Relax fixed-point tolerance to 1e-6 in point kinetics notebook for 70x speedup

Author: milanofthe

docs/source/examples/point_kinetics.ipynb

@@ -32,14 +32,14 @@
   {
    "cell_type": "markdown",
    "metadata": {},
-   "source": "The point kinetics system is very stiff — the prompt neutron generation time $\\Lambda \\sim 10^{-5}\\,\\text{s}$ creates eigenvalues on the order of $10^5$. The variable-order BDF solver GEAR52A is ideal here: it requires only one implicit solve per step and adapts both step size and order to the smooth exponential dynamics.\n\n## 1. Delayed Supercritical Step\n\nInsert a step reactivity of $\\rho = 0.003$ (about $0.46\\beta$). Since $\\rho < \\beta$, the reactor is delayed supercritical — the power rises on a slow time scale governed by the delayed neutrons."
+   "source": "The point kinetics system is very stiff — the prompt neutron generation time $\\Lambda \\sim 10^{-5}\\,\\text{s}$ creates eigenvalues on the order of $10^5$. The variable-order BDF solver GEAR52A is ideal here: it requires only one implicit solve per step and adapts both step size and order to the smooth exponential dynamics. The default fixed-point tolerance (`1e-9`) is unnecessarily tight for this problem; relaxing it to `1e-6` gives a ~70x speedup with negligible loss in accuracy.\n\n## 1. Delayed Supercritical Step\n\nInsert a step reactivity of $\\rho = 0.003$ (about $0.46\\beta$). Since $\\rho < \\beta$, the reactor is delayed supercritical — the power rises on a slow time scale governed by the delayed neutrons."
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": "reactor = PointKinetics(n0=1.0)\n\nrho_step = 0.003\nsrc_rho = Source(lambda t: rho_step if t > 0 else 0.0)\nsrc_s = Source(lambda t: 0.0)\nsco = Scope(labels=[\"n\"])\n\nsim = Simulation(\n    [src_rho, src_s, reactor, sco],\n    [\n        Connection(src_rho, reactor),       # rho\n        Connection(src_s, reactor[1]),       # S\n        Connection(reactor, sco),            # n\n    ],\n    dt=0.01,\n    Solver=GEAR52A,\n    log=True,\n)\n\nsim.run(100)"
+   "source": "reactor = PointKinetics(n0=1.0)\n\nrho_step = 0.003\nsrc_rho = Source(lambda t: rho_step if t > 0 else 0.0)\nsrc_s = Source(lambda t: 0.0)\nsco = Scope(labels=[\"n\"])\n\nsim = Simulation(\n    [src_rho, src_s, reactor, sco],\n    [\n        Connection(src_rho, reactor),       # rho\n        Connection(src_s, reactor[1]),       # S\n        Connection(reactor, sco),            # n\n    ],\n    dt=0.01,\n    Solver=GEAR52A,\n    tolerance_fpi=1e-6,\n    log=True,\n)\n\nsim.run(100)"
   },
   {
    "cell_type": "code",
@@ -74,7 +74,7 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": "reactor = PointKinetics(n0=1.0)\n\nrho_prompt = 0.008\nsrc_rho = Source(lambda t: rho_prompt if t > 0 else 0.0)\nsrc_s = Source(lambda t: 0.0)\nsco = Scope(labels=[\"n\"])\n\nsim = Simulation(\n    [src_rho, src_s, reactor, sco],\n    [\n        Connection(src_rho, reactor),\n        Connection(src_s, reactor[1]),\n        Connection(reactor, sco),\n    ],\n    dt=0.001,\n    Solver=GEAR52A,\n    log=True,\n)\n\nsim.run(0.5)"
+   "source": "reactor = PointKinetics(n0=1.0)\n\nrho_prompt = 0.008\nsrc_rho = Source(lambda t: rho_prompt if t > 0 else 0.0)\nsrc_s = Source(lambda t: 0.0)\nsco = Scope(labels=[\"n\"])\n\nsim = Simulation(\n    [src_rho, src_s, reactor, sco],\n    [\n        Connection(src_rho, reactor),\n        Connection(src_s, reactor[1]),\n        Connection(reactor, sco),\n    ],\n    dt=0.001,\n    Solver=GEAR52A,\n    tolerance_fpi=1e-6,\n    log=True,\n)\n\nsim.run(0.5)"
   },
   {
    "cell_type": "code",
@@ -111,7 +111,7 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": "rho_sub = -0.05\ns_ext = 1e5\nLambda = 1e-5\n\nreactor = PointKinetics(n0=0.001, Lambda=Lambda)\n\nsrc_rho = Source(lambda t: rho_sub)\nsrc_s = Source(lambda t: s_ext)\nsco = Scope(labels=[\"n\"])\n\nsim = Simulation(\n    [src_rho, src_s, reactor, sco],\n    [\n        Connection(src_rho, reactor),\n        Connection(src_s, reactor[1]),\n        Connection(reactor, sco),\n    ],\n    dt=0.01,\n    Solver=GEAR52A,\n    log=True,\n)\n\nsim.run(50)"
+   "source": "rho_sub = -0.05\ns_ext = 1e5\nLambda = 1e-5\n\nreactor = PointKinetics(n0=0.001, Lambda=Lambda)\n\nsrc_rho = Source(lambda t: rho_sub)\nsrc_s = Source(lambda t: s_ext)\nsco = Scope(labels=[\"n\"])\n\nsim = Simulation(\n    [src_rho, src_s, reactor, sco],\n    [\n        Connection(src_rho, reactor),\n        Connection(src_s, reactor[1]),\n        Connection(reactor, sco),\n    ],\n    dt=0.01,\n    Solver=GEAR52A,\n    tolerance_fpi=1e-6,\n    log=True,\n)\n\nsim.run(50)"
   },
   {
    "cell_type": "code",