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"\n",
"\n",
"\n",
"# Start-to-Finish Example: Evolving Maxwell's Equations with Toriodal Dipole Field Initial Data, in Flat Spacetime and Curvilinear Coordinates\n",
"\n",
"## Following the work of [Knapp, Walker & Baumgarte (2002)](https://arxiv.org/abs/gr-qc/0201051), we numerically implement the second version of Maxwell’s equations - System II (BSSN - like) in curvilinear coordinates.\n",
"\n",
"## Author: Terrence Pierre Jacques and Zachariah Etienne\n",
"### Formatting improvements courtesy Brandon Clark\n",
"\n",
"**Notebook Status:** Validated \n",
"\n",
"**Validation Notes:** This module has been validated to exhibit convergence to the exact solution for the electric field $E^i$ and vector potential $A^i$ at the expected order, *after a short numerical evolution of the initial data* (see [plots at bottom](#convergence)).\n",
"\n",
"### NRPy+ Source Code for this module: \n",
"* [Maxwell/InitialData.py](../edit/Maxwell/InitialData.py); [\\[**tutorial**\\]](Tutorial-VacuumMaxwell_InitialData.ipynb): Purely toriodal dipole field initial data; sets all electromagnetic variables in the Cartesian basis\n",
"* [Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear.py](../edit/Maxwell/VacuumMaxwell_Flat_Evol_Cartesian.py); [\\[**tutorial**\\]](Tutorial-Tutorial-VacuumMaxwell_Curvilinear_RHS-Rescaling.ipynb): Generates the right-hand sides for Maxwell's equations in curvilinear coordinates\n",
"\n",
"## Introduction:\n",
"Here we use NRPy+ to generate the C source code necessary to set up initial data for a purely toriodal dipole field, as defined in [Knapp, Walker & Baumgarte (2002)](https://arxiv.org/abs/gr-qc/0201051). We then evolve the RHSs of Maxwell's equations using the [Method of Lines](https://reference.wolfram.com/language/tutorial/NDSolveMethodOfLines.html) time integration based on an [explicit Runge-Kutta fourth-order scheme](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) (RK4 is chosen below, but multiple options exist). \n",
"\n",
"The entire algorithm is outlined as follows, with links to the relevant NRPy+ tutorial notebooks listed at each step:\n",
"\n",
"1. Allocate memory for gridfunctions, including temporary storage for the Method of Lines time integration\n",
" * [**NRPy+ tutorial on Method of Lines algorithm**](Tutorial-Method_of_Lines-C_Code_Generation.ipynb).\n",
"1. Set gridfunction values to initial data \n",
" * [**NRPy+ tutorial on purely toriodal dipole field initial data**](Tutorial-VacuumMaxwell_InitialData.ipynb)\n",
"1. Next, integrate the initial data forward in time using the Method of Lines coupled to a Runge-Kutta explicit timestepping algorithm:\n",
" 1. At the start of each iteration in time, output the divergence constraint violation \n",
" * [**NRPy+ tutorial on Maxwell's equations constraints**](Tutorial-VacuumMaxwell_Curvilinear_RHSs.ipynb)\n",
" 1. At each RK time substep, do the following:\n",
" 1. Evaluate RHS expressions \n",
" * [**NRPy+ tutorial on Maxwell's equations right-hand sides**](Tutorial-VacuumMaxwell_Curvilinear_RHSs.ipynb)\n",
" 1. Apply Sommerfeld boundary conditions in curvilinear coordinates\n",
" * [**NRPy+ tutorial on setting up Sommerfeld boundary conditions**](Tutorial-SommerfeldBoundaryCondition.ipynb) \n",
"1. Repeat above steps at two numerical resolutions to confirm convergence to zero."
]
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"\n",
"\n",
"# Table of Contents\n",
"$$\\label{toc}$$\n",
"\n",
"This notebook is organized as follows\n",
"\n",
"1. [Step 1](#initializenrpy): Set core NRPy+ parameters for numerical grids and reference metric\n",
" 1. [Step 1.a](#cfl) Output needed C code for finding the minimum proper distance between grid points, needed for [CFL](https://en.wikipedia.org/w/index.php?title=Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition&oldid=806430673)-limited timestep\n",
"1. [Step 2](#mw): Generate symbolic expressions and output C code for evolving Maxwell's equations\n",
" 1. [Step 2.a](#mwid): Generate symbolic expressions for toroidal dipole field initial data\n",
" 1. [Step 2.b](#mwevol): Generate symbolic expressions for evolution equations\n",
" 1. [Step 2.c](#mwcon): Generate symbolic expressions for constraint equations\n",
" 1. [Step 2.d](#mwcart): Generate symbolic expressions for converting $A^i$ and $E^i$ to the Cartesian basis\n",
" 1. [Step 2.e](#mwccode): Output C codes for initial data and evolution equations\n",
" 1. [Step 2.f](#mwccode_con): Output C code for constraint equations\n",
" 1. [Step 2.g](#mwccode_cart): Output C code for converting $A^i$ and $E^i$ to Cartesian coordinates\n",
" 1. [Step 2.h](#mwccode_xzloop): Output C code for printing 2D data\n",
" 1. [Step 2.i](#cparams_rfm_and_domainsize): Output C codes needed for declaring and setting Cparameters; also set `free_parameters.h`\n",
"1. [Step 3](#bc_functs): Set up Sommerfeld boundary condition functions\n",
"1. [Step 4](#mainc): `Maxwell_Playground.c`: The Main C Code\n",
"1. [Step 5](#compileexec): Compile generated C codes & perform simulation of the propagating toriodal electromagnetic field\n",
"1. [Step 6](#visualize): Visualize the output!\n",
" 1. [Step 6.a](#installdownload): Install `scipy` and download `ffmpeg` if they are not yet installed/downloaded\n",
" 1. [Step 6.b](#genimages): Generate images for visualization animation\n",
" 1. [Step 6.c](#genvideo): Generate visualization animation\n",
"1. [Step 7](#convergence): Plot the numerical error, and confirm that it converges to zero with increasing numerical resolution (sampling)\n",
"1. [Step 8](#div_e): Comparison of Divergence Constrain Violation\n",
"1. [Step 9](#latex_pdf_output): Output this notebook to $\\LaTeX$-formatted PDF file"
]
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"source": [
"\n",
"\n",
"# Step 1: Set core NRPy+ parameters for numerical grids and reference metric \\[Back to [top](#toc)\\]\n",
"$$\\label{initializenrpy}$$"
]
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"data": {
"text/plain": [
"'MaxwellEvolCurvi_Playground_Ccodes/SIMD/SIMD_intrinsics.h'"
]
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"source": [
"# Step P1: Import needed NRPy+ core modules:\n",
"from outputC import outputC,lhrh,outCfunction # NRPy+: Core C code output module\n",
"import finite_difference as fin # NRPy+: Finite difference C code generation module\n",
"import NRPy_param_funcs as par # NRPy+: Parameter interface\n",
"import grid as gri # NRPy+: Functions having to do with numerical grids\n",
"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support\n",
"import reference_metric as rfm # NRPy+: Reference metric support\n",
"import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n",
"import shutil, os, sys # Standard Python modules for multiplatform OS-level functions, benchmarking\n",
"\n",
"# Step P2: Create C code output directory:\n",
"Ccodesdir = os.path.join(\"MaxwellEvolCurvi_Playground_Ccodes/\")\n",
"# First remove C code output directory if it exists\n",
"# Courtesy https://stackoverflow.com/questions/303200/how-do-i-remove-delete-a-folder-that-is-not-empty\n",
"shutil.rmtree(Ccodesdir, ignore_errors=True)\n",
"# Then create a fresh directory\n",
"cmd.mkdir(Ccodesdir)\n",
"\n",
"# Step P3: Create executable output directory:\n",
"outdir = os.path.join(Ccodesdir,\"output/\")\n",
"cmd.mkdir(outdir)\n",
"\n",
"# Step 1: Set the spatial dimension parameter\n",
"# to three (BSSN is a 3+1 decomposition\n",
"# of Einstein's equations), and then read\n",
"# the parameter as DIM.\n",
"par.set_parval_from_str(\"grid::DIM\",3)\n",
"DIM = par.parval_from_str(\"grid::DIM\")\n",
"\n",
"# Step 2: Set some core parameters, including CoordSystem MoL BoundaryCondition timestepping algorithm,\n",
"# FD order, floating point precision, and CFL factor:\n",
"# Choices are: Spherical, SinhSpherical, SinhSphericalv2, Cylindrical, SinhCylindrical,\n",
"# SymTP, SinhSymTP\n",
"CoordSystem = \"SinhCylindrical\"\n",
"\n",
"# Step 2.a: Set boundary conditions\n",
"# Current choices are QuadraticExtrapolation (quadratic polynomial extrapolation) or Sommerfeld\n",
"BoundaryCondition = \"Sommerfeld\"\n",
"\n",
"# Step 2.b: Set defaults for Coordinate system parameters.\n",
"# These are perhaps the most commonly adjusted parameters,\n",
"# so we enable modifications at this high level.\n",
"\n",
"# domain_size sets the default value for:\n",
"# * Spherical's params.RMAX\n",
"# * SinhSpherical*'s params.AMAX\n",
"# * Cartesians*'s -params.{x,y,z}min & .{x,y,z}max\n",
"# * Cylindrical's -params.ZMIN & .{Z,RHO}MAX\n",
"# * SinhCylindrical's params.AMPL{RHO,Z}\n",
"# * *SymTP's params.AMAX\n",
"domain_size = 10.0 # Needed for all coordinate systems.\n",
"\n",
"# sinh_width sets the default value for:\n",
"# * SinhSpherical's params.SINHW\n",
"# * SinhCylindrical's params.SINHW{RHO,Z}\n",
"# * SinhSymTP's params.SINHWAA\n",
"sinh_width = 0.4 # If Sinh* coordinates chosen\n",
"\n",
"# sinhv2_const_dr sets the default value for:\n",
"# * SinhSphericalv2's params.const_dr\n",
"# * SinhCylindricalv2's params.const_d{rho,z}\n",
"sinhv2_const_dr = 0.05 # If Sinh*v2 coordinates chosen\n",
"\n",
"# SymTP_bScale sets the default value for:\n",
"# * SinhSymTP's params.bScale\n",
"SymTP_bScale = 0.5 # If SymTP chosen\n",
"\n",
"# Step 2.c: Set the order of spatial and temporal derivatives;\n",
"# the core data type, and the CFL factor.\n",
"# RK_method choices include: Euler, \"RK2 Heun\", \"RK2 MP\", \"RK2 Ralston\", RK3, \"RK3 Heun\", \"RK3 Ralston\",\n",
"# SSPRK3, RK4, DP5, DP5alt, CK5, DP6, L6, DP8\n",
"RK_method = \"RK4\"\n",
"FD_order = 4 # Finite difference order: even numbers only, starting with 2. 12 is generally unstable\n",
"REAL = \"double\" # Best to use double here.\n",
"default_CFL_FACTOR= 0.5 # (GETS OVERWRITTEN WHEN EXECUTED.) In pure axisymmetry (symmetry_axes = 2 below) 1.0 works fine. Otherwise 0.5 or lower.\n",
"\n",
"# Step 3: Generate Runge-Kutta-based (RK-based) timestepping code.\n",
"# 3.A: Evaluate RHSs (RHS_string)\n",
"# 3.B: Apply boundary conditions (RHS_string)\n",
"import MoLtimestepping.C_Code_Generation as MoL\n",
"from MoLtimestepping.RK_Butcher_Table_Dictionary import Butcher_dict\n",
"RK_order = Butcher_dict[RK_method][1]\n",
"cmd.mkdir(os.path.join(Ccodesdir,\"MoLtimestepping/\"))\n",
"\n",
"RHS_string = \"rhs_eval(&rfmstruct, ¶ms, RK_INPUT_GFS, RK_OUTPUT_GFS);\"\n",
"\n",
"if BoundaryCondition == \"QuadraticExtrapolation\":\n",
" # Extrapolation BCs are applied to the evolved gridfunctions themselves after the MoL update\n",
" post_RHS_string = \"apply_bcs_curvilinear(¶ms, &bcstruct, NUM_EVOL_GFS, evol_gf_parity, RK_OUTPUT_GFS);\"\n",
"elif BoundaryCondition == \"Sommerfeld\":\n",
" # Sommerfeld BCs are applied to the gridfunction RHSs directly\n",
" RHS_string += \"\\n apply_bcs_sommerfeld(¶ms, xx, &bcstruct, NUM_EVOL_GFS, evol_gf_parity, RK_INPUT_GFS, RK_OUTPUT_GFS);\"\n",
" post_RHS_string = \"\"\n",
"else:\n",
" print(\"Invalid choice of boundary condition\")\n",
" sys.exit(1)\n",
"\n",
"MoL.MoL_C_Code_Generation(RK_method, RHS_string = RHS_string, post_RHS_string = post_RHS_string,\n",
" outdir = os.path.join(Ccodesdir,\"MoLtimestepping/\"))\n",
"\n",
"\n",
"# Step 4: Set the coordinate system for the numerical grid\n",
"par.set_parval_from_str(\"reference_metric::CoordSystem\",CoordSystem)\n",
"rfm.reference_metric()\n",
"\n",
"# Step 5: Set the finite differencing order to 4.\n",
"par.set_parval_from_str(\"finite_difference::FD_CENTDERIVS_ORDER\",FD_order)\n",
"\n",
"# Step 6: Copy SIMD/SIMD_intrinsics.h to $Ccodesdir/SIMD/SIMD_intrinsics.h\n",
"cmd.mkdir(os.path.join(Ccodesdir,\"SIMD\"))\n",
"shutil.copy(os.path.join(\"SIMD/\")+\"SIMD_intrinsics.h\",os.path.join(Ccodesdir,\"SIMD/\"))\n",
"# par.set_parval_from_str(\"indexedexp::symmetry_axes\",\"2\")"
]
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"source": [
"\n",
"\n",
"## Step 1.a: Output needed C code for finding the minimum proper distance between grid points, needed for [CFL](https://en.wikipedia.org/w/index.php?title=Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition&oldid=806430673)-limited timestep \\[Back to [top](#toc)\\]\n",
"$$\\label{cfl}$$\n",
"\n",
"In order for our explicit-timestepping numerical solution to Maxwell's equations to be stable, it must satisfy the [CFL](https://en.wikipedia.org/w/index.php?title=Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition&oldid=806430673) condition:\n",
"$$\n",
"\\Delta t \\le \\frac{\\min(ds_i)}{c},\n",
"$$\n",
"where $c$ is the wavespeed, and\n",
"$$ds_i = h_i \\Delta x^i$$ \n",
"is the proper distance between neighboring gridpoints in the $i$th direction (in 3D, there are 3 directions), $h_i$ is the $i$th reference metric scale factor, and $\\Delta x^i$ is the uniform grid spacing in the $i$th direction:"
]
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"source": [
"# Output the find_timestep() function to a C file.\n",
"rfm.out_timestep_func_to_file(os.path.join(Ccodesdir,\"find_timestep.h\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 2: Generate symbolic expressions and output C code for evolving Maxwell's equations \\[Back to [top](#toc)\\]\n",
"$$\\label{mw}$$\n",
"\n",
"Here we read in the symbolic expressions from the NRPy+ [InitialData](../edit/Maxwell/InitialData.py) and [Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled](../edit/Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled.py) modules to define the initial data, evolution equations, and constraint equations.\n",
"\n",
"\n",
"\n",
"## Step 2.a: Generate symbolic expressions for toroidal dipole field initial data \\[Back to [top](#toc)\\]\n",
"$$\\label{mwid}$$\n",
"\n",
"\n",
"\n",
"Here we use the NRPy+ [InitialData](../edit/Maxwell/InitialData.py) module, described in [this tutorial](Tutorial-VacuumMaxwell_InitialData.ipynb), to write initial data to the grid functions for both systems.\n",
"\n",
"We define the rescaled quantities $a^i$ and $e^i$ in terms of $A^i$ and $E^i$ in curvilinear coordinates within the NRPy+ [InitialData](../edit/Maxwell/InitialData.py) module (see [this tutorial](Tutorial-VacuumMaxwell_formulation_Curvilinear.ipynb) for more detail);\n",
"\n",
"\\begin{align}\n",
"a^i &= \\frac{A^i}{\\text{ReU}[i]},\\\\ \\\\\n",
"e^i &= \\frac{E^i}{\\text{ReU}[i]}.\n",
"\\end{align}"
]
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"name": "stdout",
"output_type": "stream",
"text": [
"Currently using System_II initial data\n"
]
}
],
"source": [
"import Maxwell.InitialData as mwid\n",
"\n",
"# Set which system to use, which are defined in Maxwell/InitialData.py\n",
"par.set_parval_from_str(\"Maxwell.InitialData::System_to_use\",\"System_II\")\n",
"\n",
"mwid.InitialData()\n",
"aidU = ixp.zerorank1()\n",
"eidU = ixp.zerorank1()\n",
"for i in range(DIM):\n",
" aidU[i] = mwid.AidU[i]/rfm.ReU[i]\n",
" eidU[i] = mwid.EidU[i]/rfm.ReU[i]\n",
"\n",
"Maxwell_ID_SymbExpressions = [\\\n",
" lhrh(lhs=\"*AU0_exact\",rhs=aidU[0]),\\\n",
" lhrh(lhs=\"*AU1_exact\",rhs=aidU[1]),\\\n",
" lhrh(lhs=\"*AU2_exact\",rhs=aidU[2]),\\\n",
" lhrh(lhs=\"*EU0_exact\",rhs=eidU[0]),\\\n",
" lhrh(lhs=\"*EU1_exact\",rhs=eidU[1]),\\\n",
" lhrh(lhs=\"*EU2_exact\",rhs=eidU[2]),\\\n",
" lhrh(lhs=\"*PSI_exact\",rhs=mwid.psi_ID),\\\n",
" lhrh(lhs=\"*GAMMA_exact\",rhs=mwid.Gamma_ID)]\n",
"\n",
"Maxwell_ID_CcodeKernel = fin.FD_outputC(\"returnstring\", Maxwell_ID_SymbExpressions)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.b: Generate symbolic expressions for evolution equations \\[Back to [top](#toc)\\]\n",
"$$\\label{mwevol}$$\n",
"\n",
"Here we use the NRPy+ [Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled](../edit/Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled.py) module, described in [this tutorial](Tutorial-VacuumMaxwell_Curvilinear_RHSs.ipynb), to ascribe the evolution equations to the grid functions."
]
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"source": [
"import Maxwell.VacuumMaxwell_Flat_Evol_Curvilinear_rescaled as rhs\n",
"\n",
"# Set which system to use, which are defined in Maxwell/InitialData.py\n",
"par.set_parval_from_str(\"Maxwell.InitialData::System_to_use\",\"System_II\")\n",
"\n",
"cmd.mkdir(os.path.join(Ccodesdir,\"rfm_files/\"))\n",
"par.set_parval_from_str(\"reference_metric::enable_rfm_precompute\",\"True\")\n",
"par.set_parval_from_str(\"reference_metric::rfm_precompute_Ccode_outdir\",os.path.join(Ccodesdir,\"rfm_files/\"))\n",
"\n",
"rhs.VacuumMaxwellRHSs_rescaled()\n",
"\n",
"Maxwell_RHSs_SymbExpressions = [\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"aU0\"),rhs=rhs.arhsU[0]),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"aU1\"),rhs=rhs.arhsU[1]),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"aU2\"),rhs=rhs.arhsU[2]),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"eU0\"),rhs=rhs.erhsU[0]),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"eU1\"),rhs=rhs.erhsU[1]),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"eU2\"),rhs=rhs.erhsU[2]),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"psi\"),rhs=rhs.psi_rhs),\\\n",
" lhrh(lhs=gri.gfaccess(\"rhs_gfs\",\"Gamma\"),rhs=rhs.Gamma_rhs)]\n",
"\n",
"par.set_parval_from_str(\"reference_metric::enable_rfm_precompute\",\"False\") # Reset to False to disable rfm_precompute.\n",
"rfm.ref_metric__hatted_quantities()\n",
"\n",
"Maxwell_RHSs_string = fin.FD_outputC(\"returnstring\",\n",
" Maxwell_RHSs_SymbExpressions,\n",
" params=\"enable_SIMD=True\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.c: Generate symbolic expressions for constraint equations \\[Back to [top](#toc)\\]\n",
"$$\\label{mwcon}$$\n",
"\n",
"We now use the NRPy+ [Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled](../edit/Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled.py) module, described in [this tutorial](Tutorial-VacuumMaxwell_Curvilinear_RHSs.ipynb), to ascribe the constraint equations."
]
},
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"source": [
"C = gri.register_gridfunctions(\"AUX\", \"C\")\n",
"G = gri.register_gridfunctions(\"AUX\", \"G\")\n",
"\n",
"Constraints_string = fin.FD_outputC(\"returnstring\",\n",
" [lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"C\"), rhs=rhs.C),\n",
" lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"G\"), rhs=rhs.G)],\n",
" params=\"outCverbose=False\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.d: Generate symbolic expressions for converting $A^i$ and $E^i$ to the Cartesian basis \\[Back to [top](#toc)\\]\n",
"$$\\label{mwcart}$$\n",
"\n",
"We now use the NRPy+ [Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled](../edit/Maxwell/VacuumMaxwell_Flat_Evol_Curvilinear_rescaled.py) module, described in [this tutorial](Tutorial-VacuumMaxwell_Curvilinear_RHSs.ipynb), to ascribe the coordinate conversion, to make our convergence tests slightly easier."
]
},
{
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"outputs": [],
"source": [
"AUCart = ixp.register_gridfunctions_for_single_rank1(\"AUX\", \"AUCart\")\n",
"EUCart = ixp.register_gridfunctions_for_single_rank1(\"AUX\", \"EUCart\")\n",
"\n",
"Cartesian_Vectors_string = fin.FD_outputC(\"returnstring\",\n",
" [lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"AUCart0\"), rhs=rhs.AU_Cart[0]),\n",
" lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"AUCart1\"), rhs=rhs.AU_Cart[1]),\n",
" lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"AUCart2\"), rhs=rhs.AU_Cart[2]),\n",
" lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"EUCart0\"), rhs=rhs.EU_Cart[0]),\n",
" lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"EUCart1\"), rhs=rhs.EU_Cart[1]),\n",
" lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"EUCart2\"), rhs=rhs.EU_Cart[2])],\n",
" params=\"outCverbose=False\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.e: Output C codes for initial data and evolution equations \\[Back to [top](#toc)\\]\n",
"$$\\label{mwccode}$$\n",
"\n",
"Next we write the C codes for the initial data and evolution equations to files, to be used later by our main C code."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Output C function exact_solution_single_point() to file MaxwellEvolCurvi_Playground_Ccodes/exact_solution_single_point.h\n",
"Output C function exact_solution_all_points() to file MaxwellEvolCurvi_Playground_Ccodes/exact_solution_all_points.h\n",
"Output C function rhs_eval() to file MaxwellEvolCurvi_Playground_Ccodes/rhs_eval.h\n"
]
}
],
"source": [
"# Step 11: Generate all needed C functions\n",
"Part_P1_body = Maxwell_ID_CcodeKernel\n",
"desc=\"Part P1: Declare the function for the exact solution at a single point. time==0 corresponds to the initial data.\"\n",
"name=\"exact_solution_single_point\"\n",
"outCfunction(\n",
" outfile = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
" params =\"const REAL xx0,const REAL xx1,const REAL xx2,const paramstruct *restrict params,\\\n",
" REAL *EU0_exact, \\\n",
" REAL *EU1_exact, \\\n",
" REAL *EU2_exact, \\\n",
" REAL *AU0_exact, \\\n",
" REAL *AU1_exact, \\\n",
" REAL *AU2_exact, \\\n",
" REAL *PSI_exact,\\\n",
" REAL *GAMMA_exact\",\n",
" body = Part_P1_body,\n",
" loopopts = \"\")\n",
"\n",
"desc=\"Part P2: Declare the function for the exact solution at all points. time==0 corresponds to the initial data.\"\n",
"name=\"exact_solution_all_points\"\n",
"outCfunction(\n",
" outfile = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
" params =\"const paramstruct *restrict params,REAL *restrict xx[3], REAL *restrict in_gfs\",\n",
" body =\"\"\"\n",
"REAL xx0 = xx[0][i0]; REAL xx1 = xx[1][i1]; REAL xx2 = xx[2][i2];\n",
"exact_solution_single_point(xx0,xx1,xx2,params,&in_gfs[IDX4S(EU0GF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(EU1GF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(EU2GF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(AU0GF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(AU1GF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(AU2GF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(PSIGF,i0,i1,i2)],\n",
" &in_gfs[IDX4S(GAMMAGF,i0,i1,i2)]);\"\"\",\n",
" loopopts = \"AllPoints\")\n",
"\n",
"Part_P3_body = Maxwell_RHSs_string\n",
"\n",
"desc=\"Part P3: Declare the function to evaluate the RHSs of Maxwell's equations\"\n",
"name=\"rhs_eval\"\n",
"outCfunction(\n",
" outfile = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
" params =\"\"\"rfm_struct *restrict rfmstruct,const paramstruct *restrict params,\n",
" const REAL *restrict in_gfs, REAL *restrict rhs_gfs\"\"\",\n",
" body =Part_P3_body,\n",
" loopopts = \"InteriorPoints,enable_SIMD,enable_rfm_precompute\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.f: Output C code for constraint equations \\[Back to [top](#toc)\\]\n",
"$$\\label{mwccode_con}$$\n",
"\n",
"Finally output the C code for evaluating the divergence constraint, described in [this tutorial](Tutorial-VacuumMaxwell_Curvilinear_RHSs.ipynb). In the absence of numerical error, this constraint should evaluate to zero, but due to numerical (typically truncation and roundoff) error it does not. We will therefore measure the divergence constraint violation to gauge the accuracy of our simulation, and ultimately determine whether errors are dominated by numerical finite differencing (truncation) error as expected. Specifically, we take the L2 norm of the constraint violation, via\n",
"\n",
"\\begin{align}\n",
" \\lVert C \\rVert^2 &= \\frac{\\int C^2 d\\mathcal{V}}{\\int d\\mathcal{V}}.\n",
"\\end{align}\n",
"\n",
"Numerically approximating this integral, in spherical coordinates for example, then gives us\n",
"\n",
"\\begin{align}\n",
" \\lVert C \\rVert^2 &= \\frac{\\sum C^2 r^2 \\sin^2 (\\theta) dr d\\theta d\\phi}{\\sum r^2 \\sin^2 (\\theta) dr d\\theta d\\phi}, \\\\ \\\\\n",
" &= \\frac{\\sum C^2 r^2 \\sin^2 (\\theta)}{\\sum r^2 \\sin^2 (\\theta) } , \\\\ \\\\\n",
" &= \\frac{\\sum C^2 \\ \\sqrt{\\text{det} \\ \\hat{\\gamma}}}{\\sum \\sqrt{\\text{det} \\ \\hat{\\gamma}}},\n",
"\\end{align}\n",
"\n",
"where $\\hat{\\gamma}$ is the reference metric. Thus, along with the C code to calculate the constraints, we also print out the code required to evaluate $\\sqrt{\\text{det} \\ \\hat{\\gamma}}$ at any given point."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Output C function Constraints() to file MaxwellEvolCurvi_Playground_Ccodes/Constraints.h\n",
"Output C function diagnostic_integrand() to file MaxwellEvolCurvi_Playground_Ccodes/diagnostic_integrand.h\n"
]
}
],
"source": [
"# Set up the C function for the calculating the constraints\n",
"Part_P4_body = Constraints_string\n",
"desc=\"Evaluate the constraints\"\n",
"name=\"Constraints\"\n",
"outCfunction(\n",
" outfile = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
" params = \"\"\"rfm_struct *restrict rfmstruct,const paramstruct *restrict params,\n",
" REAL *restrict in_gfs, REAL *restrict aux_gfs\"\"\",\n",
" body = Part_P4_body,\n",
" loopopts = \"InteriorPoints,enable_rfm_precompute\")\n",
"\n",
"# intgrand to be used to calculate the L2 norm of the constraint\n",
"diagnostic_integrand_body = outputC(rfm.detgammahat,\"*detg\",filename='returnstring',\n",
" params=\"includebraces=False\")\n",
"desc=\"Evaluate the volume element at a specific point\"\n",
"name=\"diagnostic_integrand\"\n",
"outCfunction(\n",
" outfile = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
" params =\"const REAL xx0,const REAL xx1,const REAL xx2,const paramstruct *restrict params, REAL *restrict detg\",\n",
" body = diagnostic_integrand_body,\n",
" loopopts = \"\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.g: Output C code for converting $A^i$ and $E^i$ to Cartesian coordinates \\[Back to [top](#toc)\\]\n",
"$$\\label{mwccode_cart}$$\n",
"\n",
"Here we write the C code for the coordinate transformation to Cartesian coordinates."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:48.819376Z",
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"shell.execute_reply": "2021-06-15T11:39:48.821089Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Output C function Cartesian_basis() to file MaxwellEvolCurvi_Playground_Ccodes/Cartesian_basis.h\n"
]
}
],
"source": [
"desc=\"Convert EU and AU to Cartesian basis\"\n",
"name=\"Cartesian_basis\"\n",
"outCfunction(\n",
" outfile = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
" params = \"\"\"rfm_struct *restrict rfmstruct,const paramstruct *restrict params, REAL *restrict xx[3],\n",
" REAL *restrict in_gfs, REAL *restrict aux_gfs\"\"\",\n",
" body = \"REAL xx0 = xx[0][i0]; REAL xx1 = xx[1][i1]; REAL xx2 = xx[2][i2];\\n\"+Cartesian_Vectors_string,\n",
" loopopts = \"AllPoints, enable_rfm_precompute\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.h: Output C code for printing 2D data \\[Back to [top](#toc)\\]\n",
"$$\\label{mwccode_xzloop}$$\n",
"\n",
"Here we output the neccesary C code to print out a 2D slice of the data in the xz-plane, using the `xz_loop` macro"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
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"shell.execute_reply": "2021-06-15T11:39:48.826221Z"
}
},
"outputs": [],
"source": [
"def xz_loop(CoordSystem):\n",
" ret = \"\"\"// xz-plane output for \"\"\" + CoordSystem + r\"\"\" coordinates:\n",
"#define LOOP_XZ_PLANE(ii, jj, kk) \\\n",
"\"\"\"\n",
" if \"Spherical\" in CoordSystem or \"SymTP\" in CoordSystem:\n",
" ret += r\"\"\"for (int i2 = 0; i2 < Nxx_plus_2NGHOSTS2; i2++) \\\n",
" if(i2 == NGHOSTS || i2 == Nxx_plus_2NGHOSTS2/2) \\\n",
" for (int i1 = 0; i1 < Nxx_plus_2NGHOSTS1; i1++) \\\n",
" for (int i0 = 0; i0 < Nxx_plus_2NGHOSTS0; i0++)\n",
"\"\"\"\n",
" elif \"Cylindrical\" in CoordSystem:\n",
" ret += r\"\"\"for (int i2 = 0; i2 < Nxx_plus_2NGHOSTS2; i2++) \\\n",
" for (int i1 = 0; i1 < Nxx_plus_2NGHOSTS1; i1++) \\\n",
" if(i1 == NGHOSTS || i1 == Nxx_plus_2NGHOSTS1/2) \\\n",
" for (int i0 = 0; i0 < Nxx_plus_2NGHOSTS0; i0++)\n",
"\"\"\"\n",
" elif \"Cartesian\" in CoordSystem:\n",
" ret += r\"\"\"for (int i2 = 0; i2 < Nxx_plus_2NGHOSTS2; i2++) \\\n",
" for (int i1 = Nxx_plus_2NGHOSTS1/2; i1 < Nxx_plus_2NGHOSTS1/2+1; i1++) \\\n",
" for (int i0 = 0; i0 < Nxx_plus_2NGHOSTS0; i0++)\n",
"\"\"\"\n",
" return ret\n",
"\n",
"with open(os.path.join(Ccodesdir,\"xz_loop.h\"),\"w\") as file:\n",
" file.write(xz_loop(CoordSystem))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 2.i: Output C codes needed for declaring and setting Cparameters; also set `free_parameters.h` \\[Back to [top](#toc)\\]\n",
"$$\\label{cparams_rfm_and_domainsize}$$\n",
"\n",
"Based on declared NRPy+ Cparameters, first we generate `declare_Cparameters_struct.h`, `set_Cparameters_default.h`, and `set_Cparameters[-SIMD].h`.\n",
"\n",
"Then we output `free_parameters.h`, which sets initial data parameters, as well as grid domain & reference metric parameters, applying `domain_size` and `sinh_width`/`SymTP_bScale` (if applicable) as set above"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
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"outputs": [],
"source": [
"# Generate declare_Cparameters_struct.h, set_Cparameters_default.h, and set_Cparameters[-SIMD].h\n",
"par.generate_Cparameters_Ccodes(os.path.join(Ccodesdir))\n",
"\n",
"# Set free_parameters.h\n",
"with open(os.path.join(Ccodesdir,\"free_parameters.h\"),\"w\") as file:\n",
" file.write(\"\"\"\n",
"// Set free-parameter values.\n",
"params.time = 0.0; // Initial simulation time time corresponds to exact solution at time=0.\n",
"params.amp = 1.0;\n",
"params.lam = 1.0;\n",
"params.wavespeed = 1.0;\\n\"\"\")\n",
"\n",
"# Append to $Ccodesdir/free_parameters.h reference metric parameters based on generic\n",
"# domain_size,sinh_width,sinhv2_const_dr,SymTP_bScale,\n",
"# parameters set above.\n",
"rfm.out_default_free_parameters_for_rfm(os.path.join(Ccodesdir,\"free_parameters.h\"),\n",
" domain_size,sinh_width,sinhv2_const_dr,SymTP_bScale)\n",
"\n",
"# Generate set_Nxx_dxx_invdx_params__and__xx.h:\n",
"rfm.set_Nxx_dxx_invdx_params__and__xx_h(Ccodesdir, grid_centering=\"cell\")\n",
"\n",
"# Generate xx_to_Cart.h, which contains xx_to_Cart() for\n",
"# (the mapping from xx->Cartesian) for the chosen CoordSystem:\n",
"rfm.xx_to_Cart_h(\"xx_to_Cart\",\"./set_Cparameters.h\",os.path.join(Ccodesdir,\"xx_to_Cart.h\"))\n",
"\n",
"# Step 3.d.v: Generate declare_Cparameters_struct.h, set_Cparameters_default.h, and set_Cparameters[-SIMD].h\n",
"par.generate_Cparameters_Ccodes(os.path.join(Ccodesdir))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 3: Set up Sommerfeld boundary condition for Cartesian coordinate system \\[Back to [top](#toc)\\]\n",
"$$\\label{bc_functs}$$\n",
"\n",
"Next we output the C code necessary to implement the Sommerfeld boundary condition in Cartesian coordinates, [as documented in the corresponding NRPy+ tutorial notebook](Tutorial-SommerfeldBoundaryCondition.ipynb)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:49.132524Z",
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wrote to file \"MaxwellEvolCurvi_Playground_Ccodes/boundary_conditions/parity_conditions_symbolic_dot_products.h\"\n",
"Evolved parity: ( Gamma:0, aU0:1, aU1:2, aU2:3, eU0:1, eU1:2, eU2:3, psi:0\n",
" )\n",
"Auxiliary parity: ( AUCart0:1, AUCart1:2, AUCart2:3, C:0, EUCart0:1,\n",
" EUCart1:2, EUCart2:3, G:0 )\n",
"\n",
"Wrote to file \"MaxwellEvolCurvi_Playground_Ccodes/boundary_conditions/EigenCoord_Cart_to_xx.h\"\n",
"\n",
"Successfully generated Sommerfeld boundary condition C code\n"
]
}
],
"source": [
"import CurviBoundaryConditions.CurviBoundaryConditions as cbcs\n",
"cbcs.Set_up_CurviBoundaryConditions(os.path.join(Ccodesdir,\"boundary_conditions/\"),\n",
" Cparamspath=os.path.join(\"../\"),\n",
" BoundaryCondition=BoundaryCondition)\n",
"\n",
"if BoundaryCondition == \"Sommerfeld\":\n",
" bcs = cbcs.sommerfeld_boundary_condition_class(fd_order=4,\n",
" vars_radial_falloff_power_default=3,\n",
" vars_speed_default=1.,\n",
" vars_at_inf_default=0.)\n",
" bcs.write_sommerfeld_file(Ccodesdir)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 4: `Maxwell_Playground.c`: The Main C Code \\[Back to [top](#toc)\\]\n",
"$$\\label{mainc}$$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:49.916913Z",
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"outputs": [],
"source": [
"# Part P0: Define REAL, set the number of ghost cells NGHOSTS (from NRPy+'s FD_CENTDERIVS_ORDER),\n",
"# and set the CFL_FACTOR (which can be overwritten at the command line)\n",
"\n",
"with open(os.path.join(Ccodesdir,\"Maxwell_Playground_REAL__NGHOSTS__CFL_FACTOR.h\"), \"w\") as file:\n",
" file.write(\"\"\"\n",
"// Part P0.a: Set the number of ghost cells, from NRPy+'s FD_CENTDERIVS_ORDER\n",
"#define NGHOSTS \"\"\"+str(int(FD_order/2)+1)+\"\"\"\n",
"// Part P0.b: Set the numerical precision (REAL) to double, ensuring all floating point\n",
"// numbers are stored to at least ~16 significant digits\n",
"#define REAL \"\"\"+REAL+\"\"\"\n",
"// Part P0.c: Set the CFL Factor. Can be overwritten at command line.\n",
"REAL CFL_FACTOR = \"\"\"+str(default_CFL_FACTOR)+\";\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"execution": {
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}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Writing MaxwellEvolCurvi_Playground_Ccodes//Maxwell_Playground.c\n"
]
}
],
"source": [
"%%writefile $Ccodesdir/Maxwell_Playground.c\n",
"\n",
"// Step P0: Define REAL and NGHOSTS; and declare CFL_FACTOR. This header is generated in NRPy+.\n",
"#include \"Maxwell_Playground_REAL__NGHOSTS__CFL_FACTOR.h\"\n",
"\n",
"#include \"rfm_files/rfm_struct__declare.h\"\n",
"\n",
"#include \"declare_Cparameters_struct.h\"\n",
"\n",
"// All SIMD intrinsics used in SIMD-enabled C code loops are defined here:\n",
"#include \"SIMD/SIMD_intrinsics.h\"\n",
"\n",
"// Step P1: Import needed header files\n",
"#include \"stdio.h\"\n",
"#include \"stdlib.h\"\n",
"#include \"math.h\"\n",
"#include \"time.h\"\n",
"#include \"stdint.h\" // Needed for Windows GCC 6.x compatibility\n",
"#ifndef M_PI\n",
"#define M_PI 3.141592653589793238462643383279502884L\n",
"#endif\n",
"#ifndef M_SQRT1_2\n",
"#define M_SQRT1_2 0.707106781186547524400844362104849039L\n",
"#endif\n",
"\n",
"// Step P2: Declare the IDX4S(gf,i,j,k) macro, which enables us to store 4-dimensions of\n",
"// data in a 1D array. In this case, consecutive values of \"i\"\n",
"// (all other indices held to a fixed value) are consecutive in memory, where\n",
"// consecutive values of \"j\" (fixing all other indices) are separated by\n",
"// Nxx_plus_2NGHOSTS0 elements in memory. Similarly, consecutive values of\n",
"// \"k\" are separated by Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1 in memory, etc.\n",
"#define IDX4S(g,i,j,k) \\\n",
"( (i) + Nxx_plus_2NGHOSTS0 * ( (j) + Nxx_plus_2NGHOSTS1 * ( (k) + Nxx_plus_2NGHOSTS2 * (g) ) ) )\n",
"#define IDX4ptS(g,idx) ( (idx) + (Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2) * (g) )\n",
"#define IDX3S(i,j,k) ( (i) + Nxx_plus_2NGHOSTS0 * ( (j) + Nxx_plus_2NGHOSTS1 * ( (k) ) ) )\n",
"#define LOOP_REGION(i0min,i0max, i1min,i1max, i2min,i2max) \\\n",
" for(int i2=i2min;i2Cartesian via\n",
"// {xx[0][i0],xx[1][i1],xx[2][i2]}->{xCart[0],xCart[1],xCart[2]}\n",
"\n",
"#include \"xx_to_Cart.h\"\n",
"// main() function:\n",
"// Step 0: Read command-line input, set up grid structure, allocate memory for gridfunctions, set up coordinates\n",
"// Step 1: Set up initial data to an exact solution\n",
"// Step 2: Start the timer, for keeping track of how fast the simulation is progressing.\n",
"// Step 3: Integrate the initial data forward in time using the chosen RK-like Method of\n",
"// Lines timestepping algorithm, and output periodic simulation diagnostics\n",
"// Step 3.a: Output 2D data file periodically, for visualization\n",
"// Step 3.b: Step forward one timestep (t -> t+dt) in time using\n",
"// chosen RK-like MoL timestepping algorithm\n",
"// Step 3.c: If t=t_final, output x and y components of evolution variables and the\n",
"// constraint violation to 2D data file\n",
"// Step 3.d: Progress indicator printing to stderr\n",
"// Step 4: Free all allocated memory\n",
"int main(int argc, const char *argv[]) {\n",
" paramstruct params;\n",
"#include \"set_Cparameters_default.h\"\n",
"\n",
" // Step 0a: Read command-line input, error out if nonconformant\n",
" if((argc != 5 && argc != 6) || atoi(argv[1]) < NGHOSTS || atoi(argv[2]) < NGHOSTS || atoi(argv[3]) < 2 /* FIXME; allow for axisymmetric sims */) {\n",
" fprintf(stderr,\"Error: Expected three command-line arguments: ./Maxwell_Playground Nx0 Nx1 Nx2,\\n\");\n",
" fprintf(stderr,\"where Nx[0,1,2] is the number of grid points in the 0, 1, and 2 directions.\\n\");\n",
" fprintf(stderr,\"Nx[] MUST BE larger than NGHOSTS (= %d)\\n\",NGHOSTS);\n",
" exit(1);\n",
" }\n",
" if(argc == 5) {\n",
" CFL_FACTOR = strtod(argv[5],NULL);\n",
" if(CFL_FACTOR > 0.5 && atoi(argv[3])!=2) {\n",
" fprintf(stderr,\"WARNING: CFL_FACTOR was set to %e, which is > 0.5.\\n\",CFL_FACTOR);\n",
" fprintf(stderr,\" This will generally only be stable if the simulation is purely axisymmetric\\n\");\n",
" fprintf(stderr,\" However, Nx2 was set to %d>2, which implies a non-axisymmetric simulation\\n\",atoi(argv[3]));\n",
" }\n",
" }\n",
" // Step 0b: Set up numerical grid structure, first in space...\n",
" const int Nxx[3] = { atoi(argv[1]), atoi(argv[2]), atoi(argv[3]) };\n",
" if(Nxx[0]%2 != 0 || Nxx[1]%2 != 0 || Nxx[2]%2 != 0) {\n",
" fprintf(stderr,\"Error: Cannot guarantee a proper cell-centered grid if number of grid cells not set to even number.\\n\");\n",
" fprintf(stderr,\" For example, in case of angular directions, proper symmetry zones will not exist.\\n\");\n",
" exit(1);\n",
" }\n",
"\n",
" // Step 0c: Set free parameters, overwriting Cparameters defaults\n",
" // by hand or with command-line input, as desired.\n",
"#include \"free_parameters.h\"\n",
"\n",
" // Step 0d: Uniform coordinate grids are stored to *xx[3]\n",
" REAL *xx[3];\n",
" // Step 0d.i: Set bcstruct\n",
" bc_struct bcstruct;\n",
" {\n",
" int EigenCoord = 1;\n",
" // Step 0d.ii: Call set_Nxx_dxx_invdx_params__and__xx(), which sets\n",
" // params Nxx,Nxx_plus_2NGHOSTS,dxx,invdx, and xx[] for the\n",
" // chosen Eigen-CoordSystem.\n",
" set_Nxx_dxx_invdx_params__and__xx(EigenCoord, Nxx, ¶ms, xx);\n",
" // Step 0d.iii: Set Nxx_plus_2NGHOSTS_tot\n",
"#include \"set_Cparameters-nopointer.h\"\n",
" const int Nxx_plus_2NGHOSTS_tot = Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2;\n",
" // Step 0e: Find ghostzone mappings; set up bcstruct\n",
"#include \"boundary_conditions/driver_bcstruct.h\"\n",
" // Step 0e.i: Free allocated space for xx[][] array\n",
" for(int i=0;i<3;i++) free(xx[i]);\n",
" }\n",
"\n",
" // Step 0f: Call set_Nxx_dxx_invdx_params__and__xx(), which sets\n",
" // params Nxx,Nxx_plus_2NGHOSTS,dxx,invdx, and xx[] for the\n",
" // chosen (non-Eigen) CoordSystem.\n",
" int EigenCoord = 0;\n",
" set_Nxx_dxx_invdx_params__and__xx(EigenCoord, Nxx, ¶ms, xx);\n",
"\n",
" // Step 0g: Set all C parameters \"blah\" for params.blah, including\n",
" // Nxx_plus_2NGHOSTS0 = params.Nxx_plus_2NGHOSTS0, etc.\n",
"#include \"set_Cparameters-nopointer.h\"\n",
" const int Nxx_plus_2NGHOSTS_tot = Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2;\n",
"\n",
" // Step 0h: Time coordinate parameters\n",
" const REAL t_final = strtod(argv[4],NULL);\n",
"\n",
" // Step 0i: Set timestep based on smallest proper distance between gridpoints and CFL factor\n",
" REAL dt = find_timestep(¶ms, xx);\n",
" //fprintf(stderr,\"# Timestep set to = %e\\n\",(double)dt);\n",
" int N_final = (int)(t_final / dt + 0.5); // The number of points in time.\n",
" // Add 0.5 to account for C rounding down\n",
" // typecasts to integers.\n",
" int output_every_N = (int)((REAL)N_final/800.0);\n",
" if(output_every_N == 0) output_every_N = 1;\n",
"\n",
" // Step 0j: Error out if the number of auxiliary gridfunctions outnumber evolved gridfunctions.\n",
" // This is a limitation of the RK method. You are always welcome to declare & allocate\n",
" // additional gridfunctions by hand.\n",
" if(NUM_AUX_GFS > NUM_EVOL_GFS) {\n",
" fprintf(stderr,\"Error: NUM_AUX_GFS > NUM_EVOL_GFS. Either reduce the number of auxiliary gridfunctions,\\n\");\n",
" fprintf(stderr,\" or allocate (malloc) by hand storage for *diagnostic_output_gfs. \\n\");\n",
" exit(1);\n",
" }\n",
"\n",
" // Step 0k: Allocate memory for gridfunctions\n",
"#include \"MoLtimestepping/RK_Allocate_Memory.h\"\n",
" REAL *restrict y_0_gfs = (REAL *)malloc(sizeof(REAL) * NUM_EVOL_GFS * Nxx_plus_2NGHOSTS_tot);\n",
" REAL *restrict diagnostic_output_gfs_0 = (REAL *)malloc(sizeof(REAL) * NUM_AUX_GFS * Nxx_plus_2NGHOSTS_tot);\n",
"\n",
" // Step 0l: Set up precomputed reference metric arrays\n",
" // Step 0l.i: Allocate space for precomputed reference metric arrays.\n",
"#include \"rfm_files/rfm_struct__malloc.h\"\n",
"\n",
" // Step 0l.ii: Define precomputed reference metric arrays.\n",
" {\n",
" #include \"set_Cparameters-nopointer.h\"\n",
" #include \"rfm_files/rfm_struct__define.h\"\n",
" }\n",
"\n",
" LOOP_ALL_GFS_GPS(i) {\n",
" y_n_gfs[i] = 0.0/0.0;\n",
"}\n",
"\n",
" // Step 1: Set up initial data to be exact solution at time=0:\n",
" params.time = 0.0;\n",
" exact_solution_all_points(¶ms, xx, y_n_gfs);\n",
"\n",
" // Step 2: Start the timer, for keeping track of how fast the simulation is progressing.\n",
"#ifdef __linux__ // Use high-precision timer in Linux.\n",
" struct timespec start, end;\n",
" clock_gettime(CLOCK_REALTIME, &start);\n",
"#else // Resort to low-resolution, standards-compliant timer in non-Linux OSs\n",
" // http://www.cplusplus.com/reference/ctime/time/\n",
" time_t start_timer,end_timer;\n",
" time(&start_timer); // Resolution of one second...\n",
"#endif\n",
"\n",
" // Step 3: Integrate the initial data forward in time using the chosen RK-like Method of\n",
" // Lines timestepping algorithm, and output periodic simulation diagnostics\n",
" for(int n=0;n<=N_final+1;n++) { // Main loop to progress forward in time.\n",
"\n",
" // At each timestep, set Constraints to NaN in the grid interior\n",
" LOOP_REGION(NGHOSTS,NGHOSTS+Nxx0,\n",
" NGHOSTS,NGHOSTS+Nxx1,\n",
" NGHOSTS,NGHOSTS+Nxx2) {\n",
" const int idx = IDX3S(i0,i1,i2);\n",
" diagnostic_output_gfs[IDX4ptS(CGF,idx)] = 0.0/0.0;\n",
" }\n",
"\n",
" // Step 3.a: Output 2D data file periodically, for visualization\n",
" params.time = ((REAL)n)*dt;\n",
" // Evaluate Divergence constraint violation\n",
" Constraints(&rfmstruct, ¶ms, y_n_gfs, diagnostic_output_gfs);\n",
" // log_L2_Norm = log10( sqrt[Integral( [numerical - exact]^2 * dV)] )\n",
" REAL L2Norm_sum_C = 0.;\n",
" int sum = 0;\n",
" LOOP_REGION(NGHOSTS,NGHOSTS+Nxx0,\n",
" NGHOSTS,NGHOSTS+Nxx1,\n",
" NGHOSTS,NGHOSTS+Nxx2) {\n",
" const int idx = IDX3S(i0,i1,i2);\n",
" double C = (double)diagnostic_output_gfs[IDX4ptS(CGF,idx)];\n",
" REAL xx0 = xx[0][i0];\n",
" REAL xx1 = xx[1][i1];\n",
" REAL xx2 = xx[2][i2];\n",
" REAL detghat; diagnostic_integrand(xx0, xx1, xx2, ¶ms, &detghat);\n",
" L2Norm_sum_C += C*C*sqrt(detghat);\n",
" sum = sum + sqrt(detghat);\n",
" }\n",
" REAL L2Norm_C = sqrt(L2Norm_sum_C/(sum));\n",
" printf(\"%e %.15e\\n\",params.time, L2Norm_C);\n",
"\n",
" // Step 3.a: Output 2D data file periodically, for visualization\n",
" if(n%20 == 0) {\n",
" exact_solution_all_points(¶ms, xx, y_0_gfs);\n",
" Cartesian_basis(&rfmstruct, ¶ms, xx, y_n_gfs, diagnostic_output_gfs);\n",
" Cartesian_basis(&rfmstruct, ¶ms, xx, y_0_gfs, diagnostic_output_gfs_0);\n",
" char filename[100];\n",
" sprintf(filename,\"out%d-%08d.txt\",Nxx[0],n);\n",
" FILE *out2D = fopen(filename, \"w\");\n",
" LOOP_XZ_PLANE(ii, jj, kk){\n",
" REAL xCart[3];\n",
" xx_to_Cart(¶ms,xx,i0,i1,i2,xCart);\n",
" int idx = IDX3S(i0,i1,i2);\n",
" REAL Ex_num = (double)diagnostic_output_gfs[IDX4ptS(EUCART0GF,idx)];\n",
" REAL Ey_num = (double)diagnostic_output_gfs[IDX4ptS(EUCART1GF,idx)];\n",
" REAL Ax_num = (double)diagnostic_output_gfs[IDX4ptS(AUCART0GF,idx)];\n",
" REAL Ay_num = (double)diagnostic_output_gfs[IDX4ptS(AUCART1GF,idx)];\n",
" double C = (double)diagnostic_output_gfs[IDX4ptS(CGF,idx)];\n",
"\n",
" fprintf(out2D,\"%e %e %e %.15e %.15e %.15e %.15e %.15e\\n\", params.time,\n",
" xCart[0],xCart[2], Ex_num, Ey_num, Ax_num, Ay_num, C);\n",
" }\n",
" fclose(out2D);\n",
" }\n",
"\n",
" if(n==N_final-1) {\n",
" exact_solution_all_points(¶ms, xx, y_0_gfs);\n",
" Cartesian_basis(&rfmstruct, ¶ms, xx, y_n_gfs, diagnostic_output_gfs);\n",
" Cartesian_basis(&rfmstruct, ¶ms, xx, y_0_gfs, diagnostic_output_gfs_0);\n",
" char filename[100];\n",
" sprintf(filename,\"out%d.txt\",Nxx[0]);\n",
" FILE *out2D = fopen(filename, \"w\");\n",
" LOOP_XZ_PLANE(ii, jj, kk){\n",
" REAL xCart[3];\n",
" xx_to_Cart(¶ms,xx,i0,i1,i2,xCart);\n",
" int idx = IDX3S(i0,i1,i2);\n",
" REAL Ex_num = (double)diagnostic_output_gfs[IDX4ptS(EUCART0GF,idx)];\n",
" REAL Ey_num = (double)diagnostic_output_gfs[IDX4ptS(EUCART1GF,idx)];\n",
"\n",
" REAL Ax_num = (double)diagnostic_output_gfs[IDX4ptS(AUCART0GF,idx)];\n",
" REAL Ay_num = (double)diagnostic_output_gfs[IDX4ptS(AUCART1GF,idx)];\n",
"\n",
" REAL Ex_exact = (double)diagnostic_output_gfs_0[IDX4ptS(EUCART0GF,idx)];\n",
" REAL Ey_exact = (double)diagnostic_output_gfs_0[IDX4ptS(EUCART1GF,idx)];\n",
"\n",
" REAL Ax_exact = (double)diagnostic_output_gfs_0[IDX4ptS(AUCART0GF,idx)];\n",
" REAL Ay_exact = (double)diagnostic_output_gfs_0[IDX4ptS(AUCART1GF,idx)];\n",
"\n",
" REAL Ex__E_rel = log10(fabs(Ex_num - Ex_exact));\n",
" REAL Ey__E_rel = log10(fabs(Ey_num - Ey_exact));\n",
" REAL Ax__E_rel = log10(fabs(Ax_num - Ax_exact));\n",
" REAL Ay__E_rel = log10(fabs(Ay_num - Ay_exact));\n",
"\n",
" fprintf(out2D,\"%e %e %.15e %.15e %.15e %.15e\\n\",xCart[0],xCart[2],\n",
" Ex__E_rel, Ey__E_rel, Ax__E_rel, Ay__E_rel);\n",
" }\n",
" fclose(out2D);\n",
" }\n",
" // Step 3.b: Step forward one timestep (t -> t+dt) in time using\n",
" // chosen RK-like MoL timestepping algorithm\n",
"#include \"MoLtimestepping/RK_MoL.h\"\n",
"\n",
"\n",
" // Step 3.d: Progress indicator printing to stderr\n",
"\n",
" // Step 3.d.i: Measure average time per iteration\n",
"#ifdef __linux__ // Use high-precision timer in Linux.\n",
" clock_gettime(CLOCK_REALTIME, &end);\n",
" const long long unsigned int time_in_ns = 1000000000L * (end.tv_sec - start.tv_sec) + end.tv_nsec - start.tv_nsec;\n",
"#else // Resort to low-resolution, standards-compliant timer in non-Linux OSs\n",
" time(&end_timer); // Resolution of one second...\n",
" REAL time_in_ns = difftime(end_timer,start_timer)*1.0e9+0.5; // Round up to avoid divide-by-zero.\n",
"#endif\n",
" const REAL s_per_iteration_avg = ((REAL)time_in_ns / (REAL)n) / 1.0e9;\n",
"\n",
" const int iterations_remaining = N_final - n;\n",
" const REAL time_remaining_in_mins = s_per_iteration_avg * (REAL)iterations_remaining / 60.0;\n",
"\n",
" const REAL num_RHS_pt_evals = (REAL)(Nxx[0]*Nxx[1]*Nxx[2]) * 4.0 * (REAL)n; // 4 RHS evals per gridpoint for RK4\n",
" const REAL RHS_pt_evals_per_sec = num_RHS_pt_evals / ((REAL)time_in_ns / 1.0e9);\n",
"\n",
" // Step 3.d.ii: Output simulation progress to stderr\n",
" if(n % 10 == 0) {\n",
" fprintf(stderr,\"%c[2K\", 27); // Clear the line\n",
" fprintf(stderr,\"It: %d t=%.2f dt=%.2e | %.1f%%; ETA %.0f s | t/h %.2f | gp/s %.2e\\r\", // \\r is carriage return, move cursor to the beginning of the line\n",
" n, n * (double)dt, (double)dt, (double)(100.0 * (REAL)n / (REAL)N_final),\n",
" (double)time_remaining_in_mins*60, (double)(dt * 3600.0 / s_per_iteration_avg), (double)RHS_pt_evals_per_sec);\n",
" fflush(stderr); // Flush the stderr buffer\n",
" } // End progress indicator if(n % 10 == 0)\n",
"\n",
" } // End main loop to progress forward in time.\n",
" fprintf(stderr,\"\\n\"); // Clear the final line of output from progress indicator.\n",
"\n",
" // Step 4: Free all allocated memory\n",
"#include \"rfm_files/rfm_struct__freemem.h\"\n",
"#include \"boundary_conditions/bcstruct_freemem.h\"\n",
"#include \"MoLtimestepping/RK_Free_Memory.h\"\n",
" free(y_0_gfs);\n",
" free(diagnostic_output_gfs_0);\n",
" for(int i=0;i<3;i++) free(xx[i]);\n",
"\n",
" return 0;\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 5: Compile generated C codes & perform simulation of the propagating toriodal electromagnetic field \\[Back to [top](#toc)\\]\n",
"$$\\label{compileexec}$$\n",
"\n",
"To aid in the cross-platform-compatible (with Windows, MacOS, & Linux) compilation and execution, we make use of `cmdline_helper` [(**Tutorial**)](Tutorial-cmdline_helper.ipynb)."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:49.930854Z",
"iopub.status.busy": "2021-06-15T11:39:49.930432Z",
"iopub.status.idle": "2021-06-15T11:39:51.151759Z",
"shell.execute_reply": "2021-06-15T11:39:51.152253Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Compiling executable...\n",
"(EXEC): Executing `gcc -std=gnu99 -Ofast -fopenmp -march=native -funroll-loops MaxwellEvolCurvi_Playground_Ccodes/Maxwell_Playground.c -o MaxwellEvolCurvi_Playground_Ccodes/output/Maxwell_Playground -lm`...\n",
"(BENCH): Finished executing in 1.2078261375427246 seconds.\n",
"Finished compilation.\n"
]
}
],
"source": [
"import cmdline_helper as cmd\n",
"CFL_FACTOR=0.5\n",
"cmd.C_compile(os.path.join(Ccodesdir,\"Maxwell_Playground.c\"),\n",
" os.path.join(outdir,\"Maxwell_Playground\"),compile_mode=\"optimized\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:51.155796Z",
"iopub.status.busy": "2021-06-15T11:39:51.154938Z",
"iopub.status.idle": "2021-06-15T11:39:51.157008Z",
"shell.execute_reply": "2021-06-15T11:39:51.156413Z"
}
},
"outputs": [],
"source": [
"# Change to output directory\n",
"os.chdir(outdir)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:51.160600Z",
"iopub.status.busy": "2021-06-15T11:39:51.159436Z",
"iopub.status.idle": "2021-06-15T11:39:51.175079Z",
"shell.execute_reply": "2021-06-15T11:39:51.174729Z"
}
},
"outputs": [],
"source": [
"# Clean up existing output files\n",
"cmd.delete_existing_files(\"out*.txt\")\n",
"cmd.delete_existing_files(\"out*.png\")\n",
"cmd.delete_existing_files(\"out-*resolution.txt\")"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:51.181804Z",
"iopub.status.busy": "2021-06-15T11:39:51.181185Z",
"iopub.status.idle": "2021-06-15T11:39:55.631192Z",
"shell.execute_reply": "2021-06-15T11:39:55.631541Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(EXEC): Executing `taskset -c 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 ./Maxwell_Playground 50 4 100 5.0 0.5`...\n",
"\u001b[2KIt: 150 t=4.87 dt=3.25e-02 | 97.4%; ETA 0 s | t/h 17221.08 | gp/s 1.18e+07\n",
"(BENCH): Finished executing in 1.2078168392181396 seconds.\n",
"(EXEC): Executing `taskset -c 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 ./Maxwell_Playground 80 4 160 5.0 0.5`...\n",
"\u001b[2KIt: 240 t=4.87 dt=2.03e-02 | 97.6%; ETA 0 s | t/h 5779.42 | gp/s 1.62e+07\n",
"(BENCH): Finished executing in 3.213651418685913 seconds.\n"
]
}
],
"source": [
"# Set tme to end simulation\n",
"t_final = str(0.5*domain_size) + ' '\n",
"\n",
"# Run executables\n",
"if 'Spherical' in CoordSystem or 'SymTP' in CoordSystem:\n",
" cmd.Execute(\"Maxwell_Playground\", \"64 48 4 \"+t_final+str(CFL_FACTOR), \"out-lowresolution.txt\")\n",
" cmd.Execute(\"Maxwell_Playground\", \"96 72 4 \"+t_final+str(CFL_FACTOR), \"out-medresolution.txt\")\n",
" Nxx0_low = '64'\n",
" Nxx0_med = '96'\n",
"\n",
"elif 'Cylindrical' in CoordSystem:\n",
" cmd.Execute(\"Maxwell_Playground\", \"50 4 100 \"+t_final+str(CFL_FACTOR), \"out-lowresolution.txt\")\n",
" cmd.Execute(\"Maxwell_Playground\", \"80 4 160 \"+t_final+str(CFL_FACTOR), \"out-medresolution.txt\")\n",
" Nxx0_low = '50'\n",
" Nxx0_med = '80'\n",
"\n",
"else:\n",
" # Cartesian\n",
" cmd.Execute(\"Maxwell_Playground\", \"64 64 64 \"+t_final+str(CFL_FACTOR), \"out-lowresolution.txt\")\n",
" cmd.Execute(\"Maxwell_Playground\", \"128 128 128 \"+t_final+str(CFL_FACTOR), \"out-medresolution.txt\")\n",
" Nxx0_low = '64'\n",
" Nxx0_med = '128'"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:55.634591Z",
"iopub.status.busy": "2021-06-15T11:39:55.634195Z",
"iopub.status.idle": "2021-06-15T11:39:55.636485Z",
"shell.execute_reply": "2021-06-15T11:39:55.636083Z"
},
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished this code cell.\n"
]
}
],
"source": [
"# Return to root directory\n",
"os.chdir(os.path.join(\"../../\"))\n",
"\n",
"print(\"Finished this code cell.\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 6: Visualize the output! \\[Back to [top](#toc)\\]\n",
"$$\\label{visualize}$$ \n",
"\n",
"In this section we will generate a movie, plotting the x component of the electric field on a 2D grid.."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 6.a: Install `scipy` and download `ffmpeg` if they are not yet installed/downloaded \\[Back to [top](#toc)\\]\n",
"$$\\label{installdownload}$$ \n",
"\n",
"Note that if you are not running this within `mybinder`, but on a Windows system, `ffmpeg` must be installed using a separate package (on [this site](http://ffmpeg.org/)), or if running Jupyter within Anaconda, use the command: `conda install -c conda-forge ffmpeg`."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:55.648607Z",
"iopub.status.busy": "2021-06-15T11:39:55.646374Z",
"iopub.status.idle": "2021-06-15T11:39:56.266808Z",
"shell.execute_reply": "2021-06-15T11:39:56.267280Z"
}
},
"outputs": [],
"source": [
"!pip install scipy > /dev/null\n",
"\n",
"check_for_ffmpeg = !which ffmpeg >/dev/null && echo $?\n",
"if check_for_ffmpeg != ['0']:\n",
" print(\"Couldn't find ffmpeg, so I'll download it.\")\n",
" # Courtesy https://johnvansickle.com/ffmpeg/\n",
" !wget http://astro.phys.wvu.edu/zetienne/ffmpeg-static-amd64-johnvansickle.tar.xz\n",
" !tar Jxf ffmpeg-static-amd64-johnvansickle.tar.xz\n",
" print(\"Copying ffmpeg to ~/.local/bin/. Assumes ~/.local/bin is in the PATH.\")\n",
" !mkdir ~/.local/bin/\n",
" !cp ffmpeg-static-amd64-johnvansickle/ffmpeg ~/.local/bin/\n",
" print(\"If this doesn't work, then install ffmpeg yourself. It should work fine on mybinder.\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 6.b: Generate images for visualization animation \\[Back to [top](#toc)\\]\n",
"$$\\label{genimages}$$ \n",
"\n",
"Here we loop through the data files output by the executable compiled and run in [the previous step](#mainc), generating a [png](https://en.wikipedia.org/wiki/Portable_Network_Graphics) image for each data file.\n",
"\n",
"**Special thanks to Terrence Pierre Jacques. His work with the first versions of these scripts greatly contributed to the scripts as they exist below.**"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:39:56.278473Z",
"iopub.status.busy": "2021-06-15T11:39:56.277729Z",
"iopub.status.idle": "2021-06-15T11:40:06.706797Z",
"shell.execute_reply": "2021-06-15T11:40:06.706288Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[2KProcessing file MaxwellEvolCurvi_Playground_Ccodes/output/out80-00000240.txt\r"
]
}
],
"source": [
"## VISUALIZATION ANIMATION, PART 1: Generate PNGs, one per frame of movie ##\n",
"\n",
"import numpy as np\n",
"from scipy.interpolate import griddata\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib.pyplot import savefig\n",
"from IPython.display import HTML\n",
"import matplotlib.image as mgimg\n",
"\n",
"import glob\n",
"import sys\n",
"from matplotlib import animation\n",
"\n",
"globby = glob.glob(os.path.join(outdir,'out'+Nxx0_med+'-00*.txt'))\n",
"file_list = []\n",
"for x in sorted(globby):\n",
" file_list.append(x)\n",
"\n",
"bound = domain_size/2.0\n",
"pl_xmin = -bound\n",
"pl_xmax = +bound\n",
"pl_zmin = -bound\n",
"pl_zmax = +bound\n",
"\n",
"for filename in file_list:\n",
" fig = plt.figure()\n",
" t, x, z, Ex, Ey, Ax, Ay, C = np.loadtxt(filename).T #Transposed for easier unpacking\n",
"\n",
" plotquantity = Ex\n",
" time = np.round(t[0], decimals=3)\n",
" plotdescription = \"Numerical Soln.\"\n",
" plt.title(r\"$E_x$ at $t$ = \"+str(time))\n",
" plt.xlabel(\"x\")\n",
" plt.ylabel(\"z\")\n",
"\n",
" grid_x, grid_z = np.mgrid[pl_xmin:pl_xmax:200j, pl_zmin:pl_zmax:200j]\n",
" points = np.zeros((len(x), 2))\n",
" for i in range(len(x)):\n",
" # Zach says: No idea why x and y get flipped...\n",
" points[i][0] = x[i]\n",
" points[i][1] = z[i]\n",
"\n",
" grid = griddata(points, plotquantity, (grid_x, grid_z), method='nearest')\n",
" gridcub = griddata(points, plotquantity, (grid_x, grid_z), method='cubic')\n",
" im = plt.imshow(gridcub, extent=(pl_xmin,pl_xmax, pl_zmin,pl_zmax))\n",
" ax = plt.colorbar()\n",
" plt.clim(-3,3)\n",
" ax.set_label(plotdescription)\n",
" savefig(os.path.join(filename+\".png\"),dpi=150)\n",
" plt.close(fig)\n",
" sys.stdout.write(\"%c[2K\" % 27)\n",
" sys.stdout.write(\"Processing file \"+filename+\"\\r\")\n",
" sys.stdout.flush()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"## Step 6.c: Generate visualization animation \\[Back to [top](#toc)\\]\n",
"$$\\label{genvideo}$$ \n",
"\n",
"In the following step, [ffmpeg](http://ffmpeg.org) is used to generate an [mp4](https://en.wikipedia.org/wiki/MPEG-4) video file, which can be played directly from this Jupyter notebook."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:06.722931Z",
"iopub.status.busy": "2021-06-15T11:40:06.722352Z",
"iopub.status.idle": "2021-06-15T11:40:07.599761Z",
"shell.execute_reply": "2021-06-15T11:40:07.599227Z"
}
},
"outputs": [],
"source": [
"## VISUALIZATION ANIMATION, PART 2: Combine PNGs to generate movie ##\n",
"\n",
"# https://stackoverflow.com/questions/14908576/how-to-remove-frame-from-matplotlib-pyplot-figure-vs-matplotlib-figure-frame\n",
"# https://stackoverflow.com/questions/23176161/animating-pngs-in-matplotlib-using-artistanimation\n",
"\n",
"fig = plt.figure(frameon=False)\n",
"ax = fig.add_axes([0, 0, 1, 1])\n",
"ax.axis('off')\n",
"\n",
"myimages = []\n",
"\n",
"for i in range(len(file_list)):\n",
" img = mgimg.imread(file_list[i]+\".png\")\n",
" imgplot = plt.imshow(img)\n",
" myimages.append([imgplot])\n",
"\n",
"ani = animation.ArtistAnimation(fig, myimages, interval=100, repeat_delay=1000)\n",
"plt.close()\n",
"ani.save(os.path.join(outdir,'Maxwell_ToroidalDipole.mp4'), fps=5,dpi=150)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:07.602767Z",
"iopub.status.busy": "2021-06-15T11:40:07.602243Z",
"iopub.status.idle": "2021-06-15T11:40:07.604288Z",
"shell.execute_reply": "2021-06-15T11:40:07.603832Z"
}
},
"outputs": [],
"source": [
"## VISUALIZATION ANIMATION, PART 3: Display movie as embedded HTML5 (see next cell) ##\n",
"\n",
"# https://stackoverflow.com/questions/18019477/how-can-i-play-a-local-video-in-my-ipython-notebook"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:07.607819Z",
"iopub.status.busy": "2021-06-15T11:40:07.607293Z",
"iopub.status.idle": "2021-06-15T11:40:07.609703Z",
"shell.execute_reply": "2021-06-15T11:40:07.609298Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Embed video based on suggestion:\n",
"# https://stackoverflow.com/questions/39900173/jupyter-notebook-html-cell-magic-with-python-variable\n",
"HTML(\"\"\"\n",
"\n",
"\"\"\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 7: Plot the numerical error, and confirm that it converges to zero with increasing numerical resolution (sampling) \\[Back to [top](#toc)\\]\n",
"$$\\label{convergence}$$"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:07.780345Z",
"iopub.status.busy": "2021-06-15T11:40:07.614988Z",
"iopub.status.idle": "2021-06-15T11:40:08.394957Z",
"shell.execute_reply": "2021-06-15T11:40:08.394704Z"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_med, z_med, Ex__E_rel_med, Ey__E_rel_med, Ax__E_rel_med, Ay__E_rel_med = np.loadtxt(os.path.join(outdir,'out'+Nxx0_med+'.txt')).T #Transposed for easier unpacking\n",
"\n",
"pl_xmin = -domain_size/2.\n",
"pl_xmax = +domain_size/2.\n",
"pl_ymin = -domain_size/2.\n",
"pl_ymax = +domain_size/2.\n",
"\n",
"grid_x, grid_z = np.mgrid[pl_xmin:pl_xmax:100j, pl_ymin:pl_ymax:100j]\n",
"points_med = np.zeros((len(x_med), 2))\n",
"for i in range(len(x_med)):\n",
" points_med[i][0] = x_med[i]\n",
" points_med[i][1] = z_med[i]\n",
"\n",
"grid_med = griddata(points_med, Ex__E_rel_med, (grid_x, grid_z), method='nearest')\n",
"grid_medcub = griddata(points_med, Ex__E_rel_med, (grid_x, grid_z), method='cubic')\n",
"\n",
"plt.clf()\n",
"plt.title(r\"Nxx0=\"+Nxx0_med+\" Num. Err.: $\\log_{10}|Ex|$ at $t$ = \"+t_final)\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"z\")\n",
"\n",
"fig_medcub = plt.imshow(grid_medcub.T, extent=(pl_xmin,pl_xmax, pl_ymin,pl_ymax))\n",
"cb = plt.colorbar(fig_medcub)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:08.466449Z",
"iopub.status.busy": "2021-06-15T11:40:08.399958Z",
"iopub.status.idle": "2021-06-15T11:40:08.568595Z",
"shell.execute_reply": "2021-06-15T11:40:08.568162Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_low,z_low, EU0__E_rel_low, EU1__E_rel_low, AU0__E_rel_low, AU1__E_rel_low = np.loadtxt(os.path.join(outdir,'out'+Nxx0_low+'.txt')).T #Transposed for easier unpacking\n",
"\n",
"points_low = np.zeros((len(x_low), 2))\n",
"for i in range(len(x_low)):\n",
" points_low[i][0] = x_low[i]\n",
" points_low[i][1] = z_low[i]\n",
"\n",
"grid_low = griddata(points_low, EU0__E_rel_low, (grid_x, grid_z), method='nearest')\n",
"\n",
"griddiff__low_minus__med = np.zeros((100,100))\n",
"griddiff__low_minus__med_1darray = np.zeros(100*100)\n",
"gridx_1darray_yeq0 = np.zeros(100)\n",
"grid_low_1darray_yeq0 = np.zeros(100)\n",
"grid_med_1darray_yeq0 = np.zeros(100)\n",
"count = 0\n",
"for i in range(100):\n",
" for j in range(100):\n",
" griddiff__low_minus__med[i][j] = grid_low[i][j] - grid_med[i][j]\n",
" griddiff__low_minus__med_1darray[count] = griddiff__low_minus__med[i][j]\n",
" if j==49:\n",
" gridx_1darray_yeq0[i] = grid_x[i][j]\n",
" grid_low_1darray_yeq0[i] = grid_low[i][j] + np.log10((float(Nxx0_low)/float(Nxx0_med))**4)\n",
" grid_med_1darray_yeq0[i] = grid_med[i][j]\n",
" count = count + 1\n",
"\n",
"fig, ax = plt.subplots()\n",
"plt.title(r\"4th-order Convergence of $E_x$ at t = \"+t_final)\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"log10(Absolute error)\")\n",
"\n",
"ax.plot(gridx_1darray_yeq0, grid_med_1darray_yeq0, 'k-', label='Nr = '+Nxx0_med)\n",
"ax.plot(gridx_1darray_yeq0, grid_low_1darray_yeq0, 'k--', label='Nr = '+Nxx0_low+', mult. by ('+Nxx0_low+'/'+Nxx0_med+')^4')\n",
"# ax.set_ylim([-8.5,0.5])\n",
"\n",
"legend = ax.legend(loc='lower right', shadow=True, fontsize='x-large')\n",
"legend.get_frame().set_facecolor('C1')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 8: Comparison Divergence Constrain Violation \\[Back to [top](#toc)\\]\n",
"$$\\label{div_e}$$\n",
"\n",
"Here we calculate the violation quantity\n",
"\n",
"$$\n",
"\\mathcal{C} \\equiv \\nabla^i E_i,\n",
"$$\n",
"\n",
"at each point on our grid (excluding the ghost zones) then calculate the normalized L2 norm over the entire volume via\n",
"\n",
"\\begin{align}\n",
" \\lVert C \\rVert &= \\left( \\frac{\\int C^2 d\\mathcal{V}}{\\int d\\mathcal{V}} \\right)^{1/2}.\n",
"\\end{align}"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:08.572777Z",
"iopub.status.busy": "2021-06-15T11:40:08.571978Z",
"iopub.status.idle": "2021-06-15T11:40:08.800770Z",
"shell.execute_reply": "2021-06-15T11:40:08.801216Z"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plotting the constraint violation\n",
"nrpy_div_low = np.loadtxt(os.path.join(outdir,'out-lowresolution.txt')).T\n",
"nrpy_div_med = np.loadtxt(os.path.join(outdir,'out-medresolution.txt')).T\n",
"\n",
"plt.plot(nrpy_div_low[0]/domain_size, (nrpy_div_low[1]), 'k-',label='Nxx0 = '+Nxx0_low)\n",
"plt.plot(nrpy_div_med[0]/domain_size, (nrpy_div_med[1]), 'k--',label='Nxx0 = '+Nxx0_med)\n",
"\n",
"plt.yscale('log')\n",
"plt.xlabel('Light Crossing Times')\n",
"plt.ylabel('||C||')\n",
"# plt.xlim(0,2.2)\n",
"# plt.ylim(1e-4, 1e-5)\n",
"plt.title('L2 Norm of the Divergence of E - '+par.parval_from_str(\"reference_metric::CoordSystem\")+' Coordinates')\n",
"plt.legend(loc='center right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Step 9: Output this notebook to $\\LaTeX$-formatted PDF file \\[Back to [top](#toc)\\]\n",
"$$\\label{latex_pdf_output}$$\n",
"\n",
"The following code cell converts this Jupyter notebook into a proper, clickable $\\LaTeX$-formatted PDF file. After the cell is successfully run, the generated PDF may be found in the root NRPy+ tutorial directory, with filename\n",
"[Tutorial-Start_to_Finish-Solving_Maxwells_Equations_in_Vacuum-Curvilinear.pdf](Tutorial-Start_to_Finish-Solving_Maxwells_Equations_in_Vacuum-Curvilinear.pdf) (Note that clicking on this link may not work; you may need to open the PDF file through another means.)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"execution": {
"iopub.execute_input": "2021-06-15T11:40:08.804414Z",
"iopub.status.busy": "2021-06-15T11:40:08.803866Z",
"iopub.status.idle": "2021-06-15T11:40:12.097042Z",
"shell.execute_reply": "2021-06-15T11:40:12.096412Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Created Tutorial-Start_to_Finish-Solving_Maxwells_Equations_in_Vacuum-\n",
" Curvilinear.tex, and compiled LaTeX file to PDF file Tutorial-\n",
" Start_to_Finish-Solving_Maxwells_Equations_in_Vacuum-Curvilinear.pdf\n"
]
}
],
"source": [
"import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n",
"cmd.output_Jupyter_notebook_to_LaTeXed_PDF(\"Tutorial-Start_to_Finish-Solving_Maxwells_Equations_in_Vacuum-Curvilinear\")"
]
}
],
"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": "3.10.0rc2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}