dissertation_work/Programming/Python files/Nonuniform_JLP.ipynb

273 lines
114 KiB
Plaintext

{
"cells": [
{
"cell_type": "code",
"execution_count": 68,
"id": "1dc137ec",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"def f(x):\n",
" return np.sin(np.pi * x)\n",
" #return 1 - 4*(x-0.5)**2\n",
"\n",
"def nonuniform_grid(num_points,left_pt,right_pt,is_non_unif=True):\n",
" grid = np.array([(float(is_non_unif)/(num_points+1-0.5*(num_points+2))**2)*((i+1)-0.5*(num_points+2))**2 + 1 for i in range(num_points+1)])\n",
" grid *= (right_pt-left_pt)/sum(grid)\n",
" final_grid = np.zeros(num_points+2)\n",
" final_grid[0] = left_pt\n",
" for i in range(1,num_points+1) :\n",
" final_grid[i] = final_grid[i-1]+grid[i-1]\n",
" final_grid[num_points+1] = right_pt\n",
" return grid, final_grid"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "6391d3e7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x540 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"num_points = 100\n",
"h_vals, grid = nonuniform_grid(num_points,0,1)\n",
"#grid = np.linspace(0,1,num_points+2)\n",
"#h_vals = np.diff(grid)\n",
"\n",
"plt.figure(figsize=(12,7.5))\n",
"\n",
"# Plot 1\n",
"plt.subplot(1,2,1)\n",
"plt.plot(grid)\n",
"plt.title(\"Plot of nonuniform grid\")\n",
"plt.xlabel(\"Grid point index\")\n",
"plt.ylabel(\"Domain value\")\n",
"\n",
"# Plot 2\n",
"plt.subplot(1,2,2)\n",
"plt.plot(grid[:-1],h_vals)\n",
"plt.title(\"Comparison of grid spacing\")\n",
"plt.xlabel(\"Point in domain\")\n",
"plt.ylabel(\"Grid spacing\")\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "ac600ea8",
"metadata": {},
"outputs": [],
"source": [
"# Construct the coefficient matrix\n",
"A = np.zeros((num_points,num_points))\n",
"\n",
"for i in range(num_points) :\n",
" A[i,i] = -2./(h_vals[i]*h_vals[i+1])\n",
" \n",
"for i in range(num_points-1) :\n",
" A[i+1,i] = 2./(h_vals[i+1]*(h_vals[i+1]+h_vals[i+2]))\n",
" A[i,i+1] = 2./(h_vals[i+1]*(h_vals[i]+h_vals[i+1]))"
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "7343d63c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ -9343.45827382, 4718.44170984, 0. , ...,\n",
" 0. , 0. , 0. ],\n",
" [ 4813.73429872, -9724.66514761, 4910.93084888, ...,\n",
" 0. , 0. , 0. ],\n",
" [ 0. , 5010.04771244, -10121.16880196, ...,\n",
" 0. , 0. , 0. ],\n",
" ...,\n",
" [ 0. , 0. , 0. , ...,\n",
" -10121.16880196, 5010.04771244, 0. ],\n",
" [ 0. , 0. , 0. , ...,\n",
" 4910.93084888, -9724.66514761, 4813.73429872],\n",
" [ 0. , 0. , 0. , ...,\n",
" 0. , 4718.44170984, -9343.45827382]])"
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Check the resulting matrix's form\n",
"A"
]
},
{
"cell_type": "code",
"execution_count": 72,
"id": "be8ce9d4",
"metadata": {},
"outputs": [],
"source": [
"# Solve the discrete system\n",
"\n",
"bc_left = 0\n",
"bc_right = 0\n",
"\n",
"rhs = f(grid[1:-1])\n",
"rhs[0] -= (2/(h_vals[0]*(h_vals[0]+h_vals[1])))*bc_left\n",
"rhs[-1] -= (2/(h_vals[-1]*(h_vals[-2]+h_vals[-1])))*bc_right\n",
"\n",
"u = np.linalg.solve(A,rhs)"
]
},
{
"cell_type": "code",
"execution_count": 73,
"id": "ec5cd1a5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x540 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Add boundary conditions\n",
"\n",
"U = np.append(np.array([bc_left]),np.append(u,bc_right))\n",
"RHS = np.append(np.array([bc_left]),np.append(rhs,bc_right))\n",
"\n",
"plt.figure(figsize=(12,7.5))\n",
"plt.plot(grid,U,label=\"$u(x)$\")\n",
"plt.plot(grid,RHS,label=\"$f(x)$\")\n",
"plt.title(\"Solution vs. right-hand side function\")\n",
"plt.xlabel(\"$x$\")\n",
"plt.ylabel(\"$u(x)$\")\n",
"plt.legend()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 74,
"id": "6a80c620",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x540 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Check error\n",
"\n",
"def error_check(approx,true,grid) :\n",
" error_grid = np.append(0.5*(grid[:-1]+grid[1:]),grid[-1])\n",
" return np.sqrt(np.multiply(error_grid,(approx-true)**2))\n",
"\n",
"true_sol = -(1/np.pi**2)*np.sin(np.pi*grid)\n",
"\n",
"error = error_check(U,true_sol,grid)\n",
"\n",
"plt.figure(figsize=(12,7.5))\n",
"plt.plot(grid,error)\n",
"plt.title(\"Pointwise error\")\n",
"plt.ylabel(\"Error\")\n",
"plt.xlabel(\"$x$\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 75,
"id": "6ae3c077",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.000910607929436465"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# L2 error\n",
"sum(error)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aee347c7",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}