diff --git a/Docs/thornlist/spacetimex.th b/Docs/thornlist/spacetimex.th index a01f1bc2..580c5da1 100644 --- a/Docs/thornlist/spacetimex.th +++ b/Docs/thornlist/spacetimex.th @@ -171,6 +171,7 @@ SpacetimeX/AHFinderX SpacetimeX/BrillLindquist SpacetimeX/Cowling SpacetimeX/NewRadX +SpacetimeX/TestNewRadX SpacetimeX/Punctures SpacetimeX/PunctureTracker SpacetimeX/SphericalHarmonics diff --git a/NewRadX/configuration.ccl b/NewRadX/configuration.ccl index a1507080..02aa190b 100644 --- a/NewRadX/configuration.ccl +++ b/NewRadX/configuration.ccl @@ -1,7 +1,9 @@ # Configuration definition for thorn NewRadX -REQUIRES GSL Loop +REQUIRES Loop + PROVIDES NewRadX { } + REQUIRES NewRadX diff --git a/NewRadX/interface.ccl b/NewRadX/interface.ccl index a210f929..123c7162 100644 --- a/NewRadX/interface.ccl +++ b/NewRadX/interface.ccl @@ -2,28 +2,8 @@ IMPLEMENTS: NewRadX -USES INCLUDE HEADER: loop.hxx -USES INCLUDE HEADER: loop_device.hxx - -INCLUDE HEADER: newradx.hxx in newradx.hxx - INHERITS: CarpetX -# Scalar field grid functions for the unit test -CCTK_REAL state TYPE=gf CENTERING={VVV} TAGS='rhs="rhs"' -{ - uu - vv -} "Scalar wave state vector: scalar field and its time derivative" - -CCTK_REAL rhs TYPE=gf CENTERING={VVV} TAGS='checkpoint="no"' -{ - uu_rhs - vv_rhs -} "RHS of scalar wave state vector" +USES INCLUDE HEADER: loop_device.hxx -CCTK_REAL error TYPE=gf CENTERING={VVV} TAGS='checkpoint="no"' -{ - uu_err - vv_err -} "Error in scalar wave state vector" +INCLUDE HEADER: newradx.hxx in newradx.hxx diff --git a/NewRadX/param.ccl b/NewRadX/param.ccl index 3046e7ae..7ba1a5f0 100644 --- a/NewRadX/param.ccl +++ b/NewRadX/param.ccl @@ -1,52 +1 @@ # Parameter definitions for thorn NewRadX -# -# To use radiative boundary conditions in another thorn, the parameters here are not relevant. -# These parameters are only used in the unit test for NewRadX, which applies NewRadX in the evolution of a test scalar field -BOOLEAN run_test "Run scalar field evolution test" -{ -} "no" - -BOOLEAN test_use_newradx "Use radiative boundary conditions for scalar field" -{ -} "yes" - -BOOLEAN test_add_dissipation "Add Kreiss-Oliger dissipation to scalar field RHS" -{ -} "yes" - -CCTK_REAL eps_dissipation "Coefficient for Kreiss-Oliger dissipation" -{ - 0.0:1.0 :: "" -} 0.15 - -CCTK_REAL n_falloff "Exponent of the falloff term r^(-n_falloff) in the scalar field potential" -{ - 0.0:* :: "" -} 2.0 - - -# Parameters scalar field test initial data -CCTK_REAL gaussian_a0 "Scalar field initial Gaussian amplitude" -{ - *:* :: "" -} 1.0 - -CCTK_REAL gaussian_w0 "Scalar field initial Gaussian profile width" -{ - 0.0:* :: "" -} 1.0 - -CCTK_REAL gaussian_x0 "Scalar field initial Gaussian profile center" -{ - *:* :: "" -} 0.0 - -CCTK_REAL gaussian_y0 "Scalar field initial Gaussian profile center" -{ - *:* :: "" -} 0.0 - -CCTK_REAL gaussian_z0 "Scalar field initial Gaussian profile center" -{ - *:* :: "" -} 0.0 diff --git a/NewRadX/schedule.ccl b/NewRadX/schedule.ccl index 32f9e2a9..42e426b6 100644 --- a/NewRadX/schedule.ccl +++ b/NewRadX/schedule.ccl @@ -1,42 +1 @@ # Schedule definitions for thorn NewRadX - -if (run_test) { - STORAGE: state - - SCHEDULE NewRadX_Init AT initial - { - LANG: C - WRITES: state(interior) - SYNC: state - } "Initialize scalar wave state" - - SCHEDULE NewRadX_EstimateError AT postinitial - { - LANG: C - READS: state(everywhere) - WRITES: CarpetX::regrid_error(interior) - } "Estimate error for regridding" - - SCHEDULE NewRadX_EstimateError AT poststep - { - LANG: C - READS: state(everywhere) - WRITES: CarpetX::regrid_error(interior) - } "Estimate error for regridding" - - SCHEDULE NewRadX_RHS IN ODESolvers_RHS - { - LANG: C - READS: state(everywhere) - WRITES: rhs(interior) - SYNC: rhs - } "Calculate scalar wave RHS" - - SCHEDULE NewRadX_CompareSolution IN ODESolvers_PostStep - { - LANG: C - READS: state(interior) - WRITES: error(interior) - SYNC: error - } "Calculate error between numerical and analytic solutions" -} diff --git a/NewRadX/src/make.code.defn b/NewRadX/src/make.code.defn index add3937d..f9dc14f3 100644 --- a/NewRadX/src/make.code.defn +++ b/NewRadX/src/make.code.defn @@ -1,8 +1,7 @@ # Main make.code.defn file for thorn NewRadX # Source files in this directory -SRCS = newradx.cxx \ - test_newradx.cxx +SRCS = newradx.cxx # Subdirectories containing source files SUBDIRS = diff --git a/NewRadX/src/test_newradx.cxx b/NewRadX/src/test_newradx.cxx deleted file mode 100644 index 95550429..00000000 --- a/NewRadX/src/test_newradx.cxx +++ /dev/null @@ -1,182 +0,0 @@ -#include -#include -#include -#include -#include - -namespace NewRadX { - -#define ijk p.I -#define im3jk p.I - 3 * p.DI[0] -#define im2jk p.I - 2 * p.DI[0] -#define im1jk p.I - 1 * p.DI[0] -#define ip3jk p.I + 3 * p.DI[0] -#define ip2jk p.I + 2 * p.DI[0] -#define ip1jk p.I + 1 * p.DI[0] - -#define ijm3k p.I - 3 * p.DI[1] -#define ijm2k p.I - 2 * p.DI[1] -#define ijm1k p.I - 1 * p.DI[1] -#define ijp3k p.I + 3 * p.DI[1] -#define ijp2k p.I + 2 * p.DI[1] -#define ijp1k p.I + 1 * p.DI[1] - -#define ijkm3 p.I - 3 * p.DI[2] -#define ijkm2 p.I - 2 * p.DI[2] -#define ijkm1 p.I - 1 * p.DI[2] -#define ijkp3 p.I + 3 * p.DI[2] -#define ijkp2 p.I + 2 * p.DI[2] -#define ijkp1 p.I + 1 * p.DI[2] - -// Flat Laplacian operator at 4th order accuracy -template -constexpr T Laplacian_4thorder(const Loop::GF3D2 gf, - const Loop::PointDesc &p) { - return 1.0 / 12.0 * - ((-gf(ip2jk) + 16 * gf(ip1jk) - 30 * gf(ijk) - -gf(im2jk) + 16 * gf(im1jk)) / - (p.DX[0] * p.DX[0]) + - (-gf(ijp2k) + 16 * gf(ijp1k) - 30 * gf(ijk) - -gf(ijm2k) + 16 * gf(ijm1k)) / - (p.DX[1] * p.DX[1]) + - (-gf(ijkp2) + 16 * gf(ijkp1) - 30 * gf(ijk) - -gf(ijkm2) + 16 * gf(ijkm1)) / - (p.DX[2] * p.DX[2])); -} - -// 5th order Kreiss-Oliger dissipation -template -constexpr T KO_diss_5thorder(const Loop::GF3D2 gf, - const Loop::PointDesc &p) { - return 1.0 / 64.0 * - ((gf(im3jk) - 6.0 * gf(im2jk) + 15.0 * gf(im1jk) - 20.0 * gf(ijk) + - gf(ip3jk) - 6.0 * gf(ip2jk) + 15.0 * gf(ip1jk)) / - p.DX[0] + - (gf(ijm3k) - 6.0 * gf(ijm2k) + 15.0 * gf(ijm1k) - 20.0 * gf(ijk) + - gf(ijp3k) - 6.0 * gf(ijp2k) + 15.0 * gf(ijp1k)) / - p.DX[1] + - (gf(ijkm3) - 6.0 * gf(ijkm2) + 15.0 * gf(ijkm1) - 20.0 * gf(ijk) + - gf(ijkp3) - 6.0 * gf(ijkp2) + 15.0 * gf(ijkp1)) / - p.DX[2]); -} - -// Test scalar field initial data -template -constexpr void gaussian(const T t, const T A, const T W, - const T x, const T y, const T z, - T &uu, T &vv) { - using std::exp, std::pow, std::sqrt; - - const T r = sqrt(pow(x, 2) + pow(y, 2) + pow(z, 2)); - - const auto f = [&](const T v) { - return A * exp(-pow(v, 2) / (2 * pow(W, 2))); - }; - - if (r < sqrt(std::numeric_limits::epsilon())) { - // L'Hôpital - uu = f(-t) * (1 - pow(t/W, 2)); - vv = f(-t) * (3 - pow(t/W, 2)) * (-t/pow(W,2)); - } else { - uu = 0.5 * (f(r - t) * (r - t) + - f(r + t) * (r + t)) / r; - vv = 0.5 * (f(r - t) * (pow((r - t) / W, 2) - 1) - - f(r + t) * (pow((r + t) / W, 2) - 1)) / r; - } -} - -// Scheduled functions -extern "C" void NewRadX_Init(CCTK_ARGUMENTS) { - DECLARE_CCTK_ARGUMENTSX_NewRadX_Init; - DECLARE_CCTK_PARAMETERS; - - grid.loop_int_device<0, 0, 0>( - grid.nghostzones, - [=] CCTK_DEVICE(const Loop::PointDesc &p) - CCTK_ATTRIBUTE_ALWAYS_INLINE { - gaussian(cctk_time, - gaussian_a0, gaussian_w0, - p.x - gaussian_x0, p.y - gaussian_y0, - p.z - gaussian_z0, uu(p.I), vv(p.I)); - }); -} - -extern "C" void NewRadX_RHS(CCTK_ARGUMENTS) { - DECLARE_CCTK_ARGUMENTSX_NewRadX_RHS; - DECLARE_CCTK_PARAMETERS; - - if (grid.nghostzones[0] != 3 || grid.nghostzones[1] != 3 || - grid.nghostzones[2] != 3) { - CCTK_ERROR("Invalid number of ghost zones for 4th order FD"); - } - - grid.loop_int_device<0, 0, 0>( - grid.nghostzones, - [=] CCTK_DEVICE(const Loop::PointDesc &p) - CCTK_ATTRIBUTE_ALWAYS_INLINE { - uu_rhs(p.I) = vv(p.I); - vv_rhs(p.I) = Laplacian_4thorder(uu, p); - }); - - if (test_use_newradx) { - NewRadX_Apply(cctkGH, uu, uu_rhs, 0, 1, n_falloff); - NewRadX_Apply(cctkGH, vv, vv_rhs, 0, 1, n_falloff + 1); - } - - if (test_add_dissipation) { - grid.loop_int_device<0, 0, 0>( - grid.nghostzones, - [=] CCTK_DEVICE(const Loop::PointDesc &p) - CCTK_ATTRIBUTE_ALWAYS_INLINE { - uu_rhs(p.I) += eps_dissipation * KO_diss_5thorder(uu, p); - vv_rhs(p.I) += eps_dissipation * KO_diss_5thorder(vv, p); - }); - } -} - -extern "C" void NewRadX_CompareSolution(CCTK_ARGUMENTS) { - DECLARE_CCTK_ARGUMENTSX_NewRadX_CompareSolution; - DECLARE_CCTK_PARAMETERS; - - grid.loop_int_device<0, 0, 0>( - grid.nghostzones, - [=] CCTK_DEVICE(const Loop::PointDesc &p) - CCTK_ATTRIBUTE_ALWAYS_INLINE { - CCTK_REAL u_analytic, v_analytic; - gaussian(cctk_time, - gaussian_a0, gaussian_w0, - p.x - gaussian_x0, p.y - gaussian_y0, - p.z - gaussian_z0, u_analytic, v_analytic); - uu_err(p.I) = uu(p.I) - u_analytic; - vv_err(p.I) = vv(p.I) - v_analytic; - }); -} - -extern "C" void NewRadX_EstimateError(CCTK_ARGUMENTS) { - DECLARE_CCTK_ARGUMENTSX_NewRadX_EstimateError; - DECLARE_CCTK_PARAMETERS; - - grid.loop_int_device<1, 1, 1>( - grid.nghostzones, - [=] CCTK_DEVICE(const Loop::PointDesc &p) - CCTK_ATTRIBUTE_ALWAYS_INLINE { - using std::abs, std::max; - CCTK_REAL maxabs_duu = 0; - for (int d = 0; d < Loop::dim; ++d) { - const int ni = d == 0 ? 1 : 2; - const int nj = d == 1 ? 1 : 2; - const int nk = d == 2 ? 1 : 2; - for (int dk = 0; dk < nk; ++dk) { - for (int dj = 0; dj < nj; ++dj) { - for (int di = 0; di < ni; ++di) { - const auto I = p.I + di * p.DI[0] + dj * p.DI[1] + dk * p.DI[2]; - maxabs_duu = max(maxabs_duu, abs(uu(I + p.DI[d]) - uu(I))); - } - } - } - } - regrid_error(p.I) = maxabs_duu; - }); -} - -} // namespace NewRadX diff --git a/NewRadX/test/scalarwave_newradx/newradx-error.it000060.x.tsv b/NewRadX/test/scalarwave_newradx/newradx-error.it000060.x.tsv deleted file mode 100644 index d2c51b5f..00000000 --- a/NewRadX/test/scalarwave_newradx/newradx-error.it000060.x.tsv +++ /dev/null @@ -1,38 +0,0 @@ -# 1:iteration 2:time 3:patch 4:level 5:i 6:j 7:k 8:x 9:y 10:z 11:uu_err 12:vv_err -60 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-0,0 +1,369 @@ +% *======================================================================* +% 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{Cheng-Hsin Cheng, + Jake Doherty, + Michail Chabanov, + Alexandru Dima + } + +% The title of the document (not necessarily the name of the Thorn) +\title{NewRadX} + +% the date your document was last changed, if your document is in CVS, +% please use: +% \date{$ $Date$ $} +\date{July 27 2023} + +\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} +This thorn implements the radiative boundary condition originally introduced +in the Carpet-based NewRad thorn. +\end{abstract} + +% The following sections are suggestive only. +% Remove them or add your own. + +\section{Introduction} +This thorn provides routines to implement radiative boundary conditions as +described in section VI of~\cite{EinsteinEvolve_NewRad_Alcubierre:2002kk}: +\begin{equation} +f = f_0 + u(r - v t)/r\mbox{,} +\label{eqn:EinsteinEvolve_NewRad_bc} +\end{equation} +in its differential form +\begin{equation} +\partial_t f + v \partial_r f - v\,(f - f_0) = 0\mbox{,} +\label{eqn:EinsteinEvolve_NewRad_diff_bc} +\end{equation} +where $v$ is the asymptotic propagation speed of the field $f$ and $f_0$ +is its asymptotic value. + +\section{Physical System} +% RH: this is copied verbatim from Alcubierre:2002kk +Quoting~\cite{EinsteinEvolve_NewRad_Alcubierre:2002kk}: + +At the outer boundary we use a radiation (Sommerfeld) boundary +condition. We start from the assumption that near the boundary all +fields behave as spherical waves, namely we impose the condition +\begin{equation} +f = f_0 + u(r-vt)/r . +\label{eq:radiation} +\end{equation} +Where $f_0$ is the asymptotic value of a given dynamical variable +(typically 1 for the lapse and diagonal metric components, and zero +for everything else), and $v$ is some wave speed. If our +boundary is sufficiently far away one can safely assume that the speed +of light is 1, so $v=1$ for most fields. However, the gauge variables +can easily propagate with a different speed implying a different value +of $v$. + +In practice, we do not use the boundary condition~(\ref{eq:radiation}) +as it stands, but rather we use it in differential form: +\begin{equation} +\partial_t f + v \partial_r f - v \, (f - f_0)/r = 0 . +\end{equation} +Since our code is written in Cartesian coordinates, we transform the +last condition to +\begin{equation} +\frac{x_i}{r} \, \partial_t f + v \partial_i f + \frac{v x_i}{r^2} \, +\left( f - f_0 \right) = 0 . +\end{equation} +We finite difference this condition consistently to second order in +both space and time and apply it to all dynamic variables (with +possible different values of $f_0$ and $v$) at all boundaries. + +There is a final subtlety in our boundary treatment. Wave propagation +is not the only reason why fields evolve near a boundary. Simple +infall of the coordinate observers will cause some small evolution as +well, and such evolution is poorly modeled by a propagating wave. This +is particularly important at early times, when the radiative boundary +condition introduces a bad transient effect. In order to minimize the +error at our boundaries introduced by such non-wavelike evolution, we +allow for boundary behavior of the form: +\begin{equation} +f = f_0 + u(r-vt)/r + h(t)/r^n , +\label{eq:radpower} +\end{equation} +with $h$ a function of $t$ alone and $n$ some unknown power. This +leads to the differential equation +\begin{eqnarray} +\partial_t f + v \partial_r f +- \frac{v}{r} \, (f - f_0) &=& +\frac{v h(t)}{r^{n+1}} \left( 1 - n v \right) ++ \frac{h'(t)}{r^n} \nonumber \\ +&\simeq& \frac{h'(t)}{r^n} \qquad \mathrm{for\ large\ } r , +\end{eqnarray} +or in Cartesian coordinates +\begin{equation} +\frac{x_i}{r} \, \partial_t f + v \partial_i f + \frac{v x_i}{r^2} \, +\left( f - f_0 \right) \simeq \frac{x_i h'(t)}{r^{n+1}} . +\label{eqn:EinsteinEvolve_NewRad_num_bc} +\end{equation} + +This expression still contains the unknown function $h'(t)$. Having +chosen a value of $n$, one can evaluate the above expression one point +away from the boundary to solve for $h'(t)$, and then use this value +at the boundary itself. Empirically, we have found that taking $n=3$ +almost completely eliminates the bad transient caused by the radiative +boundary condition on its own. + +\section{Numerical Implementation} +The thorn implements to ingredients for the evolution. +\begin{enumerate} +\item the boundary condition~\eqref{eqn:EinsteinEvolve_NewRad_num_bc}, +\item a routine to extrapolate the contracted Christoffel symbols +$g^{jk} \Gamma^i_{jk}$ (\code{Xt1}\ldots\code{Xt3} in the code) into the +outer boundaries at $t=0$. +\end{enumerate} + +\subsection{Extrapolation} +At outer boundary points, as determined by \code{GenericFD}'s routine +\code{GenericFD\_GetBoundaryInfo} we use cubic polynomials along the +normal of the boundary to extrapolate data from the interior into the +boundary region. Due to the use of cubic polynomial we require at least +four (4) points of valid data to be available for the extrapolation. +This \emph{includes} ghost zones, which are assumed to contain valid +data in the interior of the domain. + +\subsection{Radiative boundary condition} +The derivatives $\partial_i f$ appearing in +\eqref{eqn:EinsteinEvolve_NewRad_num_bc} are approximated as +2\textsuperscript{nd} order accurate finite difference expressions using +centred expressions +\begin{equation} +f'(x) \approx \frac{f(x-\Delta x) - f(x+\Delta x)}{2\Delta x} +\end{equation} +and one sided expressions +\begin{equation} +f'(x) \approx \pm\frac{3 f(x) - 4 f(x\mp\Delta x) + f(x\mp2\Delta +x)}{2\Delta x}\mbox{,} +\end{equation} +for boundaries around the $\pm$ coordinate direction. + +% copied from newrad.cc so likely originally written by Miguel +% Alcubierre. +Finally we try to extrapolate for the part of the boundary +that does not behave as a pure wave (i.e.\ Coulomb type +terms caused by infall of the coordinate lines). + +This we do by comparing the source term one grid point +away from the boundary (which we already have), to what +we would have obtained if we had used the boundary +condition there. The difference gives us an idea of the +missing part and we extrapolate that to the boundary +assuming a power-law decay. + +\section{Using This Thorn} +The thorn exports two aliased functions \code{ExtrapolateGammas} and +\code{NewRad\_Apply} that should be used in \code{INITIAL} and +\code{MoL\_CalcRHS} respectively to extrapolate the contracted +Christoffel symbols and apply radiative boundary conditions to evolved +variables respectively. + +There call signatures are: +\begin{verbatim} +CCTK_INT FUNCTION \ + ExtrapolateGammas \ + (CCTK_POINTER_TO_CONST IN cctkGH, \ + CCTK_REAL ARRAY INOUT var) + +CCTK_INT FUNCTION \ + NewRad_Apply \ + (CCTK_POINTER_TO_CONST IN cctkGH, \ + CCTK_REAL ARRAY IN var, \ + CCTK_REAL ARRAY INOUT rhs, \ + CCTK_REAL IN var0, \ + CCTK_REAL IN v0, \ + CCTK_INT IN radpower) +\end{verbatim} +where \code{var0} corresponds to $f_0$, \code{v0} is $v$ and +\code{radpower} is the assumed decay exponent $n$. + +\subsection{Obtaining This Thorn} +The thorn is part of the EinsteinEvolve arrangement available on +bitbucket. +\begin{verbatim} +git clone git@bitbucket.org:einsteintoolkit/einsteinevolve.git +\end{verbatim} + +\subsection{Basic Usage} + +\subsection{Special Behaviour} +If the parameter \code{z\_is\_radial} is set it assumes that the $z$ +direction is a radial direction and uses this to evaluate the radial +derivative in \eqref{eqn:EinsteinEvolve_NewRad_num_bc}. This is the case +for the multi-patch coordinate systems provided by the +\code{Llama}~\cite{EinsteinEvolve_NewRad_llamacode} infrastructure. + +\subsection{Interaction With Other Thorns} +This thorn requires thorn \code{GenericFD} which is part of +\code{Kranc}~\cite{EinsteinEvolve_NewRad_kranccode}. + +\subsection{Examples} +The best example is likely to inspect the source code \code{ML\_BSSN} +and \code{ML\_BSSN\_Helper}, namely: + +\begin{verbatim} + +CCTK_INT FUNCTION \ + NewRad_Apply \ + (CCTK_POINTER_TO_CONST IN cctkGH, \ + CCTK_REAL ARRAY IN var, \ + CCTK_REAL ARRAY INOUT rhs, \ + CCTK_REAL IN var0, \ + CCTK_REAL IN v0, \ + CCTK_INT IN radpower) +USES FUNCTION NewRad_Apply +\end{verbatim} + +\begin{verbatim} + +SCHEDULE ML_BSSN_NewRad IN MoL_CalcRHS AFTER ML_BSSN_EvolutionInterior +{ + LANG: C + # No need to sync here -- the RHS variables are never synced +} "Apply NewRad boundary conditions to RHS" +\end{verbatim} + +\begin{verbatim} + +#include "cctk_Arguments.h" +#include "cctk_Functions.h" + +void ML_BSSN_NewRad(CCTK_ARGUMENTS) +{ + DECLARE_CCTK_ARGUMENTS; + + const int radpower = 2; // for example + + NewRad_Apply(cctkGH, gt12, gt12rhs, 0.0, 1.0, radpower); +} +\end{verbatim} + +\subsection{Support and Feedback} +Please use the Einstein Toolkit mailing list +\url{users@einsteintoolkit.org} to report issues and ask for help. + +\section{History} + +\subsection{Thorn Source Code} +\begin{itemize} +\item Initial version of method likely by Miguel Alcubierre; +\item Carpet version of code by Erik Schnetter; +\item CarpetX version of code by Cheng-Hsin Cheng, Jake Doherty, Michail Chabanov, Alexandru Dima. +\end{itemize} + +\subsection{Thorn Documentation} +\begin{itemize} +\item Initial version by Roland Haas using text by Miguel, Erik. +\item Current version by Alexandru Dima. +\end{itemize} + +\subsection{Acknowledgements} +This documentation copies text from comments in the source code as well +as the paper~\cite{EinsteinEvolve_NewRad_Alcubierre:2002kk}. + +\begin{thebibliography}{9} +\bibitem{EinsteinEvolve_NewRad_Alcubierre:2002kk} + M.~Alcubierre, B.~Bruegmann, P.~Diener, M.~Koppitz, D.~Pollney, E.~Seidel and R.~Takahashi, + ``Gauge conditions for long term numerical black hole evolutions without excision,'' + Phys.\ Rev.\ D {\bf 67}, 084023 (2003) + doi:10.1103/PhysRevD.67.084023 + [gr-qc/0206072]. +\bibitem{EinsteinEvolve_NewRad_kranccode} ``Kranc: Kranc assembles +numerical code``, \url{http://kranccode.org/}. +\bibitem{EinsteinEvolve_NewRad_llamacode} ``The Llama code``, \url{https://llamacode.bitbucket.io/}. + +\end{thebibliography} + +% Do not delete next line +% END CACTUS THORNGUIDE + +\end{document} diff --git a/TestNewRadX/interface.ccl b/TestNewRadX/interface.ccl new file mode 100644 index 00000000..16e338e2 --- /dev/null +++ b/TestNewRadX/interface.ccl @@ -0,0 +1,27 @@ +# Interface definition for thorn TestNewRadX + +IMPLEMENTS: TestNewRadX + +INHERITS: CarpetX + +USES INCLUDE HEADER: loop_device.hxx +USES INCLUDE HEADER: newradx.hxx + +# Scalar field grid functions for the unit test +CCTK_REAL state TYPE=gf CENTERING={VVV} TAGS='rhs="rhs"' +{ + uu + vv +} "Scalar wave state vector: scalar field and its time derivative" + +CCTK_REAL rhs TYPE=gf CENTERING={VVV} TAGS='checkpoint="no"' +{ + uu_rhs + vv_rhs +} "RHS of scalar wave state vector" + +CCTK_REAL error TYPE=gf CENTERING={VVV} TAGS='checkpoint="no"' +{ + uu_err + vv_err +} "Error in scalar wave state vector" diff --git a/TestNewRadX/param.ccl b/TestNewRadX/param.ccl new file mode 100644 index 00000000..28284ebb --- /dev/null +++ b/TestNewRadX/param.ccl @@ -0,0 +1,46 @@ +# Parameter definitions for thorn TestNewRadX +# +BOOLEAN test_use_newradx "Use radiative boundary conditions for scalar field" +{ +} "yes" + +BOOLEAN test_add_dissipation "Add Kreiss-Oliger dissipation to scalar field RHS" +{ +} "yes" + +CCTK_REAL eps_dissipation "Coefficient for Kreiss-Oliger dissipation" +{ + 0.0:1.0 :: "" +} 0.15 + +CCTK_REAL n_falloff "Exponent of the falloff term r^(-n_falloff) in the scalar field potential" +{ + 0.0:* :: "" +} 2.0 + + +# Parameters scalar field test initial data +CCTK_REAL gaussian_a0 "Scalar field initial Gaussian amplitude" +{ + *:* :: "" +} 1.0 + +CCTK_REAL gaussian_w0 "Scalar field initial Gaussian profile width" +{ + 0.0:* :: "" +} 1.0 + +CCTK_REAL gaussian_x0 "Scalar field initial Gaussian profile center" +{ + *:* :: "" +} 0.0 + +CCTK_REAL gaussian_y0 "Scalar field initial Gaussian profile center" +{ + *:* :: "" +} 0.0 + +CCTK_REAL gaussian_z0 "Scalar field initial Gaussian profile center" +{ + *:* :: "" +} 0.0 diff --git a/TestNewRadX/schedule.ccl b/TestNewRadX/schedule.ccl new file mode 100644 index 00000000..86e3ec07 --- /dev/null +++ b/TestNewRadX/schedule.ccl @@ -0,0 +1,40 @@ +# Schedule definitions for thorn TestNewRadX + +STORAGE: state + +SCHEDULE TestNewRadX_Init AT initial +{ + LANG: C + WRITES: state(interior) + SYNC: state +} "Initialize scalar wave state" + +SCHEDULE TestNewRadX_EstimateError AT postinitial +{ + LANG: C + READS: state(everywhere) + WRITES: CarpetX::regrid_error(interior) +} "Estimate error for regridding" + +SCHEDULE TestNewRadX_EstimateError AT poststep +{ + LANG: C + READS: state(everywhere) + WRITES: CarpetX::regrid_error(interior) +} "Estimate error for regridding" + +SCHEDULE TestNewRadX_RHS IN ODESolvers_RHS +{ + LANG: C + READS: state(everywhere) + WRITES: rhs(interior) + SYNC: rhs +} "Calculate scalar wave RHS" + +SCHEDULE TestNewRadX_CompareSolution IN ODESolvers_PostStep +{ + LANG: C + READS: state(interior) + WRITES: error(interior) + SYNC: error +} "Calculate error between numerical and analytic solutions" diff --git a/TestNewRadX/src/make.code.defn b/TestNewRadX/src/make.code.defn new file mode 100644 index 00000000..38b9b874 --- /dev/null +++ b/TestNewRadX/src/make.code.defn @@ -0,0 +1,7 @@ +# Main make.code.defn file for thorn TestNewRadX + +# Source files in this directory +SRCS = test_newradx.cxx + +# Subdirectories containing source files +SUBDIRS = diff --git a/TestNewRadX/src/test_newradx.cxx b/TestNewRadX/src/test_newradx.cxx new file mode 100644 index 00000000..f87e0e43 --- /dev/null +++ b/TestNewRadX/src/test_newradx.cxx @@ -0,0 +1,173 @@ +#include +#include +#include +#include +#include + +namespace TestNewRadX { + +#define ijk p.I +#define im3jk p.I - 3 * p.DI[0] +#define im2jk p.I - 2 * p.DI[0] +#define im1jk p.I - 1 * p.DI[0] +#define ip3jk p.I + 3 * p.DI[0] +#define ip2jk p.I + 2 * p.DI[0] +#define ip1jk p.I + 1 * p.DI[0] + +#define ijm3k p.I - 3 * p.DI[1] +#define ijm2k p.I - 2 * p.DI[1] +#define ijm1k p.I - 1 * p.DI[1] +#define ijp3k p.I + 3 * p.DI[1] +#define ijp2k p.I + 2 * p.DI[1] +#define ijp1k p.I + 1 * p.DI[1] + +#define ijkm3 p.I - 3 * p.DI[2] +#define ijkm2 p.I - 2 * p.DI[2] +#define ijkm1 p.I - 1 * p.DI[2] +#define ijkp3 p.I + 3 * p.DI[2] +#define ijkp2 p.I + 2 * p.DI[2] +#define ijkp1 p.I + 1 * p.DI[2] + +// Flat Laplacian operator at 4th order accuracy +template +constexpr T Laplacian_4thorder(const Loop::GF3D2 gf, + const Loop::PointDesc &p) { + return 1.0 / 12.0 * + ((-gf(ip2jk) + 16 * gf(ip1jk) - 30 * gf(ijk) - gf(im2jk) + + 16 * gf(im1jk)) / + (p.DX[0] * p.DX[0]) + + (-gf(ijp2k) + 16 * gf(ijp1k) - 30 * gf(ijk) - gf(ijm2k) + + 16 * gf(ijm1k)) / + (p.DX[1] * p.DX[1]) + + (-gf(ijkp2) + 16 * gf(ijkp1) - 30 * gf(ijk) - gf(ijkm2) + + 16 * gf(ijkm1)) / + (p.DX[2] * p.DX[2])); +} + +// 5th order Kreiss-Oliger dissipation +template +constexpr T KO_diss_5thorder(const Loop::GF3D2 gf, + const Loop::PointDesc &p) { + return 1.0 / 64.0 * + ((gf(im3jk) - 6.0 * gf(im2jk) + 15.0 * gf(im1jk) - 20.0 * gf(ijk) + + gf(ip3jk) - 6.0 * gf(ip2jk) + 15.0 * gf(ip1jk)) / + p.DX[0] + + (gf(ijm3k) - 6.0 * gf(ijm2k) + 15.0 * gf(ijm1k) - 20.0 * gf(ijk) + + gf(ijp3k) - 6.0 * gf(ijp2k) + 15.0 * gf(ijp1k)) / + p.DX[1] + + (gf(ijkm3) - 6.0 * gf(ijkm2) + 15.0 * gf(ijkm1) - 20.0 * gf(ijk) + + gf(ijkp3) - 6.0 * gf(ijkp2) + 15.0 * gf(ijkp1)) / + p.DX[2]); +} + +// Test scalar field initial data +template +constexpr void gaussian(const T t, const T A, const T W, const T x, const T y, + const T z, T &uu, T &vv) { + using std::exp, std::pow, std::sqrt; + + const T r = sqrt(pow(x, 2) + pow(y, 2) + pow(z, 2)); + + const auto f = [&](const T v) { + return A * exp(-pow(v, 2) / (2 * pow(W, 2))); + }; + + if (r < sqrt(std::numeric_limits::epsilon())) { + // L'Hôpital + uu = f(-t) * (1 - pow(t / W, 2)); + vv = f(-t) * (3 - pow(t / W, 2)) * (-t / pow(W, 2)); + } else { + uu = 0.5 * (f(r - t) * (r - t) + f(r + t) * (r + t)) / r; + vv = 0.5 * + (f(r - t) * (pow((r - t) / W, 2) - 1) - + f(r + t) * (pow((r + t) / W, 2) - 1)) / + r; + } +} + +// Scheduled functions +extern "C" void TestNewRadX_Init(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_TestNewRadX_Init; + DECLARE_CCTK_PARAMETERS; + + grid.loop_int_device<0, 0, 0>( + grid.nghostzones, + [=] CCTK_DEVICE(const Loop::PointDesc &p) CCTK_ATTRIBUTE_ALWAYS_INLINE { + gaussian(cctk_time, gaussian_a0, gaussian_w0, p.x - gaussian_x0, + p.y - gaussian_y0, p.z - gaussian_z0, uu(p.I), vv(p.I)); + }); +} + +extern "C" void TestNewRadX_RHS(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_TestNewRadX_RHS; + DECLARE_CCTK_PARAMETERS; + + if (grid.nghostzones[0] != 3 || grid.nghostzones[1] != 3 || + grid.nghostzones[2] != 3) { + CCTK_ERROR("Invalid number of ghost zones for 4th order FD"); + } + + grid.loop_int_device<0, 0, 0>(grid.nghostzones, + [=] CCTK_DEVICE(const Loop::PointDesc &p) + CCTK_ATTRIBUTE_ALWAYS_INLINE { + uu_rhs(p.I) = vv(p.I); + vv_rhs(p.I) = Laplacian_4thorder(uu, p); + }); + + if (test_use_newradx) { + NewRadX::NewRadX_Apply(cctkGH, uu, uu_rhs, 0, 1, n_falloff); + NewRadX::NewRadX_Apply(cctkGH, vv, vv_rhs, 0, 1, n_falloff + 1); + } + + if (test_add_dissipation) { + grid.loop_int_device<0, 0, 0>( + grid.nghostzones, + [=] CCTK_DEVICE(const Loop::PointDesc &p) CCTK_ATTRIBUTE_ALWAYS_INLINE { + uu_rhs(p.I) += eps_dissipation * KO_diss_5thorder(uu, p); + vv_rhs(p.I) += eps_dissipation * KO_diss_5thorder(vv, p); + }); + } +} + +extern "C" void TestNewRadX_CompareSolution(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_TestNewRadX_CompareSolution; + DECLARE_CCTK_PARAMETERS; + + grid.loop_int_device<0, 0, 0>( + grid.nghostzones, + [=] CCTK_DEVICE(const Loop::PointDesc &p) CCTK_ATTRIBUTE_ALWAYS_INLINE { + CCTK_REAL u_analytic, v_analytic; + gaussian(cctk_time, gaussian_a0, gaussian_w0, p.x - gaussian_x0, + p.y - gaussian_y0, p.z - gaussian_z0, u_analytic, v_analytic); + uu_err(p.I) = uu(p.I) - u_analytic; + vv_err(p.I) = vv(p.I) - v_analytic; + }); +} + +extern "C" void TestNewRadX_EstimateError(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_TestNewRadX_EstimateError; + DECLARE_CCTK_PARAMETERS; + + grid.loop_int_device<1, 1, 1>( + grid.nghostzones, + [=] CCTK_DEVICE(const Loop::PointDesc &p) CCTK_ATTRIBUTE_ALWAYS_INLINE { + using std::abs, std::max; + CCTK_REAL maxabs_duu = 0; + for (int d = 0; d < Loop::dim; ++d) { + const int ni = d == 0 ? 1 : 2; + const int nj = d == 1 ? 1 : 2; + const int nk = d == 2 ? 1 : 2; + for (int dk = 0; dk < nk; ++dk) { + for (int dj = 0; dj < nj; ++dj) { + for (int di = 0; di < ni; ++di) { + const auto I = p.I + di * p.DI[0] + dj * p.DI[1] + dk * p.DI[2]; + maxabs_duu = max(maxabs_duu, abs(uu(I + p.DI[d]) - uu(I))); + } + } + } + } + regrid_error(p.I) = maxabs_duu; + }); +} + +} // namespace TestNewRadX diff --git a/NewRadX/test/scalarwave_newradx.par b/TestNewRadX/test/scalarwave_newradx.par similarity index 76% rename from NewRadX/test/scalarwave_newradx.par rename to TestNewRadX/test/scalarwave_newradx.par index 15791533..929691b4 100644 --- a/NewRadX/test/scalarwave_newradx.par +++ b/TestNewRadX/test/scalarwave_newradx.par @@ -2,6 +2,7 @@ ActiveThorns = " CarpetX ODESolvers NewRadX + TestNewRadX " $nlevels = 1 @@ -58,22 +59,21 @@ IO::out_every = 1 CarpetX::out_metadata = no CarpetX::out_tsv_every = 30 CarpetX::out_tsv_vars = " - NewRadX::uu - NewRadX::vv - NewRadX::uu_err - NewRadX::vv_err + TestNewRadX::uu + TestNewRadX::vv + TestNewRadX::uu_err + TestNewRadX::vv_err " # CarpetX::out_norm_omit_unstable = yes # CarpetX::out_norm_vars = "all" # CarpetX::out_silo_vars = "all" -NewRadX::run_test = yes -NewRadX::test_use_newradx = yes -NewRadX::test_add_dissipation = yes -NewRadX::eps_dissipation = 0.2 -NewRadX::n_falloff = 2.0 -NewRadX::gaussian_a0 = 1.0 -NewRadX::gaussian_w0 = 0.5 -NewRadX::gaussian_x0 = 3.0 -NewRadX::gaussian_y0 = 4.0 -NewRadX::gaussian_z0 = 0.0 +TestNewRadX::test_use_newradx = yes +TestNewRadX::test_add_dissipation = yes +TestNewRadX::eps_dissipation = 0.2 +TestNewRadX::n_falloff = 2.0 +TestNewRadX::gaussian_a0 = 1.0 +TestNewRadX::gaussian_w0 = 0.5 +TestNewRadX::gaussian_x0 = 3.0 +TestNewRadX::gaussian_y0 = 4.0 +TestNewRadX::gaussian_z0 = 0.0 diff --git a/NewRadX/test/scalarwave_newradx/newradx-error.it000000.x.tsv b/TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000000.x.tsv similarity index 100% rename from NewRadX/test/scalarwave_newradx/newradx-error.it000000.x.tsv rename to TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000000.x.tsv diff --git a/NewRadX/test/scalarwave_newradx/newradx-error.it000000.y.tsv b/TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000000.y.tsv similarity index 100% rename from NewRadX/test/scalarwave_newradx/newradx-error.it000000.y.tsv rename to TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000000.y.tsv diff --git a/NewRadX/test/scalarwave_newradx/newradx-error.it000000.z.tsv b/TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000000.z.tsv similarity index 100% rename from NewRadX/test/scalarwave_newradx/newradx-error.it000000.z.tsv rename to TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000000.z.tsv diff --git a/NewRadX/test/scalarwave_newradx/newradx-error.it000030.x.tsv b/TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000030.x.tsv similarity index 54% rename from NewRadX/test/scalarwave_newradx/newradx-error.it000030.x.tsv rename to TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000030.x.tsv index bc07b7ce..d868ce81 100644 --- a/NewRadX/test/scalarwave_newradx/newradx-error.it000030.x.tsv +++ b/TestNewRadX/test/scalarwave_newradx/testnewradx-error.it000030.x.tsv @@ -1,38 +1,38 @@ # 1:iteration 2:time 3:patch 4:level 5:i 6:j 7:k 8:x 9:y 10:z 11:uu_err 12:vv_err -30 5.0000000000000000e+00 0 0 -3 15 15 -1.2000000000000000e+01 0.0000000000000000e+00 0.0000000000000000e+00 -1.8952024923060783e-08 1.1715425070830426e-07 -30 5.0000000000000000e+00 0 0 -2 15 15 -1.1333333333333334e+01 0.0000000000000000e+00 0.0000000000000000e+00 -1.8952024923060783e-08 1.1715425070830426e-07 -30 5.0000000000000000e+00 0 0 -1 15 15 -1.0666666666666666e+01 0.0000000000000000e+00 0.0000000000000000e+00 -1.8952024923060783e-08 1.1715425070830426e-07 -30 5.0000000000000000e+00 0 0 0 15 15 -1.0000000000000000e+01 0.0000000000000000e+00 0.0000000000000000e+00 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