our BE step vs simkit.integrators.backward_euler: max difference {np.abs(x_ours - x_lib).max():.1e} \"\n", " f\"(the step itself moves vertices by up to {np.abs(x_ours - x_rest).max():.1e})\")\n", "\n", "fig, ax = plt.subplots(figsize=(6.5, 4))\n", "for h, col in zip(DTS, [\"#9ecae1\", \"#4292c6\", \"#08519c\"]):\n", " energy_func, gradient_func, hessian_func = implicit_step_system(x_rest, 1.0, h)\n", " x_final, info = simkit.solvers.newton_solver(x_rest.copy(), energy_func, gradient_func, hessian_func,\n", " tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS,\n", " do_line_search=True, return_info=True)\n", " g_norms = [np.linalg.norm(g) for g in info[\"g\"]] + [np.linalg.norm(gradient_func(x_final))]\n", " ax.semilogy(g_norms, \"-o\", ms=4, color=col, label=f\"Backward Euler, h={h}\")\n", "ax.set_xlabel(\"Newton steps taken\"); ax.set_ylabel(r\"$\\|\\nabla E\\|$\")\n", "ax.xaxis.set_major_locator(plt.MaxNLocator(integer=True))\n", "ax.set_title(\"First implicit step from rest: Newton convergence\")\n", "ax.grid(True, which=\"both\", color=\"0.9\"); ax.legend(fontsize=9)\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"newton_convergence.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_newton_convergence.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0611cba0", "metadata": {}, "source": [ "## A driver that records every step\n", "\n", "`simulate` releases the beam from rest and takes **exactly** `round(T/h)` steps, so every timestep ends\n", "at the same final time. It records all positions and velocities; BDF2 needs one step of history, so its\n", "first step is a Backward Euler step. A run that blows up (non-finite, or beyond `BLOW_LIMIT`) stops early.\n", "A short recorded BDF2 run then cross-checks `bdf2_step` against `simkit.integrators.bdf2`, which rebuilds\n", "both velocities from the last four positions; the two should agree to rounding." ] }, { "cell_type": "code", "execution_count": 8, "id": "f08a2d8f", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:30.144606Z", "iopub.status.busy": "2026-09-24T03:44:30.144517Z", "iopub.status.idle": "2026-09-24T03:44:30.158391Z", "shell.execute_reply": "2026-09-24T03:44:30.157961Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "our BDF2 step vs simkit.integrators.bdf2: max difference 0.0e+00 (the step itself moves vertices by up to 4.5e-03)\n" ] } ], "source": [ "def simulate(scheme, h, T_total):\n", " \"\"\"Integrate from rest with `scheme`; return times (K,), positions and velocities (K, n*dim).\"\"\"\n", " x, v = x_rest.copy(), np.zeros_like(x_rest)\n", " x_prev, v_prev = x, v\n", " xs, vs = [x], [v]\n", " for k in range(int(round(T_total / h))):\n", " if scheme == \"Forward Euler\":\n", " x_next, v_next = forward_euler_step(x, v, h)\n", " elif scheme == \"Backward Euler\" or k == 0: # BDF2 bootstraps with one BE step\n", " x_next, v_next = backward_euler_step(x, v, h)\n", " else:\n", " x_next, v_next = bdf2_step(x, v, x_prev, v_prev, h)\n", " x_prev, v_prev, x, v = x, v, x_next, v_next\n", " xs.append(x); vs.append(v)\n", " if not np.isfinite(x).all() or np.abs(x).max() > BLOW_LIMIT:\n", " break\n", " ts = h * np.arange(len(xs))\n", " return ts, np.hstack(xs).T, np.hstack(vs).T\n", "\n", "_, xs_check, vs_check = simulate(\"BDF2\", H_CHECK, 4 * H_CHECK) # states x_0 .. x_4\n", "x_hist = [x.reshape(-1, 1) for x in xs_check[::-1]] # x_4, x_3, x_2, x_1, x_0\n", "v_hist = [v.reshape(-1, 1) for v in vs_check[::-1]]\n", "x_ours, _ = bdf2_step(x_hist[0], v_hist[0], x_hist[1], v_hist[1], H_CHECK)\n", "V_energy, V_gradient, V_hessian = beam_potential_system()\n", "x_lib = simkit.integrators.bdf2(x_hist[0], x_hist[1], x_hist[2], x_hist[3], V_energy, V_gradient, V_hessian,\n", " M, H_CHECK, tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS, do_line_search=True)\n", "print(f\"our BDF2 step vs simkit.integrators.bdf2: max difference {np.abs(x_ours - x_lib).max():.1e} \"\n", " f\"(the step itself moves vertices by up to {np.abs(x_ours - x_hist[0]).max():.1e})\")" ] }, { "cell_type": "markdown", "id": "8ccbefb2", "metadata": {}, "source": [ "## Order of accuracy, measured on our beam\n", "\n", "We run the beam to $T = 0.5$ at four timesteps and compare the final pose with a fine-timestep BDF2\n", "reference on the same mesh. On a log-log plot an order-$p$ method is a line of slope $p$. Forward Euler\n", "is left out: it needs a far smaller $h$ just to stay stable, as we'll see next." ] }, { "cell_type": "code", "execution_count": 9, "id": "93105135", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:30.159549Z", "iopub.status.busy": "2026-09-24T03:44:30.159486Z", "iopub.status.idle": "2026-09-24T03:44:33.782474Z", "shell.execute_reply": "2026-09-24T03:44:33.781896Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Backward Euler errors [0.0985 0.0657 0.0399 0.0228] fitted order 0.70 slope between the two smallest h 0.81\n", "BDF2 errors [0.041 0.0144 0.0044 0.0011] fitted order 1.72 slope between the two smallest h 1.95\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, xs_ref, _ = simulate(\"BDF2\", H_REF, T_ORDER)\n", "x_ref = xs_ref[-1]\n", "final = {(scheme, h): simulate(scheme, h, T_ORDER)[1][-1]\n", " for scheme in [\"Backward Euler\", \"BDF2\"] for h in H_ORDER}\n", "errors = {scheme: np.array([np.linalg.norm(final[scheme, h] - x_ref) for h in H_ORDER])\n", " for scheme in [\"Backward Euler\", \"BDF2\"]}\n", "for scheme, e in errors.items():\n", " fitted = np.polyfit(np.log(H_ORDER), np.log(e), 1)[0]\n", " last_pair = np.log(e[-2] / e[-1]) / np.log(H_ORDER[-2] / H_ORDER[-1])\n", " print(f\"{scheme:16s} errors {np.array2string(e, precision=4)} fitted order {fitted:.2f} \"\n", " f\"slope between the two smallest h {last_pair:.2f}\")\n", "\n", "fig, ax = utils.loglog_plot(H_ORDER, errors, xlabel=\"timestep h\", ylabel=\"error vs fine reference\",\n", " colors=utils.INTEGRATOR_COLORS, ref_slopes={\"O(h)\": 1, \"O(h^2)\": 2},\n", " title=\"Order of accuracy on the beam\")\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"order_of_accuracy.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_order_of_accuracy.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a15d5d46", "metadata": {}, "source": [ "BDF2 is both more accurate and steeper. The fitted slopes (0.70, 1.72) sit below 1 and 2 because the\n", "largest timesteps are not yet asymptotic; between the two smallest they are 0.81 and 1.95. Where on the\n", "beam does the error live? Below is the per-vertex error $\\lVert x_i - x_i^{\\text{ref}}\\rVert$ at\n", "$h = 0.01$, on the reference pose with a shared color scale: it is largest near the free tip, and\n", "BDF2's is about four times smaller." ] }, { "cell_type": "code", "execution_count": 10, "id": "7ee03043", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:33.783926Z", "iopub.status.busy": "2026-09-24T03:44:33.783805Z", "iopub.status.idle": "2026-09-24T03:44:33.931460Z", "shell.execute_reply": "2026-09-24T03:44:33.931168Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_ref = x_ref.reshape(n, dim)\n", "err_fields = {scheme: np.linalg.norm((final[scheme, H_ERROR_FIELD] - x_ref).reshape(n, dim), axis=1)\n", " for scheme in [\"Backward Euler\", \"BDF2\"]}\n", "vmax = max(e.max() for e in err_fields.values())\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4.2))\n", "for ax, (scheme, e) in zip(axes, err_fields.items()):\n", " utils.plot_scalar_field(ax, X_ref, T, e, vmin=0.0, vmax=vmax, cmap=\"magma\", label=\"error\",\n", " title=f\"{scheme}, h={H_ERROR_FIELD}: max error {e.max():.3f}\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"error_field.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_error_field.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6084028f", "metadata": {}, "source": [ "## Forward Euler explodes; Backward Euler doesn't\n", "\n", "On a vibration mode of frequency $\\omega$, one Forward Euler step multiplies the amplitude by\n", "$\\sqrt{1 + \\omega^2 h^2} > 1$, so the stiffest mode ($\\omega_{\\max}$ of $K u = \\omega^2 M u$ at rest)\n", "grows fastest. We compute it and run both integrators at $h = 0.008$. Left, the largest vertex\n", "displacement: Forward Euler follows Backward Euler while its unstable stiff modes are still tiny, then\n", "shoots up from $t \\approx 0.07$ s and leaves the scene after 13 steps. It survives the same 0.3 s only\n", "at $h = 0.0002$ (dotted, on top of Backward Euler), a timestep 40 times smaller. Right, the amplitude\n", "$a = \\sqrt{q^2 + (\\dot q/\\omega_{\\max})^2}$ of the stiffest mode $u_{\\max}$ itself, with\n", "$q = u_{\\max}^\\top M (x - X)$: it grows at the predicted rate from the very first step." ] }, { "cell_type": "code", "execution_count": 11, "id": "7e6653c0", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:33.932641Z", "iopub.status.busy": "2026-09-24T03:44:33.932540Z", "iopub.status.idle": "2026-09-24T03:44:34.339521Z", "shell.execute_reply": "2026-09-24T03:44:34.339189Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "omega_max = 733 rad/s -> Forward Euler amplifies it x5.95 per step at h=0.008\n", "measured: the stiffest mode grows x5.98 per step (median), FE leaves the scene after 13 steps\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "free = np.setdiff1d(np.arange(n * dim), pin_dofs)\n", "M_free = M[free][:, free]\n", "K_rest = simkit.energies.elastic_hessian_x(X, J, mu, lam, vol, MATERIAL, psd=True)[free][:, free]\n", "omega_sq, U = sp.linalg.eigh(K_rest.toarray(), M_free.toarray()) # K u = omega^2 M u, M-orthonormal u\n", "omega_max, u_max = np.sqrt(omega_sq[-1]), U[:, -1]\n", "growth = np.sqrt(1 + (omega_max * H_BLOW) ** 2)\n", "print(f\"omega_max = {omega_max:.0f} rad/s -> Forward Euler amplifies it x{growth:.2f} per step at h={H_BLOW}\")\n", "\n", "runs_blow = {scheme: simulate(scheme, H_BLOW, T_BLOW) for scheme in [\"Forward Euler\", \"Backward Euler\"]}\n", "ts_small, xs_small, _ = simulate(\"Forward Euler\", H_FE_SMALL, T_BLOW)\n", "ts_fe, xs_fe, vs_fe = runs_blow[\"Forward Euler\"]\n", "q = np.array([u_max @ (M_free @ (x - x_rest.ravel())[free]) for x in xs_fe]) # stiffest-mode coordinate\n", "q_dot = np.array([u_max @ (M_free @ v[free]) for v in vs_fe]) # and its velocity\n", "amp = np.hypot(q, q_dot / omega_max)\n", "print(f\"measured: the stiffest mode grows x{np.median(amp[2:] / amp[1:-1]):.2f} per step (median), \"\n", " f\"FE leaves the scene after {len(ts_fe) - 1} steps\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 4.4))\n", "ax = axes[0]\n", "for scheme, (ts, xs, _) in runs_blow.items():\n", " disp = np.abs(xs - x_rest.ravel()).max(axis=1)\n", " ax.semilogy(ts[2:], disp[2:], \"-o\", ms=3, color=utils.INTEGRATOR_COLORS[scheme], label=f\"{scheme}, h={H_BLOW}\")\n", "disp_small = np.abs(xs_small - x_rest.ravel()).max(axis=1)\n", "ax.semilogy(ts_small[2:], disp_small[2:], \":\", lw=2.5, color=utils.INTEGRATOR_COLORS[\"Forward Euler\"],\n", " zorder=4, label=f\"Forward Euler, h={H_FE_SMALL}\")\n", "ax.set_xlabel(\"time (s)\"); ax.set_ylabel(r\"max vertex displacement $|x - X|$\")\n", "ax.set_title(\"Explicit blow-up vs bounded motion\"); ax.set_ylim(bottom=1e-4)\n", "ax.grid(True, which=\"both\", color=\"0.9\"); ax.legend(fontsize=9, loc=\"upper left\")\n", "ax = axes[1]\n", "k = np.arange(1, len(ts_fe))\n", "ax.semilogy(ts_fe[k], amp[k], \"-o\", ms=3, color=utils.INTEGRATOR_COLORS[\"Forward Euler\"],\n", " label=f\"Forward Euler, h={H_BLOW}\")\n", "ax.semilogy(ts_fe[k], amp[1] * growth ** (k - 1), \"--\", color=\"0.4\",\n", " label=rf\"predicted growth $\\times{growth:.2f}$ per step\")\n", "ax.set_xlabel(\"time (s)\"); ax.set_ylabel(r\"stiffest-mode amplitude $a$\")\n", "ax.set_title(rf\"Stiffest mode ($\\omega_{{\\max}}$ = {omega_max:.0f} rad/s)\")\n", "ax.grid(True, which=\"both\", color=\"0.9\"); ax.legend(fontsize=9, loc=\"upper left\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"fe_growth.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_fe_growth.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "79b0c00f", "metadata": {}, "source": [ "The same two runs side by side: Forward Euler flies apart after about 0.1 s, while Backward Euler\n", "calmly sags under gravity. This is why stiff elasticity is integrated implicitly." ] }, { "cell_type": "code", "execution_count": 12, "id": "ebbeea0f", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:34.340893Z", "iopub.status.busy": "2026-09-24T03:44:34.340800Z", "iopub.status.idle": "2026-09-24T03:44:35.452190Z", "shell.execute_reply": "2026-09-24T03:44:35.451476Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_blow = np.linspace(0, T_BLOW, N_FRAMES_BLOW)\n", "panels = [{\"states\": utils.states_at_times(ts, xs.reshape(-1, n, dim), sample_blow), \"T\": T,\n", " \"title\": f\"{scheme} h={H_BLOW}\" + (\" (EXPLODES)\" if scheme == \"Forward Euler\" else \" (stable)\")}\n", " for scheme, (ts, xs, _) in runs_blow.items()]\n", "lims_blow = utils.auto_limits([runs_blow[\"Backward Euler\"][1].reshape(-1, dim)], pad=0.3) # frame the stable run\n", "fig, anim = utils.animate_meshes_grid(panels, lims=lims_blow, fps=FPS_BLOW,\n", " suptitle=\"Same timestep: explicit blows up, implicit is fine\")\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"fe_vs_be.mp4\"), fps=FPS_BLOW,\n", " copy_to=os.path.join(MEDIA_DIR, \"007_fe_vs_be.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "02dd8a3c", "metadata": {}, "source": [ "## Numerical damping: the timestep changes perceived stiffness\n", "\n", "Release the beam under gravity and step **Backward Euler** for 3 s at $h$ = 0.001, 0.01 and 0.1. The\n", "physics is identical, yet the larger the step, the more artificial damping: the swing dies out faster\n", "and the material looks stiffer. The cell simulates BDF2 at the same timesteps too, for the next sections." ] }, { "cell_type": "code", "execution_count": 13, "id": "00733e2e", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:35.453476Z", "iopub.status.busy": "2026-09-24T03:44:35.453381Z", "iopub.status.idle": "2026-09-24T03:44:48.270395Z", "shell.execute_reply": "2026-09-24T03:44:48.269826Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_damp = np.linspace(0, T_DAMP, N_FRAMES_DAMP)\n", "runs = {(scheme, h): simulate(scheme, h, T_DAMP) for scheme in [\"Backward Euler\", \"BDF2\"] for h in DTS}\n", "lims_damp = utils.auto_limits([xs.reshape(-1, dim) for _, xs, _ in runs.values()], pad=0.15)\n", "\n", "panels = [{\"states\": utils.states_at_times(runs[\"Backward Euler\", h][0],\n", " runs[\"Backward Euler\", h][1].reshape(-1, n, dim), sample_damp),\n", " \"T\": T, \"title\": f\"Backward Euler h={h}\"} for h in DTS]\n", "fig, anim = utils.animate_meshes_grid(panels, lims=lims_damp, fps=FPS_DAMP,\n", " suptitle=\"Backward Euler: bigger timestep -> more numerical damping\")\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"be_damping.mp4\"), fps=FPS_DAMP,\n", " copy_to=os.path.join(MEDIA_DIR, \"007_be_damping.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "480e443d", "metadata": {}, "source": [ "## BDF2 barely damps\n", "\n", "The same three timesteps with **BDF2**: it keeps swinging at all of them. Second-order accuracy buys\n", "far less numerical dissipation than Backward Euler." ] }, { "cell_type": "code", "execution_count": 14, "id": "0f2c2b60", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:48.271862Z", "iopub.status.busy": "2026-09-24T03:44:48.271783Z", "iopub.status.idle": "2026-09-24T03:44:50.492806Z", "shell.execute_reply": "2026-09-24T03:44:50.492218Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "panels = [{\"states\": utils.states_at_times(runs[\"BDF2\", h][0], runs[\"BDF2\", h][1].reshape(-1, n, dim),\n", " sample_damp),\n", " \"T\": T, \"title\": f\"BDF2 h={h}\"} for h in DTS]\n", "fig, anim = utils.animate_meshes_grid(panels, lims=lims_damp, fps=FPS_DAMP,\n", " suptitle=\"BDF2: much less numerical damping at the same timesteps\")\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"bdf2_damping.mp4\"), fps=FPS_DAMP,\n", " copy_to=os.path.join(MEDIA_DIR, \"007_bdf2_damping.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "23ebaef9", "metadata": {}, "source": [ "The two videos as one plot: the vertical position of the tip (mean of the orange vertices) over time.\n", "At $h = 0.001$ both schemes agree. As $h$ grows, Backward Euler's rebound shrinks (to about a third at\n", "$h = 0.1$), while BDF2 keeps most of it even there." ] }, { "cell_type": "code", "execution_count": 15, "id": "f30a484a", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:50.494527Z", "iopub.status.busy": "2026-09-24T03:44:50.494440Z", "iopub.status.idle": "2026-09-24T03:44:50.657002Z", "shell.execute_reply": "2026-09-24T03:44:50.656333Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, len(DTS), figsize=(14, 3.8), sharey=True)\n", "for ax, h in zip(axes, DTS):\n", " for scheme in [\"Backward Euler\", \"BDF2\"]:\n", " ts, xs, _ = runs[scheme, h]\n", " tip_y = xs.reshape(-1, n, dim)[:, tip_idx, 1].mean(axis=1)\n", " ax.plot(ts, tip_y, color=utils.INTEGRATOR_COLORS[scheme], lw=1.8, label=scheme)\n", " ax.set_title(f\"h = {h}\"); ax.set_xlabel(\"time (s)\"); ax.grid(True, color=\"0.9\")\n", "axes[0].set_ylabel(\"tip height\"); axes[-1].legend(fontsize=9, loc=\"upper right\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"tip_trajectory.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_tip_trajectory.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1706b6c8", "metadata": {}, "source": [ "## The damping, quantified: total energy bleeds away\n", "\n", "The artificial damping removes **mechanical energy**. We track elastic + gravitational + kinetic energy\n", "(the pins do no work) along the same runs. For Backward Euler, the bigger the timestep, the faster the\n", "energy drops; BDF2 (dashed) holds on to far more of it at every timestep." ] }, { "cell_type": "code", "execution_count": 16, "id": "e8e9f865", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:50.658801Z", "iopub.status.busy": "2026-09-24T03:44:50.658640Z", "iopub.status.idle": "2026-09-24T03:44:50.887507Z", "shell.execute_reply": "2026-09-24T03:44:50.887100Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def mechanical_energy(x, v):\n", " \"\"\"Elastic + gravitational + kinetic energy of one state (x, v).\"\"\"\n", " E_elastic = simkit.energies.elastic_energy_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL)\n", " E_gravity = -(f_g.T @ x).item()\n", " E_kinetic = 0.5 * (v.T @ M @ v).item()\n", " E_total = E_elastic + E_gravity + E_kinetic\n", " return E_total\n", "\n", "fig, ax = plt.subplots(figsize=(9.5, 4.8))\n", "shades = {\"Backward Euler\": [\"#9ecae1\", \"#4292c6\", \"#08519c\"], \"BDF2\": [\"#a1d99b\", \"#41ab5d\", \"#006d2c\"]}\n", "for (scheme, h), (ts, xs, vs) in runs.items():\n", " E = [mechanical_energy(x.reshape(-1, 1), v.reshape(-1, 1)) for x, v in zip(xs, vs)]\n", " ax.plot(ts, E, color=shades[scheme][DTS.index(h)], lw=2, ls=\"-\" if scheme == \"Backward Euler\" else \"--\",\n", " label=f\"{scheme} h={h}\")\n", "ax.set_xlabel(\"time (s)\"); ax.set_ylabel(\"total mechanical energy\")\n", "ax.set_title(\"Numerical damping drains energy faster at larger h\")\n", "ax.grid(True, color=\"0.9\"); ax.legend(fontsize=9, loc=\"upper left\", bbox_to_anchor=(1.01, 1.0))\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"energy.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"007_energy.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f460aac0", "metadata": {}, "source": [ "### Takeaways\n", "* **Backward Euler** is order 1 and **BDF2** order 2, measured on the beam itself.\n", "* **Forward Euler** amplifies the stiffest mode every step and explodes at a timestep the implicit methods handle easily.\n", "* **Backward Euler** damps motion (and drains total energy) more as $h$ grows; **BDF2** stays lively and keeps far more energy.\n", "* Every implicit step is one Newton solve of $V(x) + \\tfrac{c}{2h^2}\\lVert x - \\tilde x\\rVert_M^2$; only $\\tilde x$ and $c$ change." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }