{ "cells": [ { "cell_type": "markdown", "id": "52b585e4", "metadata": {}, "source": [ "# 12 · Quadratic (P2) finite elements\n", "\n", "So far every element in these tutorials has been **linear (P1)**: positions vary\n", "linearly inside each triangle/tet, so the deformation gradient $F$ is *constant*\n", "per element. **Quadratic (P2)** elements add a node at every edge midpoint and let\n", "positions vary *quadratically*, so $F$ varies *within* an element and bending is\n", "captured far more accurately for the same mesh.\n", "\n", "This tutorial covers the three ingredients and one extra piece:\n", "\n", "1. `linear_to_quadratic_elements` — build the midpoint-enriched mesh ($t \\times 6$ / $t \\times 10$).\n", "2. `gauss_legendre_quadrature` — symmetric per-element cubature points + weights.\n", "3. `deformation_jacobian_p2` — the constant operator mapping nodal positions to\n", " one $F$ **per cubature point**.\n", "4. `p2_massmatrix` / `p2_gravity_force` — inertia and gravity over the P2 nodes.\n", "\n", "### Is the P2 deformation-Jacobian constant?\n", "\n", "**Yes** — exactly like P1 it is a fixed sparse matrix built once from the rest\n", "geometry and the fixed reference quadrature points, independent of the deformed\n", "state. The only difference: P2 shape-function gradients are *linear* in the\n", "reference coordinates, so $F$ is no longer constant inside an element. That is\n", "why the operator maps to a *stack* of per-cubature $F$ blocks.\n", "\n", "### How does P2 change energy integration?\n", "\n", "With P1 the energy is a one-point rule, $E = \\sum_t \\text{vol}_t \\, \\psi(F_t)$. With P2 the\n", "energy becomes a sum over cubature points, $E = \\sum_t \\sum_q w_{tq} \\, \\psi(F_{tq})$.\n", "**No energy code changes** — treat each cubature point as a pseudo-element: stack\n", "$F$ to $(t \\cdot n_\\text{quad}, \\dim, \\dim)$ and pass `weights.reshape(-1, 1)` as the `vol`." ] }, { "cell_type": "code", "execution_count": 1, "id": "1daf75bf", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:56.759988Z", "iopub.status.busy": "2026-06-09T05:30:56.759821Z", "iopub.status.idle": "2026-06-09T05:30:57.295383Z", "shell.execute_reply": "2026-06-09T05:30:57.295104Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import matplotlib.tri as mtri\n", "from matplotlib.collections import PolyCollection\n", "from matplotlib.animation import FuncAnimation\n", "import simkit\n", "import simkit.energies as energies\n", "from simkit.solvers import newton_solver\n", "import utils" ] }, { "cell_type": "markdown", "id": "df45df1c", "metadata": {}, "source": [ "## Part A — Visualizing the basis functions\n", "\n", "On a single reference triangle we plot all three **P1** hat functions and all six\n", "**P2** basis functions. The P1 hats are exactly the barycentric coordinates\n", "(planar ramps). The P2 corner functions $N_i = L_i(2 L_i - 1)$ curve and even dip\n", "slightly negative near the opposite edge, while the midpoint functions\n", "$N = 4 L_a L_b$ are bumps centered on their edge. `simkit.p2_shape_functions`\n", "returns these values (and their gradients)." ] }, { "cell_type": "code", "execution_count": 2, "id": "8730d351", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:57.296523Z", "iopub.status.busy": "2026-06-09T05:30:57.296434Z", "iopub.status.idle": "2026-06-09T05:30:57.525539Z", "shell.execute_reply": "2026-06-09T05:30:57.525202Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample the reference triangle: barycentric L = (L0, L1, L2), cartesian (x, y) = (L1, L2).\n", "m = 70\n", "samples = []\n", "for x in np.linspace(0.0, 1.0, m):\n", " for y in np.linspace(0.0, 1.0 - x, max(2, int(m * (1.0 - x)) + 1)):\n", " samples.append((x, y))\n", "xy = np.array(samples)\n", "L = np.column_stack([1.0 - xy[:, 0] - xy[:, 1], xy[:, 0], xy[:, 1]])\n", "tri = mtri.Triangulation(xy[:, 0], xy[:, 1])\n", "\n", "# P1 hats are just the barycentric coordinates; P2 basis from simkit.\n", "P1 = L # (npts, 3)\n", "P2 = np.array([simkit.p2_shape_functions(Li, 3)[0] for Li in L]) # (npts, 6)\n", "\n", "p1_titles = [r\"P1 $N_0$\", r\"P1 $N_1$\", r\"P1 $N_2$\"]\n", "p2_titles = [r\"P2 $N_0$ (corner 0)\", r\"P2 $N_1$ (corner 1)\", r\"P2 $N_2$ (corner 2)\",\n", " r\"P2 $N_3$ mid(0,1)\", r\"P2 $N_4$ mid(1,2)\", r\"P2 $N_5$ mid(2,0)\"]\n", "\n", "def draw(ax, vals, title):\n", " tcf = ax.tricontourf(tri, vals, levels=24, cmap=\"viridis\")\n", " ax.plot([0, 1, 0, 0], [0, 0, 1, 0], \"k\", lw=1.2) # reference-triangle outline\n", " ax.set_title(title, fontsize=10); ax.set_aspect(\"equal\"); ax.axis(\"off\")\n", " return tcf\n", "\n", "fig, axes = plt.subplots(3, 3, figsize=(11.5, 10.5))\n", "for j in range(3):\n", " draw(axes[0, j], P1[:, j], p1_titles[j])\n", "for k in range(6):\n", " draw(axes[1 + k // 3, k % 3], P2[:, k], p2_titles[k])\n", "fig.suptitle(\"Linear (top row) vs quadratic (bottom two rows) basis functions\",\n", " fontsize=13)\n", "fig.tight_layout(rect=(0, 0, 1, 0.97))\n", "fig.savefig(\"media/12_p2_basis.png\", dpi=110)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d759633c", "metadata": {}, "source": [ "## Part B — A beam sagging under gravity: P1 vs P2\n", "\n", "We drop a cantilever beam (left edge pinned) under gravity with inertia, using a\n", "backward-Euler implicit step (the integrator from tutorial 7). We run the **same**\n", "material and timestep twice: once with linear elements, once with quadratic\n", "elements on the same coarse mesh, and animate them side by side. The energy code\n", "(`macklin_mueller_neo_hookean_*`) is identical in both — only $J$, the weights,\n", "the mass matrix and gravity differ.\n", "\n", "### One simulator, two element sets\n", "\n", "`FEMBeam` is a single backward-Euler neo-Hookean beam parametrized purely by its\n", "assembled operators: the deformation Jacobian $J$, the per-cubature weights `vol`,\n", "the Lame parameters, the mass matrix $M$, the gravity force $f_g$, and the pin\n", "penalty $(Q, b)$. Whether those came from the P1 pipeline (`deformation_jacobian`\n", "/ `volume` / `massmatrix` / `gravity_force`) or the P2 pipeline\n", "(`deformation_jacobian_p2` / `gauss_legendre_quadrature` / `p2_massmatrix` /\n", "`p2_gravity_force`) makes no difference to the physics. The `energy / gradient /\n", "hessian` methods build their elastic, pin, gravity and inertia terms **one per\n", "line**, and `step()` drives one implicit step with `utils.Inertia` + `newton_solver`." ] }, { "cell_type": "code", "execution_count": 3, "id": "029b9f23", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:57.526671Z", "iopub.status.busy": "2026-06-09T05:30:57.526599Z", "iopub.status.idle": "2026-06-09T05:30:57.530713Z", "shell.execute_reply": "2026-06-09T05:30:57.530445Z" } }, "outputs": [], "source": [ "class FEMBeam:\n", " \"\"\"Backward-Euler neo-Hookean beam; works for P1 or P2 depending on the\n", " (vertices, J, vol, mass M, gravity f_g, pin penalty) passed in.\n", "\n", " The elastic energy is integrated as sum_blk vol_blk * psi(F_blk): for P1 a\n", " block is an element, for P2 a block is a per-element cubature point. Nothing\n", " else in the dynamics is aware of which space it is running in.\"\"\"\n", "\n", " def __init__(self, nodes, J, vol, mu, lam, M, f_g, Q_pin, b_pin, h):\n", " self.nodes = nodes\n", " self.n, self.dim = nodes.shape\n", " self.J, self.vol = J, vol\n", " self.mu, self.lam = mu, lam\n", " self.M, self.f_g = M, f_g\n", " self.Q_pin, self.b_pin = Q_pin, b_pin\n", " self.inertia = utils.Inertia(M, h)\n", " self.h = h\n", "\n", " def energy(self, x):\n", " xn, xc = x.reshape(-1, self.dim), x.reshape(-1, 1)\n", " E_elastic = energies.macklin_mueller_neo_hookean_energy_x(xn, self.J, self.mu, self.lam, self.vol)\n", " E_pin = 0.5 * (xc.T @ (self.Q_pin @ xc))[0, 0] + (self.b_pin.T @ xc)[0, 0]\n", " E_gravity = -(self.f_g.T @ xc)[0, 0]\n", " E_inertia = self.inertia.energy(xc)\n", " return E_elastic + E_pin + E_gravity + E_inertia\n", "\n", " def gradient(self, x):\n", " xn, xc = x.reshape(-1, self.dim), x.reshape(-1, 1)\n", " g_elastic = energies.macklin_mueller_neo_hookean_gradient_x(xn, self.J, self.mu, self.lam, self.vol)\n", " g_pin = self.Q_pin @ xc + self.b_pin\n", " g_gravity = -self.f_g\n", " g_inertia = self.inertia.gradient(xc)\n", " return g_elastic + g_pin + g_gravity + g_inertia\n", "\n", " def hessian(self, x):\n", " xn = x.reshape(-1, self.dim)\n", " H_elastic = energies.macklin_mueller_neo_hookean_hessian_x(xn, self.J, self.mu, self.lam, self.vol, psd=True)\n", " H_pin = self.Q_pin\n", " H_inertia = self.inertia.hessian(x.reshape(-1, 1))\n", " return H_elastic + H_pin + H_inertia\n", "\n", " def step(self, U, V):\n", " self.inertia.update(U.reshape(-1, 1), V.reshape(-1, 1))\n", " x = newton_solver(U.reshape(-1, 1).copy(), self.energy, self.gradient, self.hessian,\n", " max_iter=30, tolerance=1e-8)\n", " U_next = x.reshape(self.n, self.dim)\n", " return U_next, (U_next - U) / self.h" ] }, { "cell_type": "markdown", "id": "feb2e645", "metadata": {}, "source": [ "### Assembling the two operator sets\n", "\n", "P1 reuses the standard `precompute`-style operators. P2 needs its own assembly\n", "(the midpoint-enriched mesh, cubature points/weights, and the per-cubature\n", "deformation Jacobian, mass matrix and gravity), which `utils.precompute` does not\n", "cover — so we build them with a small precompute helper. The energy term\n", "structure stays out in the simulator class; this helper only *assembles* operators." ] }, { "cell_type": "code", "execution_count": 4, "id": "8f47f03e", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:57.531912Z", "iopub.status.busy": "2026-06-09T05:30:57.531840Z", "iopub.status.idle": "2026-06-09T05:30:57.539784Z", "shell.execute_reply": "2026-06-09T05:30:57.539515Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P1: 20 nodes, 24 elements, 40 dofs\n", "P2: 63 nodes, 24 elements, 126 dofs\n" ] } ], "source": [ "# Shared coarse beam (deliberately coarse so the P1-vs-P2 difference is visible).\n", "X, T = utils.triangulated_grid(nx=5, ny=4, width=2.0, height=0.3)\n", "YM, PR, RHO, GRAV = 300.0, 0.4, 1.0, -9.8\n", "H, T_TOTAL, N_FRAMES = 0.01, 1.2, 48\n", "MU_NH, LAM_NH = simkit.ympr_to_lame(YM, PR)\n", "\n", "def assemble_p2_operators(X, T, rho, grav, order=2):\n", " \"\"\"Build the P2 operator set on the midpoint-enriched mesh: vertices, the\n", " per-cubature deformation Jacobian + weights, the mass matrix and gravity.\"\"\"\n", " V2, T2 = simkit.linear_to_quadratic_elements(X, T)\n", " bary, w = simkit.gauss_legendre_quadrature(X, T, order) # cubature for the elastic energy\n", " J2 = simkit.deformation_jacobian_p2(V2, T2, bary, w)\n", " vol = w.reshape(-1, 1) # per-cubature physical weights\n", " M2 = sp.sparse.kron(simkit.p2_massmatrix(V2, T2, bary, w, rho=rho), sp.sparse.eye(X.shape[1])).tocsc()\n", " fg2 = simkit.p2_gravity_force(V2, T2, bary, w, a=grav, rho=rho).reshape(-1, 1)\n", " return V2, T2, J2, vol, M2, fg2\n", "\n", "# ---- P1 (linear) operators on (X, T) ----\n", "n1, dim = X.shape\n", "J1 = simkit.deformation_jacobian(X, T)\n", "vol1 = simkit.volume(X, T)\n", "M1 = sp.sparse.kron(simkit.massmatrix(X, T, rho=RHO), sp.sparse.eye(dim)).tocsc()\n", "fg1 = simkit.gravity_force(X, T, a=GRAV, rho=RHO).reshape(-1, 1)\n", "pin1 = np.where(X[:, 0] <= X[:, 0].min() + 1e-6)[0]\n", "Q1, b1 = simkit.dirichlet_penalty(pin1, X[pin1], n1, 1e7)\n", "mu1 = np.full((vol1.shape[0], 1), MU_NH); lam1 = np.full((vol1.shape[0], 1), LAM_NH)\n", "\n", "# ---- P2 (quadratic) operators on the midpoint-enriched mesh ----\n", "V2, T2, J2, vol2, M2, fg2 = assemble_p2_operators(X, T, RHO, GRAV, order=2)\n", "n2 = V2.shape[0]\n", "pin2 = np.where(V2[:, 0] <= V2[:, 0].min() + 1e-6)[0]\n", "Q2, b2 = simkit.dirichlet_penalty(pin2, V2[pin2], n2, 1e7)\n", "mu2 = np.full((vol2.shape[0], 1), MU_NH); lam2 = np.full((vol2.shape[0], 1), LAM_NH)\n", "\n", "beam_p1 = FEMBeam(X, J1, vol1, mu1, lam1, M1, fg1, Q1, b1, H)\n", "beam_p2 = FEMBeam(V2, J2, vol2, mu2, lam2, M2, fg2, Q2, b2, H)\n", "\n", "print(f\"P1: {n1} nodes, {T.shape[0]} elements, {n1*dim} dofs\")\n", "print(f\"P2: {n2} nodes, {T2.shape[0]} elements, {n2*dim} dofs\")" ] }, { "cell_type": "markdown", "id": "1b3ee048", "metadata": {}, "source": [ "### Curved (true-geometry) rendering of P2 elements\n", "\n", "A P2 element edge between corners $a, b$ (with shared midpoint node $m$) is a\n", "*parabola* in the edge parameter $t \\in [0, 1]$:\n", "\n", "$$\n", "x(t) = N_a(t)\\, U_a + N_b(t)\\, U_b + N_m(t)\\, U_m,\n", "$$\n", "\n", "$$\n", "N_a = (1-t)(1-2t), \\quad N_b = t(2t-1), \\quad N_m = 4 t (1-t).\n", "$$\n", "\n", "Sampling $t$ densely traces the REAL curved boundary — something straight-line\n", "subdivision (or any linear P1 element) can never produce." ] }, { "cell_type": "code", "execution_count": 5, "id": "eb7e82e3", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:57.540880Z", "iopub.status.busy": "2026-06-09T05:30:57.540820Z", "iopub.status.idle": "2026-06-09T05:30:57.543649Z", "shell.execute_reply": "2026-06-09T05:30:57.543457Z" } }, "outputs": [], "source": [ "S = 12\n", "_t = np.linspace(0.0, 1.0, S)\n", "_W = np.column_stack([(1 - _t) * (1 - 2 * _t), _t * (2 * _t - 1), 4 * _t * (1 - _t)]) # (S, 3)\n", "# Boundary edges for our node order [c0,c1,c2, m01,m12,m20]: (corner_a, corner_b, mid).\n", "_EDGES = [(0, 1, 3), (1, 2, 4), (2, 0, 5)]\n", "\n", "def p2_curved_loops(U2, T2):\n", " \"\"\"One (3*S, 2) curved boundary polygon per P2 element (parabolic edges).\"\"\"\n", " loops = []\n", " for el in np.asarray(T2):\n", " pieces = [_W @ U2[[el[a], el[b], el[m]]] for (a, b, m) in _EDGES]\n", " loops.append(np.vstack(pieces))\n", " return loops\n", "\n", "class CurvedP2Artist:\n", " \"\"\"Like utils.PolyMeshArtist, but draws each P2 element's true curved edges.\"\"\"\n", " def __init__(self, ax, U2, T2, facecolor=utils.MESH_FACE,\n", " edgecolor=utils.MESH_EDGE, lw=1.0, zorder=2, alpha=0.95):\n", " self.T2 = np.asarray(T2)\n", " self.coll = PolyCollection(p2_curved_loops(np.asarray(U2, float), self.T2),\n", " facecolors=facecolor, edgecolors=edgecolor,\n", " linewidths=lw, zorder=zorder, alpha=alpha)\n", " ax.add_collection(self.coll)\n", " def update(self, U2):\n", " self.coll.set_verts(p2_curved_loops(np.asarray(U2, float), self.T2))\n", "\n", "def animate_p1_p2(states_p1, states_p2, T_p1, T2, *, lims, fps=24, suptitle=None,\n", " titles=(\"Linear (P1) - straight edges\",\n", " \"Quadratic (P2) - true curved edges\")):\n", " \"\"\"1x2 animation: P1 via PolyMeshArtist (straight) vs P2 via CurvedP2Artist.\"\"\"\n", " (xlim, ylim) = lims\n", " fig, axes = plt.subplots(1, 2, figsize=(9.4, 4.4))\n", " utils.setup_axes(axes[0], xlim, ylim, title=titles[0])\n", " utils.setup_axes(axes[1], xlim, ylim, title=titles[1])\n", " a1 = utils.PolyMeshArtist(axes[0], states_p1[0], T_p1)\n", " a2 = CurvedP2Artist(axes[1], states_p2[0], T2)\n", " if suptitle:\n", " fig.suptitle(suptitle)\n", " nframes = max(len(states_p1), len(states_p2))\n", " def update(i):\n", " a1.update(states_p1[min(i, len(states_p1) - 1)])\n", " a2.update(states_p2[min(i, len(states_p2) - 1)])\n", " return ()\n", " anim = FuncAnimation(fig, update, frames=nframes, interval=1000 / fps, blit=False)\n", " fig.tight_layout()\n", " return fig, anim" ] }, { "cell_type": "markdown", "id": "8e1c452c", "metadata": {}, "source": [ "### Running both beams\n", "\n", "Each beam is stepped with its own explicit backward-Euler loop, sampling\n", "`N_FRAMES` evenly-spaced frames. P1 is drawn with its native straight triangles;\n", "P2 with its TRUE curved geometry (parabolic edges) — not straight\n", "sub-triangles." ] }, { "cell_type": "code", "execution_count": 6, "id": "0c8b57c1", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:57.544491Z", "iopub.status.busy": "2026-06-09T05:30:57.544440Z", "iopub.status.idle": "2026-06-09T05:30:59.641555Z", "shell.execute_reply": "2026-06-09T05:30:59.641287Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample = np.linspace(0, T_TOTAL, N_FRAMES)\n", "\n", "# ---- P1 backward-Euler rollout ----\n", "U, V = X.copy(), np.zeros_like(X)\n", "t, si, states_p1 = 0.0, 0, [X.copy()]\n", "while si < N_FRAMES - 1:\n", " U, V = beam_p1.step(U, V); t += H\n", " while si < N_FRAMES - 1 and t >= sample[si + 1]:\n", " si += 1; states_p1.append(U.copy())\n", "\n", "# ---- P2 backward-Euler rollout ----\n", "U, V = V2.copy(), np.zeros_like(V2)\n", "t, si, states_p2 = 0.0, 0, [V2.copy()]\n", "while si < N_FRAMES - 1:\n", " U, V = beam_p2.step(U, V); t += H\n", " while si < N_FRAMES - 1 and t >= sample[si + 1]:\n", " si += 1; states_p2.append(U.copy())\n", "\n", "fig, anim = animate_p1_p2(\n", " states_p1, states_p2, T, T2,\n", " lims=((-1.25, 1.45), (-1.6, 0.4)), fps=24,\n", " suptitle=\"Same mesh, same material, same dt: only P2's edges can curve\")\n", "utils.show_video(fig, anim, \"media/12_p1_vs_p2_beam.mp4\", fps=24)" ] }, { "cell_type": "markdown", "id": "efa77182", "metadata": {}, "source": [ "### Wait — is this just a subdivided mesh?\n", "\n", "A fair question, because the P2 element and a triangle **subdivided into 4 linear\n", "sub-triangles** use the *exact same 6 nodes* (3 corners + 3 edge midpoints). The\n", "difference is not the nodes, it is the **function space**:\n", "\n", "| scheme | nodes | within an element | edges |\n", "|---|---|---|---|\n", "| **P1 linear** | 3 corners | constant $F$ | straight (cannot curve) |\n", "| **Subdivided P1** | same 6 | piecewise-constant $F$, kinks at midpoints | straight chords |\n", "| **P2 quadratic** | same 6 | $F$ varies linearly & smoothly | **curved (parabolic)** |\n", "\n", "Below we apply one known quadratic bending field, $\\phi(x, y) = (x, y + 0.5 x^2)$,\n", "to a single triangle and render it three ways. The dashed grey curve is the *true*\n", "smooth shape. P1 is flat; subdivision is a kinked, piecewise-straight chord on the\n", "same nodes; **only the quadratic basis curves to match the truth** — which is also\n", "why the P2 patch test (`test_quadratic_field_gradient_matches_analytic`)\n", "reproduces such fields to ~1e-10 while no linear scheme on these nodes can." ] }, { "cell_type": "code", "execution_count": 7, "id": "72736cff", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:59.642781Z", "iopub.status.busy": "2026-06-09T05:30:59.642699Z", "iopub.status.idle": "2026-06-09T05:30:59.759765Z", "shell.execute_reply": "2026-06-09T05:30:59.759552Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# One triangle under a known quadratic bending phi, rendered three ways on identical nodes.\n", "def phi(P):\n", " P = np.atleast_2d(np.asarray(P, float))\n", " return np.column_stack([P[:, 0], P[:, 1] + 0.5 * P[:, 0] ** 2])\n", "\n", "c = np.array([[-1.0, 0.0], [1.0, 0.0], [0.0, 1.2]]) # corners\n", "mids = np.array([0.5 * (c[0] + c[1]), 0.5 * (c[1] + c[2]), 0.5 * (c[2] + c[0])])\n", "node6 = np.vstack([c, mids]) # [c0,c1,c2,m01,m12,m20]\n", "U6, Uc = phi(node6), phi(c)\n", "\n", "def ref_boundary(npts=160): # true smooth deformed outline\n", " segs = [(c[0], c[1]), (c[1], c[2]), (c[2], c[0])]\n", " pts = [A * (1 - ts) + B * ts for A, B in segs for ts in [np.linspace(0, 1, npts)[:, None]]]\n", " return phi(np.vstack(pts))\n", "truth = ref_boundary()\n", "\n", "sub = np.array([[0, 3, 5], [3, 1, 4], [5, 4, 2], [3, 4, 5]]) # 4-way subdivision\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(13.8, 4.7))\n", "lims = ((-1.5, 1.5), (-0.35, 2.0))\n", "titles = [\"P1 linear\\n(3 nodes, straight - cannot curve)\",\n", " \"Subdivided P1\\n(same 6 nodes, straight chords + kinks)\",\n", " \"P2 quadratic\\n(same 6 nodes, true curved edges)\"]\n", "for ax, title in zip(axes, titles):\n", " utils.setup_axes(ax, *lims, title=title)\n", " ax.plot(np.r_[truth[:, 0], truth[0, 0]], np.r_[truth[:, 1], truth[0, 1]],\n", " color=\"0.6\", lw=1.6, ls=\"--\", zorder=1, label=\"true smooth shape\")\n", "\n", "def add_poly(ax, polys):\n", " ax.add_collection(PolyCollection(polys, facecolors=utils.MESH_FACE,\n", " edgecolors=utils.MESH_EDGE, lw=1.8, alpha=0.95, zorder=2))\n", "\n", "add_poly(axes[0], [Uc]) # P1: one flat triangle\n", "add_poly(axes[1], [U6[f] for f in sub]) # subdivided: straight chords\n", "add_poly(axes[2], p2_curved_loops(U6, np.array([[0, 1, 2, 3, 4, 5]]))) # P2: curved\n", "\n", "for ax, pts in zip(axes, [Uc, U6, U6]):\n", " ax.plot(pts[:3, 0], pts[:3, 1], \"o\", color=\"#08519c\", ms=7, zorder=3, label=\"corner nodes\")\n", " if len(pts) > 3:\n", " ax.plot(pts[3:, 0], pts[3:, 1], \"s\", color=\"#e6550d\", ms=7, zorder=3, label=\"midpoint nodes\")\n", "axes[0].legend(loc=\"upper center\", fontsize=8, framealpha=0.9)\n", "fig.suptitle(\"Same nodes, three function spaces: only the quadratic basis bends within the element\",\n", " fontsize=12)\n", "fig.tight_layout(rect=(0, 0, 1, 0.93))\n", "fig.savefig(\"media/12_p1_vs_subdivided_vs_p2.png\", dpi=120)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1d1bba9d", "metadata": {}, "source": [ "### Static equilibrium: the unambiguous stiffness comparison\n", "\n", "The animation above includes inertia, so at any instant both beams are still\n", "swinging (and their different mass distributions put them slightly out of phase).\n", "To compare *stiffness* cleanly we drop the inertia term and solve directly for the\n", "gravity equilibrium — the shape each beam eventually settles into. Linear\n", "triangles cannot bend within an element, so the P1 beam is artificially **stiff**\n", "and deflects less than the more accurate P2 beam.\n", "\n", "We reuse the *same* `FEMBeam` operators, but solve the static problem (no inertia)\n", "by stepping each beam with a zero timestep contribution: we simply minimize\n", "elastic + pin + gravity directly. Each beam writes its own explicit solve." ] }, { "cell_type": "code", "execution_count": 8, "id": "fb3f1072", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:59.760777Z", "iopub.status.busy": "2026-06-09T05:30:59.760715Z", "iopub.status.idle": "2026-06-09T05:30:59.872825Z", "shell.execute_reply": "2026-06-09T05:30:59.872553Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P1 tip deflection: -1.5130\n", "P2 tip deflection: -1.8640 (P2 is 23.2% more compliant)\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def static_equilibrium(beam, nodes):\n", " \"\"\"Minimize elastic + pin + gravity potential (no inertia) for a FEMBeam's operators.\"\"\"\n", " n, dim = nodes.shape\n", " def E(x):\n", " xn, xc = x.reshape(-1, dim), x.reshape(-1, 1)\n", " E_elastic = energies.macklin_mueller_neo_hookean_energy_x(xn, beam.J, beam.mu, beam.lam, beam.vol)\n", " E_pin = 0.5 * (xc.T @ (beam.Q_pin @ xc))[0, 0] + (beam.b_pin.T @ xc)[0, 0]\n", " E_gravity = -(beam.f_g.T @ xc)[0, 0]\n", " return E_elastic + E_pin + E_gravity\n", " def G(x):\n", " xn, xc = x.reshape(-1, dim), x.reshape(-1, 1)\n", " g_elastic = energies.macklin_mueller_neo_hookean_gradient_x(xn, beam.J, beam.mu, beam.lam, beam.vol)\n", " g_pin = beam.Q_pin @ xc + beam.b_pin\n", " g_gravity = -beam.f_g\n", " return g_elastic + g_pin + g_gravity\n", " def Hf(x):\n", " xn = x.reshape(-1, dim)\n", " H_elastic = energies.macklin_mueller_neo_hookean_hessian_x(xn, beam.J, beam.mu, beam.lam, beam.vol, psd=True)\n", " H_pin = beam.Q_pin\n", " return H_elastic + H_pin\n", " x = newton_solver(nodes.reshape(-1, 1).copy(), E, G, Hf, max_iter=200, tolerance=1e-9)\n", " return x.reshape(n, dim)\n", "\n", "eq1 = static_equilibrium(beam_p1, X)\n", "eq2 = static_equilibrium(beam_p2, V2)\n", "tip1, tip2 = eq1[:, 1].min(), eq2[:, 1].min()\n", "print(f\"P1 tip deflection: {tip1:.4f}\")\n", "print(f\"P2 tip deflection: {tip2:.4f} (P2 is {100*(tip2-tip1)/tip1:.1f}% more compliant)\")\n", "\n", "fig, anim = animate_p1_p2(\n", " [X, eq1], [V2, eq2], T, T2,\n", " lims=((-1.25, 1.45), (-2.1, 0.4)), fps=2,\n", " titles=(f\"P1 equilibrium (tip {tip1:.3f})\", f\"P2 equilibrium (tip {tip2:.3f}, curved)\"),\n", " suptitle=\"Static gravity equilibrium: linear elements are stiffer (deflect less)\")\n", "utils.show_video(fig, anim, \"media/12_p1_vs_p2_static.mp4\", fps=2)" ] }, { "cell_type": "markdown", "id": "a6f8bf8c", "metadata": {}, "source": [ "## Part C — Convergence: P1 is first order, P2 is second order\n", "\n", "The real payoff of quadratic elements is **accuracy per refinement**. We solve a\n", "problem whose exact answer we know (the *method of manufactured solutions*) on a\n", "sequence of meshes and watch the error shrink as the element size $h$ decreases.\n", "\n", "We use **linear elasticity** (a linear PDE, so the rates are textbook-clean) on\n", "the unit square with the smooth exact displacement\n", "$u^*(x,y) = (s, s)$, $s = \\sin(\\pi a) \\sin(\\pi b)$, $a = x + 1/2$, $b = y + 1/2$ (which vanishes\n", "on the boundary). We pick the body force $b = -\\operatorname{div} \\sigma(u^*)$ that makes $u^*$ the\n", "exact solution, solve with both P1 and P2, and measure two error norms:\n", "\n", "- **L2 (displacement):** $\\lVert u_h - u^* \\rVert$\n", "- **H1 seminorm (strain / energy):** $\\lVert \\nabla u_h - \\nabla u^* \\rVert$\n", "\n", "For a smooth solution and degree-$p$ elements the theory says:\n", "\n", "| norm | rate | P1 ($p=1$) | P2 ($p=2$) |\n", "|---|---|---|---|\n", "| **H1 / strain** | $O(h^p)$ | $O(h)$ | $O(h^2)$ |\n", "| **L2 / displacement** | $O(h^{p+1})$ | $O(h^2)$ | $O(h^3)$ |\n", "\n", "So yes — exactly your intuition: in the energy/strain norm P1 is **first order**\n", "and P2 is **second order**. Halving the element size cuts P1's strain error by ~2\n", "but P2's by ~4, so P2 reaches a target accuracy on a far coarser mesh." ] }, { "cell_type": "code", "execution_count": 9, "id": "eb950c21", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:59.873955Z", "iopub.status.busy": "2026-06-09T05:30:59.873874Z", "iopub.status.idle": "2026-06-09T05:30:59.877509Z", "shell.execute_reply": "2026-06-09T05:30:59.877309Z" } }, "outputs": [], "source": [ "# ---- Method of manufactured solutions on the unit square [-1/2, 1/2]^2 ----\n", "MU, LAM = simkit.ympr_to_lame(1.0, 0.3)\n", "\n", "def u_star(P): # exact displacement; zero on the boundary\n", " a, b = P[..., 0] + 0.5, P[..., 1] + 0.5\n", " s = np.sin(np.pi * a) * np.sin(np.pi * b)\n", " return np.stack([s, s], axis=-1)\n", "\n", "def grad_u_star(P): # rows = component i, cols = d/dX_j\n", " a, b = P[0] + 0.5, P[1] + 0.5\n", " sx = np.pi * np.cos(np.pi * a) * np.sin(np.pi * b)\n", " sy = np.pi * np.sin(np.pi * a) * np.cos(np.pi * b)\n", " return np.array([[sx, sy], [sx, sy]])\n", "\n", "def body_force(P): # b = -mu*Lap(u) - (mu+lam)*grad(div u)\n", " a, b = P[0] + 0.5, P[1] + 0.5\n", " s = np.sin(np.pi * a) * np.sin(np.pi * b)\n", " c = np.cos(np.pi * a) * np.cos(np.pi * b)\n", " val = 2 * MU * np.pi**2 * s - (MU + LAM) * np.pi**2 * (c - s)\n", " return np.array([val, val])\n", "\n", "def boundary_idx(V):\n", " return np.where((np.abs(V[:, 0] - 0.5) < 1e-9) | (np.abs(V[:, 0] + 0.5) < 1e-9) |\n", " (np.abs(V[:, 1] - 0.5) < 1e-9) | (np.abs(V[:, 1] + 0.5) < 1e-9))[0]\n", "\n", "def assemble_load(nodes, Telem, bary, weights, shape_at):\n", " \"\"\"Consistent load vector f_i = integral N_i . b dV, by quadrature.\"\"\"\n", " n, dim = nodes.shape\n", " t, nq, s = bary.shape\n", " f = np.zeros((n, dim))\n", " for e in range(t):\n", " Xc = nodes[Telem[e, :s]] # corners -> affine rest map\n", " for q in range(nq):\n", " L = bary[e, q]; xq = L @ Xc\n", " N = shape_at(L); bq = body_force(xq)\n", " for i, node in enumerate(Telem[e]):\n", " f[node] += weights[e, q] * N[i] * bq\n", " return f\n", "\n", "def solve_linear_elastic(nodes, J, vol, f_load, bnd):\n", " \"\"\"One linear solve (linear elasticity) with u=0 pinned on the boundary.\"\"\"\n", " n, dim = nodes.shape\n", " mu = np.full((vol.shape[0], 1), MU); lam = np.full((vol.shape[0], 1), LAM)\n", " Q, b = simkit.dirichlet_penalty(bnd, nodes[bnd], n, 1e10)\n", " x0 = nodes.reshape(-1, 1)\n", " g = energies.linear_elasticity_gradient_x(nodes, J, mu, lam, vol) + Q @ x0 + b - f_load.reshape(-1, 1)\n", " H = energies.linear_elasticity_hessian_x(nodes, J, mu, lam, vol, psd=True) + Q\n", " dx = sp.sparse.linalg.spsolve(H.tocsc(), -g).reshape(-1, 1)\n", " return (x0 + dx).reshape(n, dim)\n", "\n", "def error_norms(nodes, Telem, x, bary, weights, F, shape_at):\n", " \"\"\"L2 displacement error and H1 (strain) seminorm error vs the exact field.\"\"\"\n", " n, dim = nodes.shape\n", " t, nq, s = bary.shape\n", " l2 = h1 = 0.0\n", " for e in range(t):\n", " Xc = nodes[Telem[e, :s]]\n", " uel = x[Telem[e]] - nodes[Telem[e]] # nodal displacements\n", " for q in range(nq):\n", " L = bary[e, q]; wq = weights[e, q]; xq = L @ Xc\n", " uh = shape_at(L) @ uel # interpolated FE displacement\n", " l2 += wq * np.sum((uh - u_star(xq))**2)\n", " h1 += wq * np.sum((F[e, q] - np.eye(dim) - grad_u_star(xq))**2) # grad u_h = F - I\n", " return np.sqrt(l2), np.sqrt(h1)\n", "\n", "P1_SHAPE = lambda L: L # linear hats = barycentric coords\n", "P2_SHAPE = lambda L: simkit.p2_shape_functions(L, 3)[0] # quadratic shape functions" ] }, { "cell_type": "markdown", "id": "be6cb2ef", "metadata": {}, "source": [ "### Refinement sweep\n", "\n", "We loop over a sequence of mesh resolutions, solving the manufactured problem with\n", "both P1 and P2 on each mesh and recording both error norms. The loop is explicit:\n", "each iteration builds its own meshes, operators, loads and errors inline." ] }, { "cell_type": "code", "execution_count": 10, "id": "609d994a", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:59.878385Z", "iopub.status.busy": "2026-06-09T05:30:59.878337Z", "iopub.status.idle": "2026-06-09T05:31:00.727891Z", "shell.execute_reply": "2026-06-09T05:31:00.727686Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P1 H1 (strain) order = 0.99 (theory 1)\n", "P2 H1 (strain) order = 1.98 (theory 2)\n", "P1 L2 (displ.) order = 1.98 (theory 2)\n", "P2 L2 (displ.) order = 2.97 (theory 3)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resolutions = [4, 8, 16, 32]\n", "hs = []\n", "err = {\"P1 L2\": [], \"P1 H1\": [], \"P2 L2\": [], \"P2 H1\": []}\n", "for nn in resolutions:\n", " X, T = utils.triangulated_grid(nx=nn + 1, ny=nn + 1, width=1.0, height=1.0)\n", " hs.append(1.0 / nn)\n", " bq, wq = simkit.gauss_legendre_quadrature(X, T, 4) # accurate load + error quadrature\n", "\n", " # --- P1 ---\n", " J1, v1 = simkit.deformation_jacobian(X, T), simkit.volume(X, T)\n", " f1 = assemble_load(X, T, bq, wq, P1_SHAPE)\n", " x1 = solve_linear_elastic(X, J1, v1, f1, boundary_idx(X))\n", " F1 = np.repeat(simkit.deformation_gradient(X, T, x1)[:, None], bq.shape[1], axis=1)\n", " l2, h1 = error_norms(X, T, x1, bq, wq, F1, P1_SHAPE)\n", " err[\"P1 L2\"].append(l2); err[\"P1 H1\"].append(h1)\n", "\n", " # --- P2 ---\n", " V2, T2 = simkit.linear_to_quadratic_elements(X, T)\n", " b2, w2 = simkit.gauss_legendre_quadrature(X, T, 2) # order 2 for the elastic stiffness\n", " J2, v2 = simkit.deformation_jacobian_p2(V2, T2, b2, w2), w2.reshape(-1, 1)\n", " f2 = assemble_load(V2, T2, bq, wq, P2_SHAPE)\n", " x2 = solve_linear_elastic(V2, J2, v2, f2, boundary_idx(V2))\n", " F2 = simkit.deformation_gradient_p2(V2, T2, bq, x2)\n", " l2, h1 = error_norms(V2, T2, x2, bq, wq, F2, P2_SHAPE)\n", " err[\"P2 L2\"].append(l2); err[\"P2 H1\"].append(h1)\n", "\n", "hs = np.array(hs)\n", "slope = lambda e: np.polyfit(np.log(hs), np.log(e), 1)[0]\n", "print(f\"P1 H1 (strain) order = {slope(err['P1 H1']):.2f} (theory 1)\")\n", "print(f\"P2 H1 (strain) order = {slope(err['P2 H1']):.2f} (theory 2)\")\n", "print(f\"P1 L2 (displ.) order = {slope(err['P1 L2']):.2f} (theory 2)\")\n", "print(f\"P2 L2 (displ.) order = {slope(err['P2 L2']):.2f} (theory 3)\")\n", "\n", "colors = {\"P1 (linear)\": \"#d62728\", \"P2 (quadratic)\": \"#1f77b4\"}\n", "fig, axes = plt.subplots(1, 2, figsize=(12.5, 4.8))\n", "utils.loglog_plot(hs, {\"P1 (linear)\": err[\"P1 H1\"], \"P2 (quadratic)\": err[\"P2 H1\"]},\n", " xlabel=\"element size h\", ylabel=\"H1 (strain) error\", colors=colors,\n", " ref_slopes={\"O(h)\": 1, \"O(h^2)\": 2},\n", " title=\"Energy / strain norm: 1st vs 2nd order\", ax=axes[0])\n", "utils.loglog_plot(hs, {\"P1 (linear)\": err[\"P1 L2\"], \"P2 (quadratic)\": err[\"P2 L2\"]},\n", " xlabel=\"element size h\", ylabel=\"L2 (displacement) error\", colors=colors,\n", " ref_slopes={\"O(h^2)\": 2, \"O(h^3)\": 3},\n", " title=\"Displacement norm: 2nd vs 3rd order\", ax=axes[1])\n", "fig.suptitle(\"P1 vs P2 convergence under mesh refinement\", fontsize=13)\n", "fig.tight_layout(rect=(0, 0, 1, 0.95))\n", "fig.savefig(\"media/12_convergence.png\", dpi=120)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "41934c98", "metadata": {}, "source": [ "### Takeaways\n", "\n", "- At **static equilibrium** the **P1** beam is artificially **stiff** (linear\n", " elements cannot bend within an element) and deflects less, while **P2** sags\n", " further and more smoothly. The dynamic animation adds inertia on top, so both\n", " beams swing (and, having different mass distributions, do so slightly out of\n", " phase).\n", "- **It is not a subdivided mesh.** P2 and a 4-way subdivision share the *same 6\n", " nodes*, but only the quadratic basis bends *within* an element — its edges are\n", " genuine parabolas (Part B), and it reproduces quadratic fields exactly while no\n", " linear scheme on those nodes can.\n", "- **Convergence (Part C):** P1 is **first order** and P2 is **second order** in\n", " the energy/strain norm ($O(h)$ vs $O(h^2)$), and one order higher in the L2\n", " displacement norm — so P2 reaches a target accuracy on a much coarser mesh.\n", "- The elastic energy, gradient and Hessian code was **reused unchanged**\n", " throughout; P2 only changed $J$ (now mapping to per-cubature $F$), the\n", " integration weights, and the mass/gravity assembly." ] } ], "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }