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authorhawke <hawke@578cdeb0-5ea1-4b81-8215-5a3b8777ee0b>2004-07-06 15:53:20 +0000
committerhawke <hawke@578cdeb0-5ea1-4b81-8215-5a3b8777ee0b>2004-07-06 15:53:20 +0000
commit7b063721ba62b28bcc768c1c188b7a95cb5d7cc5 (patch)
treeb5e2d21fd86f74efe2610c4e25e9396db5f349b6 /doc
parent2c8448f84da0b9f4ae13cf1a02c71e0c626e4782 (diff)
AlphaThorns -> CactusBase in document labels and references.
git-svn-id: http://svn.cactuscode.org/arrangements/CactusNumerical/MoL/trunk@73 578cdeb0-5ea1-4b81-8215-5a3b8777ee0b
Diffstat (limited to 'doc')
-rw-r--r--doc/documentation.tex86
1 files changed, 43 insertions, 43 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex
index 56c03a6..b8ca497 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -136,20 +136,20 @@
% \subsection{Acknowledgements}
\section{Purpose}
-\label{AlphaThorns_MoL_sec:purpose}
+\label{CactusBase_MoL_sec:purpose}
The Method of Lines (MoL) converts a (system of) partial differential
equation(s) into an ordinary differential equation containing some
spatial differential operator. As an example, consider writing the
hyperbolic system of PDE's
\begin{equation}
- \label{AlphaThorns_MoL_eq:mol1}
+ \label{CactusBase_MoL_eq:mol1}
\partial_t {\bf q} + {\bf A}^i({\bf q}) \partial_i {\bf B}({\bf q})
= {\bf s}({\bf q})
\end{equation}
in the alternative form
\begin{equation}
- \label{AlphaThorns_MoL_eq:mol2}
+ \label{CactusBase_MoL_eq:mol2}
\partial_t {\bf q} = {\bf L}({\bf q}),
\end{equation}
which (assuming a given discretization of space) is an ODE.
@@ -165,7 +165,7 @@ coupling different physical models.
MoL can be used for hyperbolic, parabolic and even elliptic problems
(although I definitely don't recommend the latter). As it currently
stands it is set up for systems of equations in the first order type
-form of equation~(\ref{AlphaThorns_MoL_eq:mol2}). If you want to implement a
+form of equation~(\ref{CactusBase_MoL_eq:mol2}). If you want to implement a
multilevel scheme such as leapfrog it is not obvious to me that MoL is
the thing to use. However if you have lots of thorns that you want to
interact, for example ADM\_BSSN and a hydro code plus maybe EM or a
@@ -184,18 +184,18 @@ Mesh Refinement work.
For more information on the Method of Lines the most comprehensive
references are the works of Jonathan
-Thornburg~\cite{AlphaThorns_MoL_Thornburg93,AlphaThorns_MoL_Thornburg99}
+Thornburg~\cite{CactusBase_MoL_Thornburg93,CactusBase_MoL_Thornburg99}
- see especially section 7.3 of the thesis. From the CFD viewpoint the
-review of ENO methods by Shu,~\cite{AlphaThorns_MoL_Shu99}, has some
+review of ENO methods by Shu,~\cite{CactusBase_MoL_Shu99}, has some
information. For relativistic fluids the paper of Neilsen and
-Choptuik~\cite{AlphaThorns_MoL_Neilsen00} is also quite good.
+Choptuik~\cite{CactusBase_MoL_Neilsen00} is also quite good.
\section{How to use}
-\label{AlphaThorns_MoL_sec:use}
+\label{CactusBase_MoL_sec:use}
\subsection{Thorn users}
-\label{AlphaThorns_MoL_sec:useruse}
+\label{CactusBase_MoL_sec:useruse}
For those who used the old version of MoL, this version is
unfortunately slightly more effort to use. That is, for most methods
@@ -215,7 +215,7 @@ methods (first to fourth order) and {\tt ICN} for the implementation
of the Iterative Crank Nicholson method in generic form.
Full descriptions of the currently implemented methods are given in
-section~\ref{AlphaThorns_MoL_sec:methods}.
+section~\ref{CactusBase_MoL_sec:methods}.
The parameter {\tt MoL\_Intermediate\_Steps} controls the number of
intermediate steps for the ODE solver. For the generic Runge-Kutta
@@ -252,7 +252,7 @@ purely first order in space and time you may wish to set this to {\tt
"no"}.
\subsection{Thorn writers}
-\label{AlphaThorns_MoL_sec:writeruse}
+\label{CactusBase_MoL_sec:writeruse}
To port an existing thorn using the method of lines, or to write a new
thorn using it, should hopefully be relatively simple. As an example,
@@ -345,9 +345,9 @@ evolved (in ADM) or constrained (in ADM\_BSSN), both of which have
precedence. To register your GFs with MoL schedule a routine in the
bin {\tt MoL\_Register} which just contains the relevant function
calls. For an evolved variable the GF corresponding to the update
-term (${\bf L}({\bf q})$ in equation~(\ref{AlphaThorns_MoL_eq:mol2}))
+term (${\bf L}({\bf q})$ in equation~(\ref{CactusBase_MoL_eq:mol2}))
should be registered at the same time. The appropriate functions are
-given in section~\ref{AlphaThorns_MoL_sec:molfns}.
+given in section~\ref{CactusBase_MoL_sec:molfns}.
These functions are provided using function aliasing. For details on
using function aliasing, see sections B10.5 and F2.2.3 of the
@@ -389,7 +389,7 @@ USES FUNCTION MoLChangeToNone
Note that the list of paramters not complete; see the section on
parameters for the use of arrays or complex variables. However, the
list of functions is, and is expanded on in
-section~\ref{AlphaThorns_MoL_sec:molfns}. MoL will check whether a
+section~\ref{CactusBase_MoL_sec:molfns}. MoL will check whether a
group or variable is a GF or an array and whether it is real or
complex. Note that currently complex variable support is disabled.
@@ -415,7 +415,7 @@ of boundary conditions\footnote{It is possible to alter the
updated and do not need setting. This is slightly tricksy. For an
example of how this would work see the new radiative boundary
condition in ADM\_BSSN. For more on this see section 7.3.4
- of~\cite{AlphaThorns_MoL_Thornburg93}.}, the solution of elliptic
+ of~\cite{CactusBase_MoL_Thornburg93}.}, the solution of elliptic
equations (although this would be a very expensive place to solve
them, some sets of equations might require the updating of some
variables by constraints in this fashion). When applying boundary
@@ -437,7 +437,7 @@ separate processors will be dealt with by the MoL thorn, the driver
the flesh.
\subsection{Evolution method writers}
-\label{AlphaThorns_MoL_sec:evol-meth-writ}
+\label{CactusBase_MoL_sec:evol-meth-writ}
If you want to try adding a new evolution method to MoL the simplest
way is to use the generic table option to specify it completely in the
@@ -445,12 +445,12 @@ parameter file - no coding is required at all.
All the generic methods evolve the equation
\begin{equation}
- \label{AlphaThorns_MoL_eq:mol3}
+ \label{CactusBase_MoL_eq:mol3}
\partial_t {\bf q} = {\bf L}({\bf q})
\end{equation}
using the following algorithm for an $N$-step method:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:genrk1}
+ \label{CactusBase_MoL_eq:genrk1}
{\bf q}^{(0)} & = & {\bf q}^n, \nonumber \\
{\bf q}^{(i)} & = & \sum_{k=0}^{i-1} \left( \alpha_{ik} {\bf
q}^{(k)} \right) + \Delta t \beta_{i-1} {\bf L} ( {\bf q}^{(i-1)} ),
@@ -467,7 +467,7 @@ will use. This table is created from the string parameter {\tt
As an example, the standard TVD RK2 method that is implemented both in
optimized and generic form is written as
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:rk2}
+ \label{CactusBase_MoL_eq:rk2}
{\bf q}^{(1)} & = & {\bf q}^n + \Delta t {\bf L} ({\bf q}^n), \\
{\bf q}^{n+1} & = & \frac{1}{2} \left( {\bf q}^n + {\bf q}^{(1)} +
\Delta t {\bf L} ({\bf q}^{(1)}) \right).
@@ -499,7 +499,7 @@ you are happy with the method. To do this you should
\end{itemize}
\section{Example}
-\label{AlphaThorns_MoL_sec:example}
+\label{CactusBase_MoL_sec:example}
As a fairly extended example of how to use MoL I'll outline how
ADM\_BSSN works in this context. The actual implementation of this is
@@ -605,14 +605,14 @@ variables back to the standard ADM variables in {\tt
of the lapse in {\tt ADM\_BSSN\_LapseChange}.
\section{Time evolution methods provided by MoL}
-\label{AlphaThorns_MoL_sec:methods}
+\label{CactusBase_MoL_sec:methods}
The default method is Iterative Crank-Nicholson. There are many ways
of implementing this. The standard {\tt "ICN"} and {\tt
"Generic"}/{\tt"ICN"} methods both implement the following, assuming
an $N$ iteration method:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:icn}
+ \label{CactusBase_MoL_eq:icn}
{\bf q}^{(0)} & = & {\bf q}^{n}, \\
{\bf q}^{(i)} & = & {\bf q}^{(0)} + \frac{\Delta t}{2} {\bf L}({\bf
q}^{(i-1)}), \quad i = 1,\dots,N-1, \\
@@ -624,7 +624,7 @@ an $N$ iteration method:
The ``averaging'' ICN method {\tt "ICN-avg"} instead calculates
intermediate steps before averaging:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:icn-avg}
+ \label{CactusBase_MoL_eq:icn-avg}
{\bf q}^{(0)} & = & {\bf q}^{n}, \\
\tilde{{\bf q}}^{(i)} & = & \frac{1}{2}\left( {\bf q}^{(i)} + {\bf
q}^{n} \right), \quad i = 0,\dots,N-1 \\
@@ -634,10 +634,10 @@ intermediate steps before averaging:
\end{eqnarray}
The Runge-Kutta methods are those typically used in hydrodynamics by,
-e.g., Shu and others - see~\cite{AlphaThorns_MoL_Shu99} for
+e.g., Shu and others - see~\cite{CactusBase_MoL_Shu99} for
example. Explicitly the first order method is the Euler method:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:rk1}
+ \label{CactusBase_MoL_eq:rk1}
{\bf q}^{(0)} & = & {\bf q}^{n}, \\
{\bf q}^{(1)} & = & {\bf q}^{(0)} + \Delta t {\bf L}(\tilde{{\bf
q}}^{(0)}), \\
@@ -645,7 +645,7 @@ example. Explicitly the first order method is the Euler method:
\end{eqnarray}
The second order method is:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:rk2}
+ \label{CactusBase_MoL_eq:rk2}
{\bf q}^{(0)} & = & {\bf q}^{n}, \\
{\bf q}^{(1)} & = & {\bf q}^{(0)} + \Delta t {\bf L} ({\bf q}^{(0)}), \\
{\bf q}^{(2)} & = & \frac{1}{2} \left( {\bf q}^{(0)} + {\bf q}^{(1)}
@@ -654,7 +654,7 @@ The second order method is:
\end{eqnarray}
The third order method is:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:rk3}
+ \label{CactusBase_MoL_eq:rk3}
{\bf q}^{(0)} & = & {\bf q}^{n}, \\
{\bf q}^{(1)} & = & {\bf q}^{(0)} + \Delta t {\bf L} ({\bf q}^{(0)}), \\
{\bf q}^{(2)} & = & \frac{1}{4} \left( 3 {\bf q}^{(0)} + {\bf q}^{(1)} +
@@ -665,7 +665,7 @@ The third order method is:
\end{eqnarray}
The fourth order method, which is not strictly TVD, is:
\begin{eqnarray}
- \label{AlphaThorns_MoL_eq:rk4}
+ \label{CactusBase_MoL_eq:rk4}
{\bf q}^{(0)} & = & {\bf q}^{n}, \\
{\bf q}^{(1)} & = & {\bf q}^{(0)} + \frac{1}{2} \Delta t {\bf L}
({\bf q}^{(0)}), \\
@@ -680,7 +680,7 @@ The fourth order method, which is not strictly TVD, is:
\end{eqnarray}
\section{Functions provided by MoL}
-\label{AlphaThorns_MoL_sec:molfns}
+\label{CactusBase_MoL_sec:molfns}
All the functions listed below return error codes in theory. However
at this current point in time they always return 0 (success). Any
@@ -693,7 +693,7 @@ directly through header files, but this feature may be phased
out. Using function aliasing is the recommended method.
\begin{FunctionDescription}{MoLRegisterEvolved}
- \label{AlphaThorns_MoL_MoLRegisterEvolved}
+ \label{CactusBase_MoL_MoLRegisterEvolved}
Tells MoL that the given GF is in the evolved category with the
associated update GF.
@@ -772,7 +772,7 @@ ierr = MoLRegisterEvolved(EvolvedIndex, RHSIndex)
\begin{FunctionDescription}{MoLRegisterConstrained}
- \label{AlphaThorns_MoL_MoLRegisterConstrained}
+ \label{CactusBase_MoL_MoLRegisterConstrained}
Tells MoL that the given GF is in the constrained category.
@@ -843,7 +843,7 @@ ierr = MoLRegisterConstrained(ConstrainedIndex)
\begin{FunctionDescription}{MoLRegisterSaveAndRestore}
- \label{AlphaThorns_MoL_MoLRegisterSaveAndRestore}
+ \label{CactusBase_MoL_MoLRegisterSaveAndRestore}
Tells MoL that the given GF is in the Save and Restore category.
@@ -914,7 +914,7 @@ ierr = MoLRegisterSaveAndRestore(SandRIndex)
\begin{FunctionDescription}{MoLRegisterEvolvedGroup}
- \label{AlphaThorns_MoL_MoLRegisterEvolvedGroup}
+ \label{CactusBase_MoL_MoLRegisterEvolvedGroup}
Tells MoL that the given group is in the evolved category with the
associated update group.
@@ -990,7 +990,7 @@ ierr = MoLRegisterEvolvedGroup(EvolvedIndex, RHSIndex)
\begin{FunctionDescription}{MoLRegisterConstrainedGroup}
- \label{AlphaThorns_MoL_MoLRegisterConstrainedGroup}
+ \label{CactusBase_MoL_MoLRegisterConstrainedGroup}
Tells MoL that the given group is in the constrained category.
@@ -1061,7 +1061,7 @@ ierr = MoLRegisterConstrainedGroup(ConstrainedIndex)
\begin{FunctionDescription}{MoLRegisterSaveAndRestoreGroup}
- \label{AlphaThorns_MoL_MoLRegisterSaveAndRestoreGroup}
+ \label{CactusBase_MoL_MoLRegisterSaveAndRestoreGroup}
Tells MoL that the given group is in the Save and Restore category.
@@ -1129,7 +1129,7 @@ ierr = MoLRegisterSaveAndRestoreGroup(SandRIndex)
\begin{FunctionDescription}{MoLChangeToEvolved}
- \label{AlphaThorns_MoL_MoLChangeToEvolved}
+ \label{CactusBase_MoL_MoLChangeToEvolved}
Sets a GF to belong to the evolved category, with the associated
update GF. Not used for the initial setting.
@@ -1211,7 +1211,7 @@ ierr = MoLChangeToEvolved(EvolvedIndex, RHSIndex)
\begin{FunctionDescription}{MoLChangeToConstrained}
- \label{AlphaThorns_MoL_MoLChangeToConstrained}
+ \label{CactusBase_MoL_MoLChangeToConstrained}
Sets a GF to belong to the constrained category. Not used for the
initial setting.
@@ -1286,7 +1286,7 @@ ierr = MoLChangeToConstrained(EvolvedIndex)
\begin{FunctionDescription}{MoLChangeToSaveAndRestore}
- \label{AlphaThorns_MoL_MoLChangeToSaveAndRestore}
+ \label{CactusBase_MoL_MoLChangeToSaveAndRestore}
Sets a GF to belong to the Save and Restore category. Not used for the
initial setting.
@@ -1361,7 +1361,7 @@ ierr = MoLChangeToSaveAndRestore(SandRIndex)
\begin{FunctionDescription}{MoLChangeToNone}
- \label{AlphaThorns_MoL_MoLChangeToNone}
+ \label{CactusBase_MoL_MoLChangeToNone}
Sets a GF to belong to the ``unknown'' category. Not used for the
initial setting.
@@ -1437,7 +1437,7 @@ ierr = MoLChangeToNone(RemoveIndex)
\begin{thebibliography}{9}
-\bibitem{AlphaThorns_MoL_Thornburg93}
+\bibitem{CactusBase_MoL_Thornburg93}
J. Thornburg.
\newblock {N}umerical {R}elativity in {B}lack {H}ole {S}pacetimes.
\newblock Unpublished thesis, University of British Columbia.
@@ -1445,14 +1445,14 @@ J. Thornburg.
\newblock Available from \mbox{\tt
http://www.aei.mpg.de/\~{}jthorn/phd/html/phd.html}.
-\bibitem{AlphaThorns_MoL_Thornburg99}
+\bibitem{CactusBase_MoL_Thornburg99}
J. Thornburg.
\newblock A {3+1} {C}omputational {S}cheme for {D}ynamic {S}pherically
{S}ymmetric {B}lack {H}ole {S}pacetimes -- {II}: {T}ime {E}volution.
\newblock Preprint {\tt gr-qc/9906022}, submitted to {\em Phys. Rev.}
{\bf D}.
-\bibitem{AlphaThorns_MoL_Shu99}
+\bibitem{CactusBase_MoL_Shu99}
C. Shu.
\newblock {H}igh {O}rder {ENO} and {WENO} {S}chemes for
{C}omputational {F}luid {D}ynamics.
@@ -1463,7 +1463,7 @@ C. Shu.
{S}chemes for {H}yperbolic {C}onservation {L}aws} at {\tt
http://www.icase.edu/library/reports/rdp/97/97-65RDP.tex.refer.html}.
-\bibitem{AlphaThorns_MoL_Neilsen00}
+\bibitem{CactusBase_MoL_Neilsen00}
D.~W. Neilsen and M.~W. Choptuik.
\newblock Ultrarelativistic fluid dynamics.
\newblock {\em Class. Quantum Grav.}, {\bf 17}:\penalty0 733--759, 2000.