ActiveThorns = "
    AMReX
    IOUtil
    MaxwellToyAMReX
"
 
$nlevels = 1
$ncells = 32
Cactus::cctk_show_schedule = no
# Cactus::terminate = "iteration"
# Cactus::cctk_itlast = 0
Cactus::terminate = "time"
Cactus::cctk_final_time = 2.0
# AMReX::verbose = yes
AMReX::xmin = -1.0
AMReX::ymin = -1.0
AMReX::zmin = -1.0
AMReX::xmax = +1.0
AMReX::ymax = +1.0
AMReX::zmax = +1.0
AMReX::ncells_x = $ncells
AMReX::ncells_y = $ncells
AMReX::ncells_z = $ncells
AMReX::max_num_levels = $nlevels
AMReX::regrid_every = 16
AMReX::regrid_error_threshold = 0.1
AMReX::dtfac = 0.5
MaxwellToyAMReX::spatial_frequency_x = 0.5
MaxwellToyAMReX::spatial_frequency_y = 0.0
MaxwellToyAMReX::spatial_frequency_z = 0.0
IO::out_dir = $parfile
IO::out_every = $ncells * 2 ** ($nlevels - 1) / 32

Cactus Code Thorn HydroToyAMReX
Author(s)    : Erik Schnetter <schnetter@gmail.com>
Maintainer(s): Erik Schnetter <schnetter@gmail.com>
Licence      : LGPL
--------------------------------------------------------------------------
1. Purpose
Solve the non-relativistic hydrodynamics equations

# Configuration definitions for thorn HydroToyAMReX

% *======================================================================*
%  Cactus Thorn template for ThornGuide documentation
%  Author: Ian Kelley
%  Date: Sun Jun 02, 2002
%  $Header$
%
%  Thorn documentation in the latex file doc/documentation.tex
%  will be included in ThornGuides built with the Cactus make system.
%  The scripts employed by the make system automatically include
%  pages about variables, parameters and scheduling parsed from the
%  relevant thorn CCL files.
%
%  This template contains guidelines which help to assure that your
%  documentation will be correctly added to ThornGuides. More
%  information is available in the Cactus UsersGuide.
%
%  Guidelines:
%   - Do not change anything before the line
%       % START CACTUS THORNGUIDE",
%     except for filling in the title, author, date, etc. fields.
%        - Each of these fields should only be on ONE line.
%        - Author names should be separated with a \\ or a comma.
%   - You can define your own macros, but they must appear after
%     the START CACTUS THORNGUIDE line, and must not redefine standard
%     latex commands.
%   - To avoid name clashes with other thorns, 'labels', 'citations',
%     'references', and 'image' names should conform to the following
%     convention:
%       ARRANGEMENT_THORN_LABEL
%     For example, an image wave.eps in the arrangement CactusWave and
%     thorn WaveToyC should be renamed to CactusWave_WaveToyC_wave.eps
%   - Graphics should only be included using the graphicx package.
%     More specifically, with the "\includegraphics" command.  Do
%     not specify any graphic file extensions in your .tex file. This
%     will allow us to create a PDF version of the ThornGuide
%     via pdflatex.
%   - References should be included with the latex "\bibitem" command.
%   - Use \begin{abstract}...\end{abstract} instead of \abstract{...}
%   - Do not use \appendix, instead include any appendices you need as
%     standard sections.
%   - For the benefit of our Perl scripts, and for future extensions,
%     please use simple latex.
%
% *======================================================================*
%
% Example of including a graphic image:
%    \begin{figure}[ht]
% 	\begin{center}
%    	   \includegraphics[width=6cm]{MyArrangement_MyThorn_MyFigure}
% 	\end{center}
% 	\caption{Illustration of this and that}
% 	\label{MyArrangement_MyThorn_MyLabel}
%    \end{figure}
%
% Example of using a label:
%   \label{MyArrangement_MyThorn_MyLabel}
%
% Example of a citation:
%    \cite{MyArrangement_MyThorn_Author99}
%
% Example of including a reference
%   \bibitem{MyArrangement_MyThorn_Author99}
%   {J. Author, {\em The Title of the Book, Journal, or periodical}, 1 (1999),
%   1--16. {\tt http://www.nowhere.com/}}
%
% *======================================================================*
% If you are using CVS use this line to give version information
% $Header$
\documentclass{article}
% Use the Cactus ThornGuide style file
% (Automatically used from Cactus distribution, if you have a
%  thorn without the Cactus Flesh download this from the Cactus
%  homepage at www.cactuscode.org)
\usepackage{../../../../doc/latex/cactus}
\begin{document}
% The author of the documentation
\author{Erik Schnetter \textless schnetter@gmail.com\textgreater}
% The title of the document (not necessarily the name of the Thorn)
\title{WaveToyAMReX}
% the date your document was last changed, if your document is in CVS,
% please use:
%    \date{$ $Date$ $}
\date{July 10 2019}
\maketitle
% Do not delete next line
% START CACTUS THORNGUIDE
% Add all definitions used in this documentation here
%   \def\mydef etc
% Add an abstract for this thorn's documentation
\begin{abstract}
\end{abstract}
% The following sections are suggestive only.
% Remove them or add your own.
\section{Introduction}
\section{Physical System}
\section{Numerical Implementation}
\section{Using This Thorn}
\subsection{Obtaining This Thorn}
\subsection{Basic Usage}
\subsection{Special Behaviour}
\subsection{Interaction With Other Thorns}
\subsection{Examples}
\subsection{Support and Feedback}
\section{History}
\subsection{Thorn Source Code}
\subsection{Thorn Documentation}
\subsection{Acknowledgements}
\begin{thebibliography}{9}
\end{thebibliography}
% Do not delete next line
% END CACTUS THORNGUIDE
\end{document}

# Interface definition for thorn HydroToyAMReX
IMPLEMENTS: HydroToyAMReX
INHERITS: AMReX
USES INCLUDE HEADER: loop.hxx
CCTK_REAL density TYPE=gf TIMELEVELS=2
{
  rho
} "Density"
CCTK_REAL momentum TYPE=gf TIMELEVELS=2
{
  momx momy momz
} "Momentum"
CCTK_REAL energy TYPE=gf TIMELEVELS=2
{
  etot
} "Energy"

# Parameter definitions for thorn HydroToyAMReX

# Schedule definitions for thorn HydroToyAMReX
SCHEDULE HydroToyAMReX_Initialize AT initial
{
  LANG: C
} "Set up hydro initial conditions"
SCHEDULE HydroToyAMReX_Evolve AT evol
{
  LANG: C
} "Evolve the hydro equations"

#include <cctk.h>
#include <cctk_Arguments.h>
#include <cctk_Parameters.h>
#include <loop.hxx>
#include <cassert>
#include <cmath>
#include <iostream>
namespace HydroToyAMReX {
using namespace std;
constexpr int dim = 3;
////////////////////////////////////////////////////////////////////////////////
extern "C" void HydroToyAMReX_Initialize(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  const CCTK_REAL t = cctk_time;
  const CCTK_REAL dt = CCTK_DELTA_TIME;
  CCTK_REAL x0[dim], dx[dim];
  for (int d = 0; d < dim; ++d) {
    x0[d] = CCTK_ORIGIN_SPACE(d);
    dx[d] = CCTK_DELTA_SPACE(d);
  }
  Loop::loop_all(cctkGH, [&](int i, int j, int k, int idx) {
    rho[idx] = 1.0;
    momx[idx] = 0.0;
    momy[idx] = 0.0;
    momz[idx] = 0.0;
    etot[idx] = 1.0;
  });
}
extern "C" void HydroToyAMReX_Evolve(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  const CCTK_REAL dt = CCTK_DELTA_TIME;
  const CCTK_REAL dx = CCTK_DELTA_SPACE(0);
  const CCTK_REAL dy = CCTK_DELTA_SPACE(1);
  const CCTK_REAL dz = CCTK_DELTA_SPACE(2);
  constexpr int di = 1;
  const int dj = di * cctk_ash[0];
  const int dk = dj * cctk_ash[1];
  Loop::loop_int(cctkGH, [&](int i, int j, int k, int idx) {
    // dt rho + d_i (rho vel^i) = 0
    rho[idx] = rho_p[idx] - dt * ((momx_p[idx + di] - momx_p[idx]) / dx +
                                  (momy_p[idx + dj] - momy_p[idx]) / dy +
                                  (momz_p[idx + dk] - momz_p[idx]) / dz);
    //     // dt mom^i + d_j (mom^i vel^j) = 0
    //     momx[idx] = momx_p[idx] - dt * (
    // momx_p[idx] * momx_p[idx]
    //                                     );
    CCTK_REAL velx = momx[idx] / rho[idx];
    CCTK_REAL vely = momy[idx] / rho[idx];
    CCTK_REAL velz = momz[idx] / rho[idx];
  });
}
} // namespace HydroToyAMReX

# Main make.code.defn file for thorn WaveToyAMReX
# Source files in this directory
SRCS = hydrotoy.cxx
# Subdirectories containing source files
SUBDIRS = 

Cactus Code Thorn MaxwellToyAMReX
Author(s)    : Erik Schnetter <schnetter@gmail.com>
Maintainer(s): Erik Schnetter <schnetter@gmail.com>
Licence      : LGPL
--------------------------------------------------------------------------
1. Purpose
Solve the Maxwell equations

# Configuration definitions for thorn MaxwellToyAMReX

% *======================================================================*
%  Cactus Thorn template for ThornGuide documentation
%  Author: Ian Kelley
%  Date: Sun Jun 02, 2002
%  $Header$
%
%  Thorn documentation in the latex file doc/documentation.tex
%  will be included in ThornGuides built with the Cactus make system.
%  The scripts employed by the make system automatically include
%  pages about variables, parameters and scheduling parsed from the
%  relevant thorn CCL files.
%
%  This template contains guidelines which help to assure that your
%  documentation will be correctly added to ThornGuides. More
%  information is available in the Cactus UsersGuide.
%
%  Guidelines:
%   - Do not change anything before the line
%       % START CACTUS THORNGUIDE",
%     except for filling in the title, author, date, etc. fields.
%        - Each of these fields should only be on ONE line.
%        - Author names should be separated with a \\ or a comma.
%   - You can define your own macros, but they must appear after
%     the START CACTUS THORNGUIDE line, and must not redefine standard
%     latex commands.
%   - To avoid name clashes with other thorns, 'labels', 'citations',
%     'references', and 'image' names should conform to the following
%     convention:
%       ARRANGEMENT_THORN_LABEL
%     For example, an image wave.eps in the arrangement CactusWave and
%     thorn WaveToyC should be renamed to CactusWave_WaveToyC_wave.eps
%   - Graphics should only be included using the graphicx package.
%     More specifically, with the "\includegraphics" command.  Do
%     not specify any graphic file extensions in your .tex file. This
%     will allow us to create a PDF version of the ThornGuide
%     via pdflatex.
%   - References should be included with the latex "\bibitem" command.
%   - Use \begin{abstract}...\end{abstract} instead of \abstract{...}
%   - Do not use \appendix, instead include any appendices you need as
%     standard sections.
%   - For the benefit of our Perl scripts, and for future extensions,
%     please use simple latex.
%
% *======================================================================*
%
% Example of including a graphic image:
%    \begin{figure}[ht]
% 	\begin{center}
%    	   \includegraphics[width=6cm]{MyArrangement_MyThorn_MyFigure}
% 	\end{center}
% 	\caption{Illustration of this and that}
% 	\label{MyArrangement_MyThorn_MyLabel}
%    \end{figure}
%
% Example of using a label:
%   \label{MyArrangement_MyThorn_MyLabel}
%
% Example of a citation:
%    \cite{MyArrangement_MyThorn_Author99}
%
% Example of including a reference
%   \bibitem{MyArrangement_MyThorn_Author99}
%   {J. Author, {\em The Title of the Book, Journal, or periodical}, 1 (1999),
%   1--16. {\tt http://www.nowhere.com/}}
%
% *======================================================================*
% If you are using CVS use this line to give version information
% $Header$
\documentclass{article}
% Use the Cactus ThornGuide style file
% (Automatically used from Cactus distribution, if you have a
%  thorn without the Cactus Flesh download this from the Cactus
%  homepage at www.cactuscode.org)
\usepackage{../../../../doc/latex/cactus}
\begin{document}
% The author of the documentation
\author{Erik Schnetter \textless schnetter@gmail.com\textgreater}
% The title of the document (not necessarily the name of the Thorn)
\title{WaveToyAMReX}
% the date your document was last changed, if your document is in CVS,
% please use:
%    \date{$ $Date$ $}
\date{July 10 2019}
\maketitle
% Do not delete next line
% START CACTUS THORNGUIDE
% Add all definitions used in this documentation here
%   \def\mydef etc
% Add an abstract for this thorn's documentation
\begin{abstract}
\end{abstract}
% The following sections are suggestive only.
% Remove them or add your own.
\section{Introduction}
\section{Physical System}
\section{Numerical Implementation}
\section{Using This Thorn}
\subsection{Obtaining This Thorn}
\subsection{Basic Usage}
\subsection{Special Behaviour}
\subsection{Interaction With Other Thorns}
\subsection{Examples}
\subsection{Support and Feedback}
\section{History}
\subsection{Thorn Source Code}
\subsection{Thorn Documentation}
\subsection{Acknowledgements}
\begin{thebibliography}{9}
\end{thebibliography}
% Do not delete next line
% END CACTUS THORNGUIDE
\end{document}

# Interface definition for thorn MaxwellToyAMReX
IMPLEMENTS: MaxwellToyAMReX
INHERITS: AMReX
USES INCLUDE HEADER: loop.hxx
# Wikipedia, <https://en.wikipedia.org/wiki/Maxwell%27s_equations>
CCTK_REAL potential TYPE=gf TIMELEVELS=2
{
  # d*dA = mu J   A^a,^b_b - A^b,^a_b = mu J^a
  # d*A  = 0      A^a,a   = 0
  # -d*(dphi + A,t)      = rho/epsilon
  # d*dA + dt*(dphi+A,t) = mu J
  # *phi,t + d*A         = 0             phi,t + A^i,i = 0
  phi
  ax ay az
} "Electromagnetic potential"
CCTK_REAL field TYPE=gf TIMELEVELS=2
{
  # F   = dA     F_ab                     = A_a,b - A_b,a
  # dF  = 0      F_ab,c + F_bc,a + F_ca,b = 0
  # d*F = mu J   F^ab,a                   = mu J^b
  # E          = -dphi - A,t   E_i                     = - phi,i - A_i,t
  # B          = dA            B_ij                    = A_j,i - A_i,j
  # dE + B,t   = 0             E_j,i - E_i,j + B_ij,t  = 0
  # dB         = 0             B_jk,i + B_ki,j + B_ijk = 0
  # d*E        = rho/epsilon   E^i,i                   = rho/epsilon
  # d*B - dt*E = mu J          - B^ij,i - E^j,t        = mu J^j
  ex ey ez
  bx by bz   # B_yz B_zx B_xy
} "Electromagnetic field"
CCTK_REAL current TYPE=gf TIMELEVELS=2
{
  rho
  jx jy jz
} "Electric charge current"
CCTK_REAL errors TYPE=gf
{
  phierr
  axerr ayerr azerr
  exerr eyerr ezerr
  bxerr byerr bzerr
  rhoerr
  jxerr jyerr jzerr
} "Errors"
# CCTK_REAL constraints TYPE=gf
# {
#   dive
#   divb
# } "Constraints"
# 
# CCTK_REAL poynting TYPE=gf
# {
#   sx sy sz
# } "Poynting vector"
# 
# CCTK_REAL energy TYPE=gf
# {
#   eps
# } "Electromagnetic energy density"

# Parameter definitions for thorn MaxwellToyAMReX
KEYWORD initial_condition "Initial condition"
{
  "plane wave" :: ""
} "plane wave"
CCTK_REAL spatial_frequency_x "spatial frequency"
{
  *:* :: ""
} 0.5
CCTK_REAL spatial_frequency_y "spatial frequency"
{
  *:* :: ""
} 0.5
CCTK_REAL spatial_frequency_z "spatial frequency"
{
  *:* :: ""
} 0.5

# Schedule definitions for thorn MaxwellToyAMReX
SCHEDULE MaxwellToyAMReX_Initialize AT initial
{
  LANG: C
} "Set up initial conditions for the Maxwell equations"
SCHEDULE MaxwellToyAMReX_EstimateError AT postinitial
{
  LANG: C
} "Estimate local error for regridding initial conditions"
SCHEDULE MaxwellToyAMReX_Evolve1 AT evol
{
  LANG: C
  SYNC: potential field current
} "Evolve the Maxwell equations, step 1"
SCHEDULE MaxwellToyAMReX_Evolve2 AT evol AFTER MaxwellToyAMReX_Evolve1
{
  LANG: C
  SYNC: potential field current
} "Evolve the Maxwell equations step 2"
# SCHEDULE MaxwellToyAMReX_Constraints AT analysis
# {
#   LANG: C
# } "Calculate constraints of the Maxwell equations"
# SCHEDULE MaxwellToyAMReX_Energy AT analysis
# {
#   LANG: C
# } "Calculate energy density for the Maxwell equations"
SCHEDULE MaxwellToyAMReX_EstimateError AT poststep
{
  LANG: C
} "Estimate local error for regridding during evolution"
SCHEDULE MaxwellToyAMReX_Error AT analysis
{
  LANG: C
} "Calculate error for the Maxwell equations"

# Main make.code.defn file for thorn MaxwellToyAMReX
# Source files in this directory
SRCS = maxwelltoy.cxx
# Subdirectories containing source files
SUBDIRS = 

#include <cctk.h>
#include <cctk_Arguments.h>
#include <cctk_Parameters.h>
#include <loop.hxx>
#include <cassert>
#include <cmath>
#include <iostream>
namespace MaxwellToyAMReX {
using namespace std;
constexpr int dim = 3;
////////////////////////////////////////////////////////////////////////////////
template <typename T> struct potential {
  T phi, ax, ay, az;
  potential operator-(const potential &y) const {
    const auto &x = *this;
    return {.phi = x.phi - y.phi,
            .ax = x.ax - y.ax,
            .ay = x.ay - y.ay,
            .az = x.az - y.az};
  }
  potential operator/(T a) const {
    const auto &x = *this;
    return {.phi = x.phi / a, .ax = x.ax / a, .ay = x.ay / a, .az = x.az / a};
  }
};
template <typename T> potential<T> plane_wave(T t, T x, T y, T z) {
  DECLARE_CCTK_PARAMETERS;
  T kx = 2 * M_PI * spatial_frequency_x;
  T ky = 2 * M_PI * spatial_frequency_y;
  T kz = 2 * M_PI * spatial_frequency_z;
  T omega = sqrt(pow(kx, 2) + pow(ky, 2) + pow(kz, 2));
  return {.phi = cos(omega * t - kx * x - ky * y - kz * z),
          .ax = omega / kx * cos(omega * t - kx * x - ky * y - kz * z),
          .ay = 0,
          .az = 0};
}
////////////////////////////////////////////////////////////////////////////////
// Derivatives
template <typename T, typename R> auto tderiv(R f(T t, T x, T y, T z), T dt) {
  return [=](T t, T x, T y, T z) {
    return (f(t + dt / 2, x, y, z) - f(t - dt / 2, x, y, z)) / dt;
  };
}
template <typename T, typename R> auto xderiv(R f(T t, T x, T y, T z), T dx) {
  return [=](T t, T x, T y, T z) {
    return (f(t, x + dx / 2, y, z) - f(t, x - dx / 2, y, z)) / dx;
  };
}
template <typename T, typename R> auto yderiv(R f(T t, T x, T y, T z), T dy) {
  return [=](T t, T x, T y, T z) {
    return (f(t, x, y + dy / 2, z) - f(t, x, y - dy / 2, z)) / dy;
  };
}
template <typename T, typename R> auto zderiv(R f(T t, T x, T y, T z), T dz) {
  return [=](T t, T x, T y, T z) {
    return (f(t, x, y, z + dz / 2) - f(t, x, y, z - dz / 2)) / dz;
  };
}
////////////////////////////////////////////////////////////////////////////////
extern "C" void MaxwellToyAMReX_Initialize(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  const CCTK_REAL t = cctk_time;
  const CCTK_REAL x0 = CCTK_ORIGIN_SPACE(0);
  const CCTK_REAL y0 = CCTK_ORIGIN_SPACE(1);
  const CCTK_REAL z0 = CCTK_ORIGIN_SPACE(2);
  const CCTK_REAL dt = CCTK_DELTA_TIME;
  const CCTK_REAL dx = CCTK_DELTA_SPACE(0);
  const CCTK_REAL dy = CCTK_DELTA_SPACE(1);
  const CCTK_REAL dz = CCTK_DELTA_SPACE(2);
  if (CCTK_EQUALS(initial_condition, "plane wave")) {
    Loop::loop_all(cctkGH, [&](int i, int j, int k, int idx) {
      CCTK_REAL x = x0 + (cctk_lbnd[0] + i) * dx;
      CCTK_REAL y = y0 + (cctk_lbnd[1] + j) * dy;
      CCTK_REAL z = z0 + (cctk_lbnd[2] + k) * dz;
      phi[idx] = plane_wave(t + dt / 2, x, y, z).phi;
      ax[idx] = plane_wave(t, x + dx / 2, y, z).ax;
      ay[idx] = plane_wave(t, x, y + dy / 2, z).ay;
      az[idx] = plane_wave(t, x, y, z + dz / 2).az;
      ex[idx] =
          -xderiv(plane_wave<CCTK_REAL>, dx)(t + dt / 2, x + dx / 2, y, z).phi -
          tderiv(plane_wave<CCTK_REAL>, dt)(t + dt / 2, x + dx / 2, y, z).ax;
      ey[idx] =
          -yderiv(plane_wave<CCTK_REAL>, dy)(t + dt / 2, x, y + dy / 2, z).phi -
          tderiv(plane_wave<CCTK_REAL>, dt)(t + dt / 2, x, y + dy / 2, z).ay;
      ez[idx] =
          -zderiv(plane_wave<CCTK_REAL>, dz)(t + dt / 2, x, y, z + dz / 2).phi -
          tderiv(plane_wave<CCTK_REAL>, dt)(t + dt / 2, x, y, z + dz / 2).az;
      bx[idx] =
          yderiv(plane_wave<CCTK_REAL>, dy)(t, x, y + dy / 2, z + dz / 2).az -
          zderiv(plane_wave<CCTK_REAL>, dz)(t, x, y + dy / 2, z + dz / 2).ay;
      by[idx] =
          zderiv(plane_wave<CCTK_REAL>, dz)(t, x + dx / 2, y, z + dz / 2).ax -
          xderiv(plane_wave<CCTK_REAL>, dx)(t, x + dx / 2, y, z + dz / 2).az;
      bz[idx] =
          xderiv(plane_wave<CCTK_REAL>, dx)(t, x, y + dy / 2, z + dz / 2).ay -
          yderiv(plane_wave<CCTK_REAL>, dy)(t, x, y + dy / 2, z + dz / 2).ax;
      rho[idx] = 0.0;
      jx[idx] = 0.0;
      jy[idx] = 0.0;
      jz[idx] = 0.0;
    });
  } else {
    assert(0);
  }
}
extern "C" void MaxwellToyAMReX_Evolve1(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  const CCTK_REAL dt = CCTK_DELTA_TIME;
  const CCTK_REAL dx = CCTK_DELTA_SPACE(0);
  const CCTK_REAL dy = CCTK_DELTA_SPACE(1);
  const CCTK_REAL dz = CCTK_DELTA_SPACE(2);
  constexpr int di = 1;
  const int dj = di * cctk_ash[0];
  const int dk = dj * cctk_ash[1];
  Loop::loop_int(cctkGH, [&](int i, int j, int k, int idx) {
    jx[idx] = jx_p[idx];
    jy[idx] = jy_p[idx];
    jz[idx] = jz_p[idx];
    bx[idx] = bx_p[idx] + dt * ((ey_p[idx + dk] - ey_p[idx]) / dz -
                                (ez_p[idx + dj] - ez_p[idx]) / dy);
    by[idx] = by_p[idx] + dt * ((ez_p[idx + di] - ez_p[idx]) / dx -
                                (ex_p[idx + dk] - ex_p[idx]) / dz);
    bz[idx] = bz_p[idx] + dt * ((ex_p[idx + dj] - ex_p[idx]) / dy -
                                (ey_p[idx + di] - ey_p[idx]) / dx);
    ax[idx] =
        ax_p[idx] - dt * ((phi_p[idx + di] - phi_p[idx]) / dx + ex_p[idx]);
    ay[idx] =
        ay_p[idx] - dt * ((phi_p[idx + dj] - phi_p[idx]) / dy + ey_p[idx]);
    az[idx] =
        az_p[idx] - dt * ((phi_p[idx + dk] - phi_p[idx]) / dz + ez_p[idx]);
  });
}
extern "C" void MaxwellToyAMReX_Evolve2(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  const CCTK_REAL dt = CCTK_DELTA_TIME;
  const CCTK_REAL dx = CCTK_DELTA_SPACE(0);
  const CCTK_REAL dy = CCTK_DELTA_SPACE(1);
  const CCTK_REAL dz = CCTK_DELTA_SPACE(2);
  constexpr int di = 1;
  const int dj = di * cctk_ash[0];
  const int dk = dj * cctk_ash[1];
  Loop::loop_int(cctkGH, [&](int i, int j, int k, int idx) {
    rho[idx] = rho_p[idx] - dt * ((jx[idx] - jx[idx - di]) / dx +
                                  (jy[idx] - jy[idx - dj]) / dy +
                                  (jz[idx] - jz[idx - dk]) / dz);
    ex[idx] = ex_p[idx] - dt * ((by[idx] - by[idx - dk]) / dz -
                                (bz[idx] - bz[idx - dj]) / dy + jx[idx]);
    ey[idx] = ey_p[idx] - dt * ((bz[idx] - bz[idx - di]) / dx -
                                (bx[idx] - bx[idx - dk]) / dz + jy[idx]);
    ez[idx] = ez_p[idx] - dt * ((bx[idx] - bx[idx - dj]) / dy -
                                (by[idx] - by[idx - di]) / dx + jz[idx]);
    phi[idx] = phi_p[idx] - dt * ((ax[idx] - ax[idx - di]) / dx +
                                  (ay[idx] - ay[idx - dj]) / dy +
                                  (ay[idx] - az[idx - dk]) / dz);
  });
}
extern "C" void MaxwellToyAMReX_EstimateError(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  Loop::loop_int(cctkGH,
                 [&](int i, int j, int k, int idx) { regrid_error[idx] = 0; });
}
extern "C" void MaxwellToyAMReX_Error(CCTK_ARGUMENTS) {
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  const CCTK_REAL t = cctk_time;
  const CCTK_REAL x0 = CCTK_ORIGIN_SPACE(0);
  const CCTK_REAL y0 = CCTK_ORIGIN_SPACE(1);
  const CCTK_REAL z0 = CCTK_ORIGIN_SPACE(2);
  const CCTK_REAL dt = CCTK_DELTA_TIME;
  const CCTK_REAL dx = CCTK_DELTA_SPACE(0);
  const CCTK_REAL dy = CCTK_DELTA_SPACE(1);
  const CCTK_REAL dz = CCTK_DELTA_SPACE(2);
  if (CCTK_EQUALS(initial_condition, "plane wave")) {
    Loop::loop_all(cctkGH, [&](int i, int j, int k, int idx) {
      CCTK_REAL x = x0 + (cctk_lbnd[0] + i) * dx;
      CCTK_REAL y = y0 + (cctk_lbnd[1] + j) * dy;
      CCTK_REAL z = z0 + (cctk_lbnd[2] + k) * dz;
      phierr[idx] = phi[idx] - plane_wave(t + dt / 2, x, y, z).phi;
      axerr[idx] = ax[idx] - plane_wave(t, x + dx / 2, y, z).ax;
      ayerr[idx] = ay[idx] - plane_wave(t, x, y + dy / 2, z).ay;
      azerr[idx] = az[idx] - plane_wave(t, x, y, z + dz / 2).az;
      exerr[idx] =
          ex[idx] -
          (-xderiv(plane_wave<CCTK_REAL>, dx)(t + dt / 2, x + dx / 2, y, z)
                .phi -
           tderiv(plane_wave<CCTK_REAL>, dt)(t + dt / 2, x + dx / 2, y, z).ax);
      eyerr[idx] =
          ey[idx] -
          (-yderiv(plane_wave<CCTK_REAL>, dy)(t + dt / 2, x, y + dy / 2, z)
                .phi -
           tderiv(plane_wave<CCTK_REAL>, dt)(t + dt / 2, x, y + dy / 2, z).ay);
      ezerr[idx] =
          ez[idx] -
          (-zderiv(plane_wave<CCTK_REAL>, dz)(t + dt / 2, x, y, z + dz / 2)
                .phi -
           tderiv(plane_wave<CCTK_REAL>, dt)(t + dt / 2, x, y, z + dz / 2).az);
      bxerr[idx] =
          bx[idx] -
          (yderiv(plane_wave<CCTK_REAL>, dy)(t, x, y + dy / 2, z + dz / 2).az -
           zderiv(plane_wave<CCTK_REAL>, dz)(t, x, y + dy / 2, z + dz / 2).ay);
      byerr[idx] =
          by[idx] -
          (zderiv(plane_wave<CCTK_REAL>, dz)(t, x + dx / 2, y, z + dz / 2).ax -
           xderiv(plane_wave<CCTK_REAL>, dx)(t, x + dx / 2, y, z + dz / 2).az);
      bzerr[idx] =
          bz[idx] -
          (xderiv(plane_wave<CCTK_REAL>, dx)(t, x, y + dy / 2, z + dz / 2).ay -
           yderiv(plane_wave<CCTK_REAL>, dy)(t, x, y + dy / 2, z + dz / 2).ax);
      rhoerr[idx] = 0.0;
      jxerr[idx] = 0.0;
      jyerr[idx] = 0.0;
      jzerr[idx] = 0.0;
    });
  } else {
    assert(0);
  }
}
} // namespace MaxwellToyAMReX

                     /*TODO*/ 0 * 4 * M_PI * central_potential(t, x, y, z));

                     4 * M_PI * central_potential(t, x, y, z));

AMReX/HydroToyAMReX
AMReX/MaxwellToyAMReX