path: root/doc/documentation.tex

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% 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@aei.mpg.de\textgreater}

% The title of the document (not necessarily the name of the Thorn)
\title{SymBase}

% the date your document was last changed, if your document is in CVS,
% please use:
\date{$ $Date$ $}

\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}
Thorn SymBase contains a registry for symmetry conditions and for
symmetry faces.
\end{abstract}

% The following sections are suggestive only.
% Remove them or add your own.



\section{Introduction}

Thorn SymBase contains a registry for symmetry conditions and for
symmetry faces.  Other thorns that implement symmetry boundary
conditions register themselves with this thorn and reserve certain
faces of the grid, so that no other boundary condition is applied
there.  Thorns that implement physical boundary conditions should
query this thorn about the set of faces that have symmetry boundary
conditions and should not apply the physical boundary condition there.



\section{Registering Symmetry Conditions}

Each thorn that implements a symmetry boundary condition should
register itself with thorn SymBase.  This has no consequences per se,
but it reservers a symmetry handle for later use.  The API for
registering and querying symmetry names and handles is

\begin{verbatim}
CCTK_INT FUNCTION
    SymmetryRegister (CCTK_STRING IN sym_name)

CCTK_INT FUNCTION
    SymmetryHandleOfName (CCTK_STRING IN sym_name)

CCTK_POINTER_TO_CONST FUNCTION
    SymmetryNameOfHandle (CCTK_INT IN sym_handle)
\end{verbatim}

The routine \texttt{SymmetryRegister} should be called in a routine
that has been scheduled in the schedule group
\texttt{SymmetryRegister}.

\begin{quote}
Note: We have the API in the specification, we have it in the
interface file, in the source code, and in a header file, and I
duplicated it into grdoc headers.  I refuse to write and describe and
cross-check the API a \emph{sixth} time in latex.  At some point, we
have to start using tools for that.  Please read the grdoc headers or
the grdoc-produced html files for a detailed description.
\end{quote}



\section{Registering Symmetries for Faces}

Thorn SymBase keeps two registries.  The first, described in the
previous section, contains the set of symmetry boundary conditions
that exist at all.  The second, described here, describes which face
of the grids have which symmetry condition applied to it, if any.
Each such mapping from grid face to symmetry condition is described by
a symmetry table with the following entries:

\begin{verbatim}
CCTK_INT symmetry_handle[]
CCTK_INT symmetry_zone_width[]
\end{verbatim}

Each of these arrays contains one element per face, numbered in the
same way as the \texttt{cctk\_bbox} array.  The
\texttt{symmetry\_handle} is a symmetry handle as described in the
previous section, and the \texttt{symmetry\_zone\_width} is the width
of the symmetry zone.

Code outside SymBase should not modify these table entries.

There is one such table for the grid hierarchy, which is valid for all
grid functions.  There is additionally one such table for each grid
array group.

The API for registering symmetries for faces is

\begin{verbatim}
CCTK_INT FUNCTION
    SymmetryRegisterGrid
         (CCTK_POINTER IN cctkGH,
          CCTK_INT IN sym_handle,
          CCTK_INT IN ARRAY which_faces,
          CCTK_INT IN ARRAY symmetry_zone_width)

CCTK_INT FUNCTION
    SymmetryRegisterGI
        (CCTK_POINTER IN cctkGH,
         CCTK_INT IN sym_handle,
         CCTK_INT IN ARRAY which_faces,
         CCTK_INT IN ARRAY symmetry_zone_width,
         CCTK_INT IN group_index)

CCTK_INT FUNCTION
    SymmetryRegisterGN
        (CCTK_POINTER IN cctkGH,
         CCTK_INT IN sym_handle,
         CCTK_INT IN ARRAY which_faces,
         CCTK_INT IN ARRAY symmetry_zone_width,
         CCTK_STRING IN group_name)
\end{verbatim}

The first routine registers a symmetry condition for certain faces for
the grid hierarchy, the other two routines register for grid array
groups.  \texttt{sym\_handle} must be a symmetry handle obtained as
described in the previous section.  \texttt{which\_faces} and
\texttt{symmetry\_zone\_width} are arrays with one element per face,
numbered in the same way as the \texttt{cctk\_bbox} array.
\texttt{which\_faces} selects which faces to register, and
\texttt{symmetry\_zone\_width} sets the number of symmetry zones for
these faces.

It is obviously not possible to register multiple symmetry conditions
for the same face.



\section{Querying Symmetries of Faces}

Physical boundary conditions need to know to which faces they should
apply the boundary condition.  They need to query SymBase for the set
of faces that have a symmetry boundary condition, and they must not
apply their physical boundary condition there.  The API is

\begin{verbatim}
CCTK_INT FUNCTION
    SymmetryTableHandleForGrid (CCTK_POINTER_TO_CONST IN cctkGH)

CCTK_INT FUNCTION
    SymmetryTableHandleForGI
        (CCTK_POINTER_TO_CONST IN cctkGH,
         CCTK_INT IN group_index)

CCTK_INT FUNCTION
    SymmetryTableHandleForGN
        (CCTK_POINTER_TO_CONST IN cctkGH,
         CCTK_STRING IN group_name)
\end{verbatim}

These functions return the the handle for the symmetry table for the
grid hierarchy or for the grid array group, respectively.  The table
entry \texttt{symmetry\_handle} contains the symmetry handle for the
symmetry boundary condition, or a negative number if the face has no
symmetry boundary condition associated with it.

The code to find out which boundaries should have a physical boundary
condition applied might look as follows:

\begin{verbatim}
#include "cctk.h"
#include "util_Table.h"

CCTK_INT symtable;
CCTK_INT symbnd[6];
int face;
int ierr;

symtable = SymmetryTableHandleForGrid (cctkGH);
if (symtable<0)
  CCTK_VWarn(0, __LINE__, __FILE__, "Thorn_Name", "symtable is out of bounds");

ierr = Util_TableGetIntArray (symtable, 6, symbnd, "symmetry_handle");
if (ierr!=6)
  CCTK_VWarn(0, __LINE__, __FILE__, "Thorn_Name", "Util_TableGetIntArray returned error");

for (face=0; face<6; ++face) {
  if (cctk_bbox[face] && symbnd[face]<0) {
    /* Apply physical boundary condition here */
  }
}
\end{verbatim}

\hrule

\begin{verbatim}
#include "util_Table.h"

CCTK_INT symtable
CCTK_INT symbnd(6)
integer face
integer ierr

symtable = SymmetryTableHandleForGrid (cctkGH)
if (symtable<0) call CCTK_WARN (0, "internal error")

call Util_TableGetIntArray (ierr, int(symtable), 6, symbnd, "symmetry_handle")
if (ierr/=6) call CCTK_WARN (0, "internal error")

do face=1,6
  if (cctk_bbox(face)/=0 .and. symbnd(face)<0) then
    ! Apply physical boundary condition here
  end if
end do
\end{verbatim}



\section{Symmetry Interpolation}

When the computational domain has symmetries, then it is often very
convenient to be able to interpolate at points that are not present on
the actual computational grid, but can be mapped into the grid through
the symmetries.  Thorn SymBase provides a mechanism by which symmetry
conditions can register routines that handle this mapping when a
global interpolator is called.  Additionally, the driver has to be
aware that it calls thorn SymBase's mapping routine before it actually
interpolates.  The whole mechanism is transparent for the user.

The mechanism by which the grid points are mapped into the domain
works as follows:
\begin{enumerate}
\item The user calls \texttt{CCTK\_InterpGridArrays} with a list of coordinates.
\item The flesh forwards this call to the driver.
\item The driver calls SymBase's aliased function,
  \texttt{SymmetryInterpolate}, passing along all arguments.
\item SymBase sets a flag for all boundaries that have a symmetry
  condition associated with it, and then calls
  \texttt{SymmetryInterpolateFaces}, passing along all arguments.
  This is the beginning of a chain of recursive calls.
\item \texttt{SymmetryInterpolateFaces} checks whether any faces are
  flagged.
\item If no faces are flagged, SymBase calls the driver's aliased
  function \texttt{DriverInterpolate}, which performs the actual
  interpolation.  This ends the chain of recursive calls.
\item If there are faces with symmetry conditions flagged, SymBase
  chooses one such face, and then calls this face's symmetry
  condition's ``symmetry interpolation'' routine, passing along all
  arguments.
\item The ``symmetry interpolation'' routine maps the coordinates into
  the domain by applying the symmetry condition for this face.  It
  then removes the flag for the corresponding face, and calls
  \texttt{SymmetryInterpolateFaces}, passing along the arguments with
  the changed interpolation locations.
\item After the actual interpolation has happened in the driver, the
  recursive call will return.  The ``symmetry interpolation'' routine
  then examines the tensor types of the interpolated quantities and
  un-maps the values back onto their original locations.  That is,
  e.g., after a reflection on the lower $x$-boundary, $x$-components
  of vectors need their sign changed.
\item The chain of recursive calls unravels until the call to
  \texttt{CCTK\_InterpGridArrays} returns.
\end{enumerate}
\begin{figure}[tb]
\begin{center}
\includegraphics[scale=.833,clip=true]{fig/recursion.eps}
\end{center}
\caption[Symmetry interpolation] {
  The recursive calls involved in symmety interpolation.
  Values of grid functions $a$ at global cartesian coordinates $x$ are 
  calculated by nested calls to the symmetry interpolators, which first
  apply the symmetry transformation to the coordinates.  When all
  the symmetries have been applied, the local interpolator is called,
  producing the interpolation of grid function values in the local basis.
  As the symmetry interpolators return, they apply the inverse basis
  transformation to the interpolated grid function values.
}
\label{SymBase_recursion}
\end{figure}

This mechanism has thus four players:
\begin{itemize}
\item The driver forwards the call to SymBase so that the list of
  interpolation points can be mapped into the domain.
\item Thorn SymBase controls which symmetry conditions perform this
  mapping on which faces.
\item Each symmetry boundary condition has to register a ``symmetry
  interpolation'' routine that first maps the points into the domain,
  then calls SymBase recursively, and finally corrects the tensor
  types of the interpolated quantities.
\item Finally, the user calls \texttt{CCTK\_InterpGridArrays} as before, and
  everything happens transparently for her.
\end{itemize}



\subsection{Driver Interaction}

The driver has to call SymBase's aliased function
\texttt{SymmetryInterpolate}, and has to provide an aliased function
\texttt{DriverInterpolate}.  Both functions have essentially the same
prototype as \texttt{CCTK\_InterpGridArrays}, which are:

\begin{verbatim}
CCTK_INT FUNCTION
    SymmetryInterpolate
        (CCTK_POINTER_TO_CONST IN cctkGH,
         CCTK_INT IN N_dims,
         CCTK_INT IN local_interp_handle,
         CCTK_INT IN param_table_handle,
         CCTK_INT IN coord_system_handle,
         CCTK_INT IN N_interp_points,
         CCTK_INT IN interp_coords_type,
         CCTK_POINTER_TO_CONST ARRAY IN interp_coords,
         CCTK_INT IN N_input_arrays,
         CCTK_INT ARRAY IN input_array_indices,
         CCTK_INT IN N_output_arrays,
         CCTK_INT ARRAY IN output_array_types,
         CCTK_POINTER ARRAY IN output_arrays)
\end{verbatim}

\begin{verbatim}
CCTK_INT FUNCTION
    DriverInterpolate
        (CCTK_POINTER_TO_CONST IN cctkGH,
         CCTK_INT IN N_dims,
         CCTK_INT IN local_interp_handle,
         CCTK_INT IN param_table_handle,
         CCTK_INT IN coord_system_handle,
         CCTK_INT IN N_interp_points,
         CCTK_INT IN interp_coords_type,
         CCTK_POINTER_TO_CONST ARRAY IN interp_coords,
         CCTK_INT IN N_input_arrays,
         CCTK_INT ARRAY IN input_array_indices,
         CCTK_INT IN N_output_arrays,
         CCTK_INT ARRAY IN output_array_types,
         CCTK_POINTER ARRAY IN output_arrays)
\end{verbatim}



\subsection{Interaction With Symmetry Conditions}

The symmetry conditions have to register their ``symmetry
interpolation'' routines by calling SymBase's aliased function
\texttt{SymmetryRegisterGridInterpolator}.  The ``symmetry
interpolation'' routine must use C linkage and must have the prototype

\begin{verbatim}
CCTK_INT symmetry_interpolate
    (CCTK_POINTER_TO_CONST IN cctkGH,
     CCTK_INT IN N_dims,
     CCTK_INT IN local_interp_handle,
     CCTK_INT IN param_table_handle,
     CCTK_INT IN coord_system_handle,
     CCTK_INT IN N_interp_points,
     CCTK_INT IN interp_coords_type,
     CCTK_POINTER_TO_CONST ARRAY IN interp_coords,
     CCTK_INT IN N_input_arrays,
     CCTK_INT ARRAY IN input_array_indices,
     CCTK_INT IN N_output_arrays,
     CCTK_INT ARRAY IN output_array_types,
     CCTK_POINTER ARRAY IN output_arrays,
     CCTK_INT IN faces)
\end{verbatim}

These arguments are essentially the same as those for
\texttt{CCTK\_InterpGridArrays}, except that the bit field \texttt{faces} flags
those faces that still need their symmetry boundary condition applied to
the interpolation points.  The aliased function
\texttt{SymmetryRegisterGridInterpolator} has the prototype

\begin{verbatim}
CCTK_INT FUNCTION                                           \
    SymmetryRegisterGridInterpolator                        \
        (CCTK_POINTER IN cctkGH,                            \
         CCTK_INT IN sym_handle,                            \
         CCTK_INT CCTK_FPOINTER IN symmetry_interpolate     \
             (CCTK_POINTER_TO_CONST IN cctkGH,              \
              CCTK_INT IN N_dims,                           \
              CCTK_INT IN local_interp_handle,              \
              CCTK_INT IN param_table_handle,               \
              CCTK_INT IN coord_system_handle,              \
              CCTK_INT IN N_interp_points,                  \
              CCTK_INT IN interp_coords_type,               \
              CCTK_POINTER_TO_CONST ARRAY IN interp_coords, \
              CCTK_INT IN N_input_arrays,                   \
              CCTK_INT ARRAY IN input_array_indices,        \
              CCTK_INT IN N_output_arrays,                  \
              CCTK_INT ARRAY IN output_array_types,         \
              CCTK_POINTER ARRAY IN output_arrays,          \
              CCTK_INT IN faces))
\end{verbatim}

which takes a function pointer to the aforementioned ``symmetry
interpolation'' routine, while \texttt{sym\_handle} specifies which
symmetry condition this routine is for.  This handle must have been
obtained from \texttt{SymmetryRegister}.

\begin{quote}
  The routine \texttt{SymmetryRegisterGridInterpolator} must be called
  \emph{after} the symmetry faces have been selected by the call to
  \texttt{SymmetryRegisterGrid}.
\end{quote}



\section{Tensor Types}

Cactus supports declaring the \emph{tensor type} of grid function
groups.  These tensor types define how the grid functions, which are
supposed to be tensor components, transform under various
transformations, such as reflections and rotations.

The tensor types are not declared directly; instead, a \emph{tensor
type alias} is declared.  The following tensor type aliases are
currently known and supported:
\begin{description}
\item[\texttt{scalar}:] a scalar $\rho$
\item[\texttt{u}:] a vector $\beta^i$
\item[\texttt{d}:] a covector $s_i$
\item[\texttt{dd\_sym}:] a symmetric rank two tensor $\gamma_{ij}$
\end{description}
(More tensor type aliases are likely to be defined in the future.)

In addition to the tensor type, one can also declare the \emph{tensor
weight} and a \emph{tensor metric}.  The tensor weight specifies the
behaviour under transformations that change the volume element.  The
tensor metric specifies what metric has to be used to raise or lower
indices for that quantity.

Last but not least, a \emph{tensor special} can be defined for
quantities that do not transform as tensor.  The currently supported
tensor specials are
\begin{description}
\item[\texttt{Gamma}:]
   for the transformation behaviour of the $\Gamma^i$ variables of the
   BSSN formalism; it is $\Gamma^i := - \gamma^{jk} \Gamma^i_{jk}$
   with $\Gamma^i_{jk} := \frac{1}{2} \gamma^{il} \left( \partial_k
   \gamma_{lj} + \partial_j \gamma_{lk} - \partial_l \gamma_{jk}
   \right)$
\item[\texttt{log}:]
   for the transformation behaviour of the variable $\phi$ of the BSSN
   formalism; it is $\phi := \log \psi$ with $\psi^{12} := \det
   \gamma_{ij}$.
\end{description}

\subsection{Example Tensor Type Declarations}

From CactusWave/WaveToy:
\begin{verbatim}
CCTK_REAL scalarevolve TYPE=gf TAGS='tensortypealias="scalar"'
\end{verbatim}

From CactusEinstein/ADMBase:
\begin{verbatim}
CCTK_REAL metric TYPE=gf TAGS='tensortypealias="dd_sym" tensormetric="ADMBase::metric"'
CCTK_REAL curv TYPE=gf TAGS='tensortypealias="dd_sym" tensormetric="ADMBase::metric"'
CCTK_REAL lapse TYPE=gf TAGS='tensortypealias="scalar" tensormetric="ADMBase::metric"'
CCTK_REAL shift TYPE=gf TAGS='tensortypealias="U" tensormetric="ADMBase::metric"'
\end{verbatim}

From AEIThorns/BSSN\_MoL:
\begin{verbatim}
CCTK_REAL ADM_BSSN_B TYPE=gf \
    TAGS='tensortypealias="u" tensormetric="ADMBase::metric"'
CCTK_REAL ADM_BSSN_dtlapse TYPE=gf \
    TAGS='tensortypealias="scalar" tensormetric="ADMBase::metric"'
CCTK_REAL ADM_BSSN_phi TYPE=gf \
    TAGS='tensortypealias="scalar" tensormetric="BSSN_MoL::ADM_BSSN_metric" \
          tensorweight=0.16666666666666667 tensorspecial="log"'
CCTK_REAL ADM_BSSN_metric TYPE=gf \
    TAGS='tensortypealias="dd_sym" tensormetric="BSSN_MoL::ADM_BSSN_metric" \
          tensorweight=-0.66666666666666667'
CCTK_REAL ADM_BSSN_K TYPE=gf \
    TAGS='tensortypealias="scalar" tensormetric="BSSN_MoL::ADM_BSSN_metric"'
CCTK_REAL ADM_BSSN_curv TYPE=gf \
    TAGS='tensortypealias="dd_sym" tensormetric="BSSN_MoL::ADM_BSSN_metric" \
          tensorweight=-0.66666666666666667'
CCTK_REAL ADM_BSSN_gamma TYPE=gf \
    TAGS='tensortypealias="u" tensormetric="BSSN_MoL::ADM_BSSN_metric" \
          tensorweight=0.66666666666666667 tensorspecial="Gamma"'
\end{verbatim}

% Do not delete next line
% END CACTUS THORNGUIDE

\end{document}