Functions
	psi (r)
	Conformal factor of the Schwarzschild black hole in isotropic coordinates.

	build_and_run (directory, peano_installation, end_time, scheme, enforce, patch_size=PatchSize, load_balancing=False, threads=None)
	Generate, compile and run the tutorial setup within directory.

	probe (directory, point, output_file)
	Probe all snapshots at one point.

	profile (directory, volumes_per_axis=VolumesPerAxis)
	Probe lapse and phi in the centre of each volume along the line through the centres of the volumes next to the puncture, i.e.

	radius (x, line_offset=LineOffset)

	time_steps (directory)
	Number of time steps and average wall clock time per time step.

	plot_speeding_up (coarse, fine)
	Lapse next to the puncture over time, and along the x-axis at the end, for both meshes.

	plot_initial_data (x, lapse, phi)
	Initial lapse and conformal factor along the x-axis against the closed form.

	plot_lapse_profile (x, t, lapse)
	Lapse along the x-axis for several snapshots.

	plot_lapse_over_time (x, t, lapse)
	Lapse over time at a few distances from the puncture.

	plot_constraints (unconstrained, constrained)
	Lapse and phi next to the puncture over time with and without constraint enforcement.

Variables
	Here = os.path.dirname(os.path.abspath(__file__))

	PeanoRoot = os.path.abspath(os.path.join(Here, "..", "..", "..", ".."))

str	PatchFile = "solution-CCZ4.peano-patch-file"

float	Mass = 1.0

float	DomainOffset = -9.0

float	DomainSize = 18.0

int	CellsPerAxis = 9

int	PatchSize = 6

int	VolumesPerAxis = CellsPerAxis * PatchSize

float	TimeInBetweenPlots = 0.5

float	LineOffset = DomainSize / VolumesPerAxis / 2.0
	y and z coordinate of the line along which we probe: the centre of the first volume next to the origin

int	DecomposedPatchSize = 10
	The run of the section "Speeding up": the plain Finite Volumes with 10x10x10 patches over the same 9x9x9 mesh cells, the domain decomposed by a load balancing strategy, and four OpenMP threads.

int	DecomposedThreads = 4

list	Runs
	The runs: name, patch size, load balancing, threads, constraint enforcement.

	parser

	default

	help

	type

	float

	args = parser.parse_args()

	work_directory

dict	runs = {}

	directory = os.path.join(os.path.abspath(work_directory), name)

	runtime

int	volumes_per_axis = CellsPerAxis * patch_size

	x

	t

	lapse

	phi

	count

	average

float	h = DomainSize / volumes_per_axis

int	centre = volumes_per_axis // 2

Function Documentation

◆ build_and_run()

522_single-black-hole.build_and_run	(	directory,
		peano_installation,
		end_time,
		scheme,
		enforce,
		patch_size = `PatchSize`,
		load_balancing = `False`,
		threads = `None`
	)

Generate, compile and run the tutorial setup within directory.

Parameters

patch_size	int Number of volumes per axis within one patch. The mesh always has CellsPerAxis cells per axis.
load_balancing	bool If True, decompose the domain with toolbox::loadbalancing::strategies::SpreadOutOnceGridStagnates.
threads	int or None If not None, run with OMP_NUM_THREADS set to this value.
scheme	type Numerical scheme, i.e. a Finite Volume class from exahype2.api.fv.
enforce	exagrype.api.CCZ4Solver.EnforceCCZ4Constraint Constraint enforcement.

Returns the runtime of the executable in seconds. If the directory holds the result of a previous run, we do not rerun but return the stored runtime.

Definition at line 104 of file 522_single-black-hole.py.

References float, and exagrype.api.initialvalues.single_black_hole().

Here is the call graph for this function:

◆ plot_constraints()

522_single-black-hole.plot_constraints	(	unconstrained,
		constrained
	)

Lapse and phi next to the puncture over time with and without constraint enforcement.

Definition at line 431 of file 522_single-black-hole.py.

References radius().

Here is the call graph for this function:

◆ plot_initial_data()

522_single-black-hole.plot_initial_data	(	x,
		lapse,
		phi
	)

Initial lapse and conformal factor along the x-axis against the closed form.

Definition at line 333 of file 522_single-black-hole.py.

References psi(), and radius().

Here is the call graph for this function:

◆ plot_lapse_over_time()

522_single-black-hole.plot_lapse_over_time	(	x,
		t,
		lapse
	)

Lapse over time at a few distances from the puncture.

Definition at line 406 of file 522_single-black-hole.py.

References radius().

Here is the call graph for this function:

◆ plot_lapse_profile()

522_single-black-hole.plot_lapse_profile	(	x,
		t,
		lapse
	)

Lapse along the x-axis for several snapshots.

Definition at line 379 of file 522_single-black-hole.py.

◆ plot_speeding_up()

522_single-black-hole.plot_speeding_up	(	coarse,
		fine
	)

Lapse next to the puncture over time, and along the x-axis at the end, for both meshes.

Definition at line 300 of file 522_single-black-hole.py.

References radius().

Here is the call graph for this function:

◆ probe()

522_single-black-hole.probe	(	directory,
		point,
		output_file
	)

Probe all snapshots at one point.

Returns the time stamps, the lapse and the conformal factor phi.

Definition at line 229 of file 522_single-black-hole.py.

References float.

◆ profile()

522_single-black-hole.profile	(	directory,
		volumes_per_axis = `VolumesPerAxis`
	)

Probe lapse and phi in the centre of each volume along the line through the centres of the volumes next to the puncture, i.e.

along y=z=h/2

Returns the x coordinates, the time stamps and two 2d arrays lapse[snapshot,x] and phi[snapshot,x].

Definition at line 255 of file 522_single-black-hole.py.

◆ psi()

522_single-black-hole.psi ( r )

Conformal factor of the Schwarzschild black hole in isotropic coordinates.

Definition at line 73 of file 522_single-black-hole.py.

Referenced by plot_initial_data().

Here is the caller graph for this function:

◆ radius()

522_single-black-hole.radius	(	x,
		line_offset = `LineOffset`
	)

Definition at line 277 of file 522_single-black-hole.py.

Referenced by plot_constraints(), plot_initial_data(), plot_lapse_over_time(), and plot_speeding_up().

Here is the caller graph for this function:

◆ time_steps()

522_single-black-hole.time_steps ( directory )

Number of time steps and average wall clock time per time step.

Both stem from the final report of peano4::DefaultStepReport in run.log, i.e. from the line "TimeStep: ...s (avg=...,#measurements=...".

Definition at line 281 of file 522_single-black-hole.py.

References float.

Variable Documentation

◆ args

522_single-black-hole.args = parser.parse_args()

Definition at line 487 of file 522_single-black-hole.py.

◆ average

522_single-black-hole.average

Definition at line 508 of file 522_single-black-hole.py.

◆ CellsPerAxis

int 522_single-black-hole.CellsPerAxis = 9

Definition at line 63 of file 522_single-black-hole.py.

◆ centre

int 522_single-black-hole.centre = volumes_per_axis // 2

Definition at line 519 of file 522_single-black-hole.py.

◆ count

522_single-black-hole.count

Definition at line 508 of file 522_single-black-hole.py.

◆ DecomposedPatchSize

int 522_single-black-hole.DecomposedPatchSize = 10

The run of the section "Speeding up": the plain Finite Volumes with 10x10x10 patches over the same 9x9x9 mesh cells, the domain decomposed by a load balancing strategy, and four OpenMP threads.

Definition at line 81 of file 522_single-black-hole.py.

◆ DecomposedThreads

int 522_single-black-hole.DecomposedThreads = 4

Definition at line 82 of file 522_single-black-hole.py.

◆ default

522_single-black-hole.default

Definition at line 476 of file 522_single-black-hole.py.

◆ directory

522_single-black-hole.directory = os.path.join(os.path.abspath(work_directory), name)

Definition at line 495 of file 522_single-black-hole.py.

◆ DomainOffset

float 522_single-black-hole.DomainOffset = -9.0

Definition at line 61 of file 522_single-black-hole.py.

◆ DomainSize

float 522_single-black-hole.DomainSize = 18.0

Definition at line 62 of file 522_single-black-hole.py.

◆ float

522_single-black-hole.float

Definition at line 485 of file 522_single-black-hole.py.

Referenced by build_and_run(), probe(), and time_steps().

◆ h

522_single-black-hole.h = DomainSize / volumes_per_axis

Definition at line 509 of file 522_single-black-hole.py.

◆ help

522_single-black-hole.help

Definition at line 477 of file 522_single-black-hole.py.

◆ Here

522_single-black-hole.Here = os.path.dirname(os.path.abspath(__file__))

Definition at line 43 of file 522_single-black-hole.py.

◆ lapse

522_single-black-hole.lapse

Definition at line 507 of file 522_single-black-hole.py.

◆ LineOffset

float 522_single-black-hole.LineOffset = DomainSize / VolumesPerAxis / 2.0

y and z coordinate of the line along which we probe: the centre of the first volume next to the origin

Definition at line 70 of file 522_single-black-hole.py.

◆ Mass

float 522_single-black-hole.Mass = 1.0

Definition at line 60 of file 522_single-black-hole.py.

◆ parser

522_single-black-hole.parser

Initial value:

=  argparse.ArgumentParser(
        description="Create the PNGs of the tutorial 522_single-black-hole.ipynb"
    )

Definition at line 471 of file 522_single-black-hole.py.

◆ PatchFile

str 522_single-black-hole.PatchFile = "solution-CCZ4.peano-patch-file"

Definition at line 59 of file 522_single-black-hole.py.

◆ PatchSize

int 522_single-black-hole.PatchSize = 6

Definition at line 64 of file 522_single-black-hole.py.

◆ PeanoRoot

522_single-black-hole.PeanoRoot = os.path.abspath(os.path.join(Here, "..", "..", "..", ".."))

Definition at line 44 of file 522_single-black-hole.py.

◆ phi

522_single-black-hole.phi

Definition at line 507 of file 522_single-black-hole.py.

◆ Runs

list 522_single-black-hole.Runs

Initial value:

=  [
    ("plain", PatchSize, False, None, exagrype.api.CCZ4Solver.EnforceCCZ4Constraint.No),
    (
        "decomposed",
        DecomposedPatchSize,
        True,
        DecomposedThreads,
        exagrype.api.CCZ4Solver.EnforceCCZ4Constraint.No,
    ),
    (
        "decomposed-constrained",
        DecomposedPatchSize,
        True,
        DecomposedThreads,
        exagrype.api.CCZ4Solver.EnforceCCZ4Constraint.OnlyFinalSolution,
    ),
]

The runs: name, patch size, load balancing, threads, constraint enforcement.

Definition at line 85 of file 522_single-black-hole.py.

◆ runs

dict 522_single-black-hole.runs = {}

Definition at line 493 of file 522_single-black-hole.py.

◆ runtime

522_single-black-hole.runtime

Initial value:

=  build_and_run(
                directory,
                os.path.abspath(args.peano_root),
                args.end_time,
                exahype2.api.fv.RusanovWithExplicitEuler,
                enforce,
                patch_size=patch_size,
                load_balancing=load_balancing,
                threads=threads,
            )

Definition at line 496 of file 522_single-black-hole.py.

◆ t

522_single-black-hole.t

Definition at line 507 of file 522_single-black-hole.py.

◆ TimeInBetweenPlots

float 522_single-black-hole.TimeInBetweenPlots = 0.5

Definition at line 66 of file 522_single-black-hole.py.

◆ type

522_single-black-hole.type

Definition at line 485 of file 522_single-black-hole.py.

◆ volumes_per_axis

522_single-black-hole.volumes_per_axis = CellsPerAxis * patch_size

Definition at line 506 of file 522_single-black-hole.py.

◆ VolumesPerAxis

int 522_single-black-hole.VolumesPerAxis = CellsPerAxis * PatchSize

Definition at line 65 of file 522_single-black-hole.py.

◆ work_directory

522_single-black-hole.work_directory

Initial value:

=  args.work_directory or stack.enter_context(
            tempfile.TemporaryDirectory()
        )

Definition at line 490 of file 522_single-black-hole.py.

◆ x

522_single-black-hole.x

Definition at line 507 of file 522_single-black-hole.py.

Functions

Variables

Function Documentation

◆ build_and_run()

◆ plot_constraints()

◆ plot_initial_data()

◆ plot_lapse_over_time()

◆ plot_lapse_profile()

◆ plot_speeding_up()

◆ probe()

◆ profile()

◆ psi()

◆ radius()

◆ time_steps()

Variable Documentation

◆ args

◆ average

◆ CellsPerAxis

◆ centre

◆ count

◆ DecomposedPatchSize

◆ DecomposedThreads

◆ default

◆ directory

◆ DomainOffset

◆ DomainSize

◆ float

◆ h

◆ help

◆ Here

◆ lapse

◆ LineOffset

◆ Mass

◆ parser

◆ PatchFile

◆ PatchSize

◆ PeanoRoot

◆ phi

◆ Runs

◆ runs

◆ runtime

◆ t

◆ TimeInBetweenPlots

◆ type

◆ volumes_per_axis

◆ VolumesPerAxis

◆ work_directory

◆ x