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Devito-fied first cell of vib_gen
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@EdCaunt
EdCaunt committed Jul 31, 2020
1 parent 5a41cc0 commit 8f0db29
Showing 1 changed file with 45 additions and 43 deletions.
88 changes: 45 additions & 43 deletions fdm-devito-notebooks/01_vib/vib_gen.ipynb
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{
"cells": [
{
"cell_type": "raw",
"cell_type": "markdown",
"metadata": {},
"source": [
"<!-- Equation labels as ordinary links -->\n",
Expand Down Expand Up @@ -510,6 +510,11 @@
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import sympy as sp\n",
"from devito import Dimension, Constant, TimeFunction, Eq, solve, Operator\n",
"\n",
"\n",
"def solver(I, V, m, b, s, F, dt, T, damping='linear'):\n",
" \"\"\"\n",
" Solve m*u'' + f(u') + s(u) = F(t) for t in (0,T],\n",
Expand All @@ -519,27 +524,33 @@
" 'quadratic', f(u')=b*u'*abs(u').\n",
" F(t) and s(u) are Python functions.\n",
" \"\"\"\n",
" dt = float(dt); b = float(b); m = float(m) # avoid integer div.\n",
" dt = float(dt)\n",
" b = float(b)\n",
" m = float(m)\n",
" Nt = int(round(T/dt))\n",
" u = np.zeros(Nt+1)\n",
" t = np.linspace(0, Nt*dt, Nt+1)\n",
" t = Dimension('t', spacing=Constant('h_t'))\n",
"\n",
" u = TimeFunction(name='u', dimensions=(t,),\n",
" shape=(Nt+1,), space_order=2)\n",
"\n",
" u.data[0] = I\n",
"\n",
" u[0] = I\n",
" if damping == 'linear':\n",
" u[1] = u[0] + dt*V + dt**2/(2*m)*(-b*V - s(u[0]) + F(t[0]))\n",
" # dtc for central difference (default for time is forward, 1st order)\n",
" eqn = m*u.dt2 + b*u.dtc + s(u) - F(u)\n",
" stencil = Eq(u.forward, solve(eqn, u.forward))\n",
" elif damping == 'quadratic':\n",
" u[1] = u[0] + dt*V + \\\n",
" dt**2/(2*m)*(-b*V*abs(V) - s(u[0]) + F(t[0]))\n",
" # fd_order set as backward derivative used is 1st order\n",
" eqn = m*u.dt2 + b*u.dt*sp.Abs(u.dtl(fd_order=1)) + s(u) - F(u)\n",
" stencil = Eq(u.forward, solve(eqn, u.forward))\n",
" # First timestep needs to have the backward timestep substituted\n",
" stencil_init = stencil.subs(u.backward, u.forward-2*t.spacing*V)\n",
" op_init = Operator(stencil_init, name='first_timestep')\n",
" op = Operator(stencil, name='main_loop')\n",
" op_init.apply(h_t=dt, t_M=1)\n",
" op.apply(h_t=dt, t_m=1, t_M=Nt-1)\n",
"\n",
" for n in range(1, Nt):\n",
" if damping == 'linear':\n",
" u[n+1] = (2*m*u[n] + (b*dt/2 - m)*u[n-1] +\n",
" dt**2*(F(t[n]) - s(u[n])))/(m + b*dt/2)\n",
" elif damping == 'quadratic':\n",
" u[n+1] = (2*m*u[n] - m*u[n-1] + b*u[n]*abs(u[n] - u[n-1])\n",
" + dt**2*(F(t[n]) - s(u[n])))/\\\n",
" (m + b*abs(u[n] - u[n-1]))\n",
" return u, t"
" return u.data, np.linspace(0, Nt*dt, Nt+1)"
]
},
{
Expand Down Expand Up @@ -619,27 +630,6 @@
"the quadratic polynomial is reproduced by the numerical method (to\n",
"machine precision).\n",
"\n",
"### Catching bugs\n",
"\n",
"How good are the constant and quadratic solutions at catching\n",
"bugs in the implementation? Let us check that by introducing some bugs.\n",
"\n",
" * Use `m` instead of `2*m` in the denominator of `u[1]`: code works for constant\n",
" solution, but fails (as it should) for a quadratic one.\n",
"\n",
" * Use `b*dt` instead of `b*dt/2` in the updating formula for `u[n+1]`\n",
" in case of linear damping: constant and quadratic both fail.\n",
"\n",
" * Use `F[n+1]` instead of `F[n]` in case of linear or quadratic damping:\n",
" constant solution works, quadratic fails.\n",
"\n",
"We realize that the constant solution is very useful for catching certain bugs because\n",
"of its simplicity (easy to predict what the different terms in the\n",
"formula should evaluate to), while the quadratic solution seems\n",
"capable of detecting all (?) other kinds of typos in the scheme.\n",
"These results demonstrate why we focus so much on exact, simple polynomial\n",
"solutions of the numerical schemes in these writings.\n",
"\n",
"<!-- More: classes, cases with pendulum approx u vs sin(u), -->\n",
"<!-- making UI via parampool -->\n",
"\n",
Expand Down Expand Up @@ -1470,7 +1460,19 @@
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"ename": "ModuleNotFoundError",
"evalue": "No module named 'scitools'",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-3-b591f37272a6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mscitools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstd\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0msympy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0msym\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mvib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0msolver\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mvib_solver\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'scitools'"
]
}
],
"source": [
"# Reimplementation of vib.py using classes\n",
"\n",
Expand Down Expand Up @@ -1858,7 +1860,7 @@
},
{
"cell_type": "code",
"execution_count": 4,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -2191,9 +2193,9 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "devito",
"language": "python",
"name": "python3"
"name": "devito"
},
"language_info": {
"codemirror_mode": {
Expand All @@ -2205,7 +2207,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
"version": "3.8.1"
}
},
"nbformat": 4,
Expand Down

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