## AHFinder

Date

Abstract

Finding Apparent Horizons in a numerical spacetime

### 1 Purpose

Thorn AHFinder finds Apparent Horizons (AHs) in numerical spacetimes. It calulates various quantities like horizon area and its corresponding mass.

### 2 Using AHFinder

Thorn AHFinder can be used either with a minimization or a flow algorithm.

#### 2.1 Parameters

##### General parameters
• ahfinder::ahf_active (steerable)
To activate the thorn set ahf_active = ”yes”. This parameter is set by default to ”no”.
• ahfinder::ahf_flow (steerable)
By default the minimization algorithm is used. To switch to the flow algorithm one has to set ahf_flow = ”yes”

##### Parameters used in evolutions
• ahfinder::ahf_findevery (steerable)
Specifies how often the finder is called. The default is to find horizons at every iteration.
• ahfinder::ahf_findafter (steerable)
The number of iterations after which the thorn is called the first time can be specified by this parameter. Here the default is 0, calling the thorn also on the initial time slice.
• ahfinder::ahf_findaftertime
Instead of specifying the number of iterations, one can specify after how much coordinate time the thorn is called the first time. When different from zero, this parameter overrides the value of ahf_findafter. Default here is also 0.

##### Parameters specifying the expansion of the surface in sperical harmonics.
• ahfinder::ahf_lmax
The maximal number of terms in the expansion in $𝜃$. The default value is 8. The maximal value is 19.
• ahfinder::ahf_phi (steerable)
If axisymmetry is expected the surface does not need to be expanded in phi. This is the default. To look for non-axisymmetric surface use ahf_phi = ”yes”.
• ahfinder::ahf_[xyz]c (steerable)
Sets the x-, y-, and z-coordinates of the center of the expansion. The default is the origin (ahf_xc = 0, ahf_yc = 0, ahf_zc = 0). The center of the expansion should be set inside the expected apparent horizon, otherwise the algorithm will fail.
• ahfinder::ahf_wander
The center of the expansion can also be allowed to move. To do this use ahf_wander = ”yes”. However, this only works with the minimization algorithm. The default is for the center not to move.
• ahfinder::ahf_r0 (steerable)
Sets the radius of the initial sphere. The default is 0.0, forcing the largest sphere possible in the grid.

##### Looking for three horizons

The finder can also be used to look for three horizons each time. This is done by just running the algorithm three consecutive times with different initial guesses, and is useful for simulations of black hole collisions.

• ahfinder::ahf_find3
Set ahf_find3 = ”yes” to search for three horizons. The default is to look for only one horizon.
• ahfinder::ahf_[xyz]_[012] (steerable)
Sets the x-, y-, and z-coordinates of the center of the expansion for horizon 0, 1 and 2. The default in each case is the origin.
• ahfinder::ahf_r0_[0-2] (steerable)
Sets the radius of the initial spheres for horizon 0, 1 and 2. The default in all cases is 0.0, forcing the largest sphere possible in the grid.

##### Further parameters for the initial guess

The initial guess can be furthermore controlled by some parameters which are set to ”no” by default.

• ahfinder::ahf_guessold (steerable)
To use on old horizon as initial guess set ahf_guessold = ”yes”. However, if during the evolution the apparent horizon jumps discontinuously it might be lost by using this option.
• ahfinder::ahf_nn0, ahfinder::ahf_nn2
If no old horizon is used the inital guess can be specified further for the minimization algorithm. This algorithm is sensitive to the initial guess, so this is important. The initial guess is set up by an expansion in spherical harmonics in the first two coefficients (l=0,l=2). The default for both these parameters are 10, in which case the algorithm tests 100 different combinations to find the best initial guess.
• ahfinder::ahf_sloppyguess
It is also possible to use only a sphere as initial guess. This is much faster and is done by using ahf_sloppyguess = ”yes”. In this case a number of spheres (specified by ahf_nn0) with different radii are tested for the initial guess.
• ahfinder::ahf_inner
If one wants to look for an inner horizon instead of an outer one, use ahfinder::ahf_inner = ”yes”. This only works with the minimization algorithm.

##### Parameters for surface intergrals
• ahfinder::ahf_ntheta (steerable)
The number of subdivisions in $𝜃$. Default is 200.
• ahfinder::ahf_nphi (steerable)
The number of subdivisions in $\varphi$. Default is 200.

##### Parameters indicating symmetries
• ahfinder::ahf_ref[xyz] (steerable)
Specifies the existence of reflection symmetry on the yz-plane, xz-plane and xy-plane respectively. By default all are set to ”no”.
• ahfinder::ahf_octant (steerable)
Octant symmetry is specified by using ahf_octant = ”yes”. This is set to ”no” by default. Possible parmeter settings are ”yes” for reflection symmetries on all three coordinate planes and ”high” for an additional rotational symmetry of $\pi ∕2$ around the z axis.
• ahfinder::ahf_cartoon (steerable)
A further symmetry can (must) be specified when running with the ”axisymmetric” mode given by the Cartoon method by using ahf_cartoon = ”yes”. This is set to ”no” by default.

##### Parameters for minimization algorithm
• ahfinder::ahf_tol
Sets the tolerance for the minimization algorithm. The default value is 0.1.
• ahfinder::ahf_maxiter
Sets the maximum number if iterations for each step of the POWELL algorithm. The default value is 10.
• ahfinder::ahf_minarea
Usually the square of the expansion is minimized. To switch to minimization of the area one can use ahf_minarea = ”yes” (default is ”no”). Notice that only for time symmetric data the surface found by area minimization will correspond to an apparent horizon.

##### Parameters for the flow algorithm
• ahfinder::ahf_flow (steerable)
The fow algotithm is used by setting ahf_flow = ”yes”. The default is ”no”
• ahfinder::ahf_flowiter (steerable)
Sets the maximum number of iterations for the flow algorithm. The default value is 200.
• ahfinder::ahf_flowtol
Sets the tolerance for the flow. The default value is 0.0001.
• ahfinder::ahf_flowa
Sets the $\alpha$ parameter for the flow. The default value is 0.01.
• ahfinder::ahf_flowb
Sets the $\beta$ parameter for the flow. The default value is 0.5.
• ahfinder::ahf_flowh
Sets the weight of $H$ flow. The default value is 0.0.
• ahfinder::ahf_flowc
Sets the weight of $C$ flow. The default value is 1.0.
• ahfinder::ahf_flown
Sets the weight of $N$ flow (not yet implemented). The default value is 0.0.

The character of the different flows and the $\alpha$ and $\beta$ parameters are described in Carsten Gundlach’s paper on his pseudo-spectral apparent horizon finder (gr-qc/9707050).

##### Parameters for output
• ahfinder::ahf_logfile
By default no logfile for AHFinder is written. To obtain a log file one must set ahf_logfile = ”yes”.
• ahfinder::ahf_verbose
if ahf_verbose = ”yes” messages are printed to screen at the beginning and the end of the algorithm. This is the default.
• ahfinder::ahf_veryverbose
if ahf_veryverbose = ”yes” messages are also printed to screen during the iteration process. The default is ”no”.
• ahfinder::ahf_2Doutput (steerable)
To get 2D output of grid functions use ahf_2Doutput = ”yes” (default is ”no”). The output is controlled be the thorn itself, not by cactus standard output.
• ahfinder::ahf_3Doutput (steerable)
In future versions to get 3D output of grid functions use ahf_3Doutput = ”yes” (default is ”no”).
• ahfinder::ahf_areamap
To get an area map use ahf_areamap = ”yes” (default is ”no”). This is useful for looking at the behaviour of the area for surfaces close to the horizon.

The mask is 0 inside the horizon and 1 outside, and is used in black-hole excision techniques. By default the mask is off. It can be enabled by setting ahf_mask = ”strong”, which sets the mask only if the finder is sure that a horizon was found, or by setting ahf_mask = ”weak”, which makes the finder set the mask also if a horizon is probably there but either the resolution or lmax are to low to really resolve it.
Sets a buffer zone between the region inside the horizon and the region where the mask is 0, by limiting the mask to a region smaller than ahf_maskshrink times the horizon radius. The default value is 0.8.
Sets a buffer zone between the region inside the horizon and the region where the mask is 0 with a width of at least ahf_maskbuffer grid points. The default value is 5.

#### 2.2 Minimal parameter settings

Usually only a few of the parameters described above are needed in the parameter file. The simplest parameter settings for using the flow algorithm for a full 3D horizon with a large sphere as initial guess is

interpolation_order = 2     # Second order interpolation
ahf_active          = "yes"
ahf_flow            = "yes"
ahf_phi             = "yes"

This looks for a non-axisymmetric horizon around the origin with lmax = 8 and using the flow algorithm. It starts with the largest sphere that fits in the 3D grid and outputs 2D grid functions. The other parameters can be used if needed.

#### 2.3 Hints for parameter settings

In full 3D the flow algorithm is faster than the minimization algorithm. However, in cases when there are very few terms in the expansion in spherical harmonics the minimization can be faster. In axisymmetry this typically happens for lmax$\le 10$.

While the default settings usually work fine, they can be changed to meet special purposes:

• If the horizon is expected to be far from spherical the parameter ahf_lmax can be set to a higher value. 12 should be high enough. However, only values up to 20 are supported.
• If the latter parameter is set to a value higher than 8 then the parameter ahf_maxiter can be raised to, e.g., 14. This can be useful since more iterations can be necessary for higher coefficients of the expansion.

#### 2.4 Output to Files

The output of the thorn consists of two gridfunctions and several one dimensional output files.

• To depict the position of the horizon, the most important files are ahfgrid_2d_...ieee. These files contain a 2D gridfunction whose zero level locates the horizon.
• The files ahf_exp_2d_...ieee show the expansion of outgoing photons on the level set of the gridfunction ahfgrid. The horizon coincides with zeros of the expansion.
• The surface area of the horizon is given in ahf_area.tl
• The mass of the horizon is given in ahf_mass.tl
• The coefficients of the expansion in spherical harmonics are given in ahf_coeff.alm.
• The files ahf_circ_eq.tl, ahf_meri_p1.tl and ahf_meri_p2.tl contain the equatorial circumference of the surface, the length of the meridian at $\varphi =0$, and the length of the meridian at $\varphi =\pi ∕2$ of the surface, respectively.
• If an output of a logfile is set in the parameters, the log file for the last time the horizon was called is ahf_logfile.

#### 2.5 Some results with the finder

The finder has been examined with puncture initial data for single and binary-black hole scenarios.

Calculations with different grid spacings but constant grid size show convergence of the horizon area.

This has been checked with different linear momenta in the z direction ${P}_{z}=\left(0M,2M,5M\right)$ and vanishing spin. Also for ${P}_{z}=2M$ and a spin of $5M$ in the x direction the horizon converges. Figure 1 shows the case with ${P}_{z}=2M$ and vanishing spin.

Further, not only the area converges but also the shape of the horizon. For both the minimization and the flow algorithm the horizon converges to the same shape, as can be seen from the coefficients fo the expansion. The order of convergence for the coefficients is between 1.4 and 1.7.

By using the parameters ahf_xc, ahf_yc, ahf_zc it can also be shown that the finder also locates horizons which are not centered. This works in general as long as the surface can be expanded in spherical harmonics around this point, but the error increases with the off-centering.

The parameter ahf_r0 can be used e.g. when dealing with two black holes. If one searches for separate horizons one can center the finder on one of the locations of the holes and use an initial radius ahf_r0 smaller than the coordinate distance of the holes. With this parameter settings the single horizon can be found faster. But also a setup with an initial sphere of maximum radius should work at least for the flow algorithm. This has been checked with puncture data for two holes with vanishing linear and angular momentum for each hole (equivalent to Brill-Lindquist data) and is shown in Figure 2. Here for a coordinate distance of the holes of 1.6M the separated horizons for the holes are found but no common horizon. For a coordinate distance of 1.5M a common horizon is found and also single ones, which are inner surfaces in this case. This coincides with other work where the critical coordinate distance for a single horizon is between 1.53M and 1.56M (gr-qc/9809004).

The dashed lines show inner trapped surfaces in the left figure and the surface where the algorithm stopped without finding a horizon in the right figure.

Also the Misner case was checked. Here for $\mu$ = 1.35 a common horizon is found. For $\mu$ = 1.37 separated horizons are found. From the literature we know that (e.g. gr-qc/9809004) the critical value of $\mu$ is 1.36. This is confirmed by the horizon finder.

The information of when a horizon was found can be seen in the cactus-logfile. There will be output from the thorn even if no horizon was found.

### 3 Parameters

 ahf_1doutput Scope: private BOOLEAN Description: 1D output of grid functions? Default: no

 ahf_2doutput Scope: private BOOLEAN Description: 2D output of grid functions? Default: no

 ahf_3doutput Scope: private BOOLEAN Description: 3D output of grid functions? Default: no

 ahf_areamap Scope: private BOOLEAN Description: Find area map? Default: no

 ahf_cartoon Scope: private BOOLEAN Description: Cartoon mode? Default: no

 ahf_find3 Scope: private BOOLEAN Description: Searching for 3 surfaces? Default: no

 ahf_findafter Scope: private INT Description: After how many iterations look for horizons Range Default: (none) 0: Any positive integer

 ahf_findaftertime Scope: private REAL Description: After how much time look for horizons Range Default: 0.0 0.0: Any positive real number. If non-zero overides ahf_findafter

 ahf_findevery Scope: private INT Description: How often to look for horizons Range Default: 1 1: Set to 1 for searching each iteration

 ahf_flow Scope: private BOOLEAN Description: Use flow instead of minimization? Default: no

 ahf_flowa Scope: private REAL Description: alpha parameter for flow Range Default: 0.01 : Anything

 ahf_flowb Scope: private REAL Description: beta parameter for flow Range Default: 0.5 : Anything

 ahf_flowc Scope: private REAL Description: Weight of C flow Range Default: 1.0 : Anything

 ahf_flowh Scope: private REAL Description: Weight of H flow Range Default: 0.0 : Anything

 ahf_flowiter Scope: private INT Description: Maximum number of iterations for flow Range Default: 200 0: Anything

 ahf_flown Scope: private REAL Description: Weight of N flow Range Default: 0.0 : Anything

 ahf_flowtol Scope: private REAL Description: Tolerance for flow Range Default: 0.0001 : Anything

 ahf_gaussout Scope: private BOOLEAN Description: Output gaussian curvature of horizon? Default: yes

 ahf_guess_absmin Scope: private BOOLEAN Description: Use absolute min to start minimization? Default: no

 ahf_guessold Scope: private BOOLEAN Description: Use old horizon as initial guess? Default: no

 ahf_guessverbose Scope: private BOOLEAN Description: Print info on initial guess? Default: no

 ahf_hdf5output Scope: private BOOLEAN Description: HDF5 output of AHFinder data? Default: no

 ahf_inner Scope: private BOOLEAN Description: Look for inner horizon? Default: no

 ahf_l0_guess Scope: private REAL Description: Manual guess for l=0 component Range Default: 1.0 : Anything

 ahf_l10_guess Scope: private REAL Description: Manual guess for l=10 component Range Default: 0.0 : Anything

 ahf_l12_guess Scope: private REAL Description: Manual guess for l=12 component Range Default: 0.0 : Anything

 ahf_l14_guess Scope: private REAL Description: Manual guess for l=14 component Range Default: 0.0 : Anything

 ahf_l16_guess Scope: private REAL Description: Manual guess for l=16 component Range Default: 0.0 : Anything

 ahf_l18_guess Scope: private REAL Description: Manual guess for l=18 component Range Default: 0.0 : Anything

 ahf_l2_guess Scope: private REAL Description: Manual guess for l=2 component Range Default: 0.0 : Anything

 ahf_l4_guess Scope: private REAL Description: Manual guess for l=4 component Range Default: 0.0 : Anything

 ahf_l6_guess Scope: private REAL Description: Manual guess for l=6 component Range Default: 0.0 : Anything

 ahf_l8_guess Scope: private REAL Description: Manual guess for l=8 component Range Default: 0.0 : Anything

 ahf_lmax Scope: private INT Description: Maximum number of terms in theta expansion Range Default: 8 0:19 Range from 0 to 19

 ahf_logfile Scope: private BOOLEAN Description: Write log file? Default: no

 ahf_manual_guess Scope: private BOOLEAN Description: Use specified coefficients for guess? Default: no

 ahf_mask Scope: private KEYWORD Description: Use mask? Range Default: off off Mask is off strong Mask set only for definite horizons weak Mask set for both definite and probable horizons

 ahf_mask_0 Scope: private BOOLEAN Description: Mask for first horizon with find3? Default: yes

 ahf_mask_1 Scope: private BOOLEAN Description: Mask for second horizon with find3? Default: yes

 ahf_mask_2 Scope: private BOOLEAN Description: Mask for third horizon with find3? Default: yes

 ahf_mask_time Scope: private REAL Description: Time after which to start setting the mask Range Default: -1.0 : Anything goes. Negative number means setting the mask as soon as possible

 ahf_maskbuffer Scope: private INT Description: Number of grid points in mask buffer zone Range Default: 5 Positive please

 ahf_maskshrink Scope: private REAL Description: Shrink factor for mask Range Default: 0.8 0.0:1.0 Must be positive and not larger than 1

 ahf_maxchange Scope: private REAL Description: Maximum relative difference between 1 big and 2 small steps Range Default: 0.1 : Anything

 ahf_maxiter Scope: private INT Description: Maximum number of iterations of POWELL Range Default: 10 : Any sensible integer value

 ahf_minarea Scope: private BOOLEAN Description: Minimize area instead of expansion? Default: no

 ahf_minchange Scope: private REAL Description: Minimum relative difference between 1 big and 2 small steps Range Default: 0.01 : Anything

 ahf_nn0 Scope: private INT Description: Number of subdivisions of c0(0) for initial guess Range Default: 10 : Some positive integer

 ahf_nn2 Scope: private INT Description: Number of subdivisions of c0(2) for initial guess Range Default: 10 : Some positive integer

 ahf_nphi Scope: private INT Description: Number of subdivisions in phi Range Default: 100 1: Any sensible integer

 ahf_ntheta Scope: private INT Description: Number of subdivisions in theta Range Default: 100 1: Any sensible integer

 ahf_octant Scope: private KEYWORD Description: Octant symmetry? Range Default: no no No octant symmetry yes Octant symmetry: reflection symmetry on all three coordinate planes high Octant symmetry + symmetry of rotation of pi/2 around z axis

 ahf_offset Scope: private BOOLEAN Description: Center offset from origin? Default: no

 ahf_phi Scope: private BOOLEAN Description: Expand also in phi? (seach for non-axisymmetric surface) Default: no

 ahf_r0 Scope: private REAL Description: Radius of initial sphere (0 forces largest sphere) Range Default: 0.0 : Anything

 ahf_r0_0 Scope: private REAL Description: Radius of first initial sphere for find3 (0 forces largest sphere) Range Default: 0.0 : Anything

 ahf_r0_1 Scope: private REAL Description: Radius of second initial sphere for find3 (0 forces largest sphere) Range Default: 0.0 : Anything

 ahf_r0_2 Scope: private REAL Description: Radius of third initial sphere for find3 (0 forces largest sphere) Range Default: 0.0 : Anything

 ahf_refx Scope: private BOOLEAN Description: Reflection symmetry x->-x? Default: no

 ahf_refy Scope: private BOOLEAN Description: Reflection symmetry y->-y? Default: no

 ahf_refz Scope: private BOOLEAN Description: Reflection symmetry z->-z? Default: no

 ahf_reportalways Scope: private BOOLEAN Description: Report for all surfaces found (yes) or just for apparent horizons (no) Default: no

 ahf_shiftcoeff Scope: private REAL Description: Coefficient for shift Range Default: 0.0 : Anything goes

 ahf_sloppyguess Scope: private BOOLEAN Description: Use sphere as initial guess? Default: no

 ahf_tol Scope: private REAL Description: Tolerance for minimization routines Range Default: 0.1 0: A sensible positive number

 ahf_trapped_surface Scope: private BOOLEAN Description: Minimize (expansion + delta) to find trapped surface? Default: no

 ahf_verbose Scope: private BOOLEAN Description: Print messages to screen? Default: yes

 ahf_veryverbose Scope: private BOOLEAN Description: Print messages at each iteration step to screen? Default: no

 ahf_wander Scope: private BOOLEAN Description: Allow the center to wander? Default: no

 ahf_xc Scope: private REAL Description: x-coordinate of center of expansion Range Default: 0.0 : Anything

 ahf_xc_0 Scope: private REAL Description: x-coordinate of center of expansion for first surface with find3 Range Default: 0.0 : Anything

 ahf_xc_1 Scope: private REAL Description: x-coordinate of center of expansion for second surface with find3 Range Default: 0.0 : Anything

 ahf_xc_2 Scope: private REAL Description: x-coordinate of center of expansion for third surface with find3 Range Default: 0.0 : Anything

 ahf_yc Scope: private REAL Description: y-coordinate of center of expansion Range Default: 0.0 : Anything

 ahf_yc_0 Scope: private REAL Description: y-coordinate of center of expansion for first surface with find3 Range Default: 0.0 : Anything

 ahf_yc_1 Scope: private REAL Description: y-coordinate of center of expansion for second surface with find3 Range Default: 0.0 : Anything

 ahf_yc_2 Scope: private REAL Description: y-coordinate of center of expansion for third surface with find3 Range Default: 0.0 : Anything

 ahf_zc Scope: private REAL Description: z-coordinate of center of expansion Range Default: 0.0 : Anything

 ahf_zc_0 Scope: private REAL Description: z-coordinate of center of expansion for first surface with find3 Range Default: 0.0 : Anything

 ahf_zc_1 Scope: private REAL Description: z-coordinate of center of expansion for second surface with find3 Range Default: 0.0 : Anything

 ahf_zc_2 Scope: private REAL Description: z-coordinate of center of expansion for third surface with find3 Range Default: 0.0 : Anything

 horizon_to_announce_centroid Scope: private INT Description: For which horizon should we announce the centroid to driftcorrect Range Default: (none) don’t announce the centroid 1:3 announce this horizon’s centroid each time we find it

 horizon_to_output_centroid Scope: private INT Description: For which horizon should we output the centroid Range Default: (none) don’t output any centroids 1:3 output this horizon’s centroid each time we find it

 interpolation_operator Scope: private STRING Description: Name of interpolation operator to use Range Default: uniform cartesian .+ A valid name for a registered interpolation operator

 interpolation_order Scope: private INT Description: Order for interpolation Range Default: 2 1:4 Choose between first and fourth order interpolation

 trapped_surface_delta Scope: private REAL Description: find (expansion = delta) surface Range Default: 0.0 : Just a real number

 ahf_active Scope: restricted BOOLEAN Description: Activate AHFinder? Default: no

 ahf_persists Scope: restricted BOOLEAN Description: Do the finder grid functions stay around? Default: no

### 4 Interfaces

Implements:

ahfinder

Inherits:

staticconformal

grid

io

#### Grid Variables

##### 4.0.1 PRIVATE GROUPS
 Group Names Variable Names Details triggergroup compact 0 triggervar description For triggering output dimensions 0 distribution CONSTANT group type SCALAR timelevels 1 variable type INT ahfgradient compact 0 ahfgradx description Grid functions for gradients ahfgrady dimensions 3 ahfgradz distribution DEFAULT ahfgradn group type GF timelevels 1 variable type REAL ahfinder_gauss compact 0 ahfgauss description Grid function for gaussian curvature calculation dimensions 3 distribution DEFAULT group type GF timelevels 1 variable type REAL find3grid compact 0 ahfgrid3 description Grid functions to use in find3 algorithm ahf_exp3 dimensions 3 distribution DEFAULT group type GF timelevels 1 variable type REAL ahf_centroid compact 0 ahf_centroid_x description Centroid of one of the horizons ahf_centroid_y dimensions 0 ahf_centroid_z distribution CONSTANT group type SCALAR timelevels 1 variable type REAL drift_check compact 0 drift_first description For checking if its the first drift correction dimensions 0 distribution CONSTANT group type SCALAR timelevels 1 variable type INT
 Group Names Variable Names Details out_scalars compact 0 out_mass description Output of scalar variables out_radius dimensions 0 out_area distribution CONSTANT out_perimeter group type SCALAR out_meridian1 timelevels 1 out_meridian2 variable type REAL out_1d_legen compact 0 out_c0 description Output of c0 coefficients dimensions 1 distribution CONSTANT group type ARRAY size AHF_LMAX timelevels 1 variable type REAL out_2d_legen compact 0 out_cc description Output of cc and cs coefficients out_cs dimensions 2 distribution CONSTANT group type ARRAY size AHF_LMAX size AHF_LMAX timelevels 1 variable type REAL ahfinder_gaussian compact 0 gaussian description Gaussian Curvature dimensions 2 distribution CONSTANT group type ARRAY size AHF_NTHETA+1 size AHF_NPHI+1 timelevels 1 variable type REAL

##### 4.0.2 PUBLIC GROUPS
 Group Names Variable Names Details ahfindergrid compact 0 ahfgrid description Horizon function dimensions 3 distribution DEFAULT group type GF timelevels 1 variable type REAL ahfinderexp compact 0 ahf_exp description Expansion dimensions 3 distribution DEFAULT group type GF timelevels 1 variable type REAL ahfmask compact 0 ahmask description Grid function for masking dimensions 3 distribution DEFAULT group type GF timelevels 1 variable type REAL hole1_bounds compact 0 dhole1_xmin description Bounds of excision box for hole 1 dhole1_ymin dimensions 0 dhole1_zmin distribution CONSTANT dhole1_xmax group type SCALAR dhole1_ymax timelevels 1 dhole1_zmax variable type REAL hole2_bounds compact 0 dhole2_xmin description Bounds of excision box for hole 2 dhole2_ymin dimensions 0 dhole2_zmin distribution CONSTANT dhole2_xmax group type SCALAR dhole2_ymax timelevels 1 dhole2_zmax variable type REAL hole3_bounds compact 0 dhole3_xmin description Bounds of excision box for hole 3 dhole3_ymin dimensions 0 dhole3_zmin distribution CONSTANT dhole3_xmax group type SCALAR dhole3_ymax timelevels 1 dhole3_zmax variable type REAL

### 5 Schedule

This section lists all the variables which are assigned storage by thorn EinsteinAnalysis/AHFinder. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

#### Storage

 Conditional: hole1_bounds hole2_bounds hole3_bounds ahf_centroid out_scalars ahfinder_gaussian out_1d_legen out_2d_legen ahfindergrid ahfinderexp ahfgradient ahfinder_gauss find3grid ahfmask ahfmask hole1_bounds hole2_bounds hole3_bounds

#### Scheduled Functions

CCTK_WRAGH

ahfinder_setsym

set symmetries for ahfinder grid functions

 Language: fortran Options: global Type: function

CCTK_STARTUP

ahfinder_startup

register ahfinder as an io method

 Language: c Options: global Type: function

CCTK_PARAMCHECK

ahfinder_paramcheck

check for physical or conformal metric

 Language: fortran Options: global Type: function

CCTK_INITIAL

ahfinder_initoutput

 Language: fortran Type: function

CCTK_ANALYSIS (conditional)

ahfinder

call apparent horizon finder with persisting grid functions

 Before: driftcorrect Language: fortran Storage: triggergroup Triggers: triggergroup Type: function

CCTK_ANALYSIS (conditional)

ahfinder

call apparent horizon finder

 Before: driftcorrect Language: fortran Storage: ahfindergrid ahfinderexp ahfgradient ahfinder_gauss find3grid ahfmask triggergroup Triggers: triggergroup Type: function

CCTK_ANALYSIS (conditional)

ahfinder

call apparent horizon finder with persisting mask

 Before: driftcorrect Language: fortran Storage: ahfindergrid ahfinderexp ahfgradient ahfinder_gauss find3grid triggergroup Triggers: triggergroup Type: function