Commit 29ab5fe1 authored by Antoine RAVETTA's avatar Antoine RAVETTA

removing annoying checkpoints

parent 87ffc984
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Crank-Nicholson scheme"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cylindrical Diffraction Term"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"\"\"\"\n",
"### Adapted crank Nicholson class.\n",
"\n",
"* Prepare half-step method.\n",
"* Prepare non linear term for one of the half-step.\n",
"* Use $V$ advection to add first radial derivative.\n",
"\n",
"$V$ is a function of $r$\n",
"$$\n",
"V(r) = \\dfrac{i}{2 k_0} \\dfrac{1}{r}\n",
"$$\n",
"and $V(0) = 0$.\n",
"**Warning**: do not use $V(0)=0$ for any calculation.\n",
"\n",
"**Warning**: Test scheme matrices separately.\n",
"\"\"\"\n",
"\n",
"import numpy as np\n",
"import scipy.sparse\n",
"import scipy.linalg as la\n",
"\n",
"class CrankNicolson:\n",
" \"\"\"A class that solves dE/dz = D*d2E/dr2 + V(r)*dE/dr\"\"\"\n",
" \n",
" # Cylindrical grid\n",
" def set_grid(self, r_max, n_r, z_min, z_max, n_z):\n",
"\n",
" self.r_max, self.n_r = r_max, n_r\n",
" self.z_min, self.z_max, self.n_z = z_min, z_max, n_z\n",
" self.r_pts, self.delta_r = np.linspace(0, r_max, n_r, retstep=True, endpoint=False)\n",
" self.z_pts, self.delta_z = np.linspace(z_min, z_max, n_z, retstep=True, endpoint=False)\n",
" \n",
" # Parameters of the scheme\n",
" def set_parameters(self, D, V):\n",
" \n",
" # V has to be vectorised\n",
" self.D, self.V = D, V\n",
" \n",
" \n",
" \n",
" # One solving step for r dependency\n",
" def solve(self, E_init):\n",
" \n",
" # Coefficient of matrices\n",
" sig = self.D * self.delta_z / 2. / self.delta_r**2\n",
" nu = lambda x: - self.delta_z / 4. / self.delta_r * self.V(x) # minus sign for V convention\n",
" \n",
" # Empty solution matrix\n",
" self.E_matrix = np.zeros([self.n_z, self.n_r], dtype=complex)\n",
" \n",
" # Sparse solver\n",
" A = self._fillA_sp(sig, nu, self.n_r)\n",
" B = self._fillB_sp(sig, nu, self.n_r)\n",
" \n",
" # Set boundary conditions \n",
" # Dirichlet at infinity\n",
" A[1,-1] = 1.0\n",
" A[2,-2] = 0.0\n",
" B[-1,-1] = 0.0\n",
" B[-1,-2] = 0.0\n",
" # Neumann at r=0\n",
" A[0,1] = -2*sig\n",
" B[0,1] = 2*sig\n",
" \n",
" # Propagate\n",
" E = E_init.copy()\n",
" for n in range(self.n_z):\n",
" self.E_matrix[n,:] = E\n",
" \n",
" E = la.solve_banded((1,1),A, B.dot(E), check_finite=False)\n",
" \n",
" \n",
" \n",
" # Deep copy of results for export\n",
" # np.savetxt ?\n",
" def get_E(self):\n",
" \n",
" return self.E_matrix.copy()\n",
" \n",
" # Diagonal packing for banded\n",
" def _fillA_sp(self, sig, nu, n):\n",
" \"\"\"Returns a tridiagonal matrix in compact form ab[1+i-j,j]=a[i,j]\"\"\"\n",
" \n",
" A = np.zeros([3,n], dtype=complex) # A has three diagonals and size n\n",
" # Superdiagonal\n",
" A[0,1:] = -(sig - nu(self.r_pts[:-1]))\n",
" # Diagonal\n",
" A[1] = 1+2*sig\n",
" # Subdiagonal\n",
" A[2,:-1] = -(sig + nu(self.r_pts[1:]))\n",
" \n",
" return A\n",
" \n",
" # Sparse tridiagonal storage\n",
" def _fillB_sp(self, sig, nu, n):\n",
" \"\"\"Returns a tridiagonal sparse matrix in csr-form\"\"\"\n",
" \n",
" _o = np.ones(n, dtype=complex)\n",
" supdiag = (sig - nu(self.r_pts[:-1]))\n",
" diag = (1-2*sig)*_o\n",
" subdiag = (sig + nu(self.r_pts[1:]))\n",
" \n",
" return scipy.sparse.diags([supdiag, diag, subdiag], [1,0,-1], (n,n), format=\"csr\")\n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"DATA PRODUCTION\n",
"\n",
"We define some constants for the whole problem, as well as some functions :\n",
"\n",
"- wavevector\n",
"- potential\n",
"- initialisation of E"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"ename": "ModuleNotFoundError",
"evalue": "No module named 'CrankNicolson'",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-1-bc37d7a89e1a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\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----> 2\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mCrankNicolson\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mlambd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.7e-6\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'CrankNicolson'"
]
}
],
"source": [
"import numpy as np\n",
"import CrankNicolson\n",
"\n",
"lambd = 0.7e-6\n",
"\n",
"k = 2 * np.pi / lambd\n",
"\n",
"w0 = 1e-3\n",
"Pin = 1\n",
"\n",
"diff_coeff = 1j*1/(2 * k)\n",
"#diff_coeff = 0\n",
"#diff_coeff = 1e-4\n",
"\n",
"print('diff :', diff_coeff)\n",
"\n",
"\n",
"def potential(r):\n",
" try:\n",
" return diff_coeff / r\n",
" except ZeroDivisionError:\n",
" return 0\n",
"\n",
"\n",
"def gaussian(r, r0=0, w0=1, Pin=1):\n",
" return np.sqrt(2*Pin/(np.pi*w0**2)) * np.exp(-(r-r0)** 2/(w0**2))\n",
"\n",
"\n",
"def initial_enveloppe(r_pts, w0, Pin):\n",
" return np.array([gaussian(r_pts[i], w0=w0, Pin=Pin) for i in range(len(r_pts))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Instanciation of the CN Class"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'CrankNicolson' is not defined",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-4-4030111dc1b1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mcrank\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCrankNicolson\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mcrank\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_grid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr_max\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_r\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz_min\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz_max\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_z\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m200\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mcrank\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_parameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdiff_coeff\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mV\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpotential\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mNameError\u001b[0m: name 'CrankNicolson' is not defined"
]
}
],
"source": [
"crank = CrankNicolson()\n",
"\n",
"crank.set_grid(r_max=1e-2, n_r=100, z_min=0, z_max=10, n_z=200)\n",
"crank.set_parameters(D=diff_coeff, V=potential)\n",
"\n",
"crank.solve(initial_enveloppe(crank.r_pts, w0, Pin))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Save the result for later analysis"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"np.savetxt(\"../CN_cylindric_complex_E.dat\", np.abs(crank.E_matrix))\n",
"np.savetxt(\"../CN_cylindric_complex_r_pts.dat\", crank.r_pts)\n",
"np.savetxt(\"../CN_cylindric_complex_z_pts.dat\", crank.z_pts)"
]
}
],
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment