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Welcome to aurel’s documentation!

Aurel is an open source Python package for numerical relativity analysis. Designed with ease of use in mind, it will automatically calculate relativistic terms.

(As long as it is in the list of available entities, see descriptions.)

In addition, this package also provides tools for advanced numerical computations, including:

  • finite difference schemes for 3D grids,

  • tools for tensor calculations,

  • tools to import data from Einstein Toolkit simulations.

Installation

Install aurel using pip:

pip install aurel

all other required packages will be installed automatically.

Getting started

Start your Python session on a jupyter notebook or in a Python script and import the AurelCore class:

import aurel

# Define your grid parameters
param = {
    'Nx': 64, 'Ny': 64, 'Nz': 64,
    'xmin': -1.0, 'ymin': -1.0, 'zmin': -1.0,
    'dx': 0.03125, 'dy': 0.03125, 'dz': 0.03125,
}

# Initialize the finite difference class
fd = aurel.FiniteDifference(param)

# Initialize the AurelCore class
rel = aurel.AurelCore(fd)

At this point you need to provide the spacetime metric, extrinsic curvature and matter fields, see Assumed quantities. These are passed as numpy arrays to aurel in the following way:

# Define the xx component of the spacetime metric
rel.data['gxx'] = np.ones((param['Nx'], param['Ny'], param['Nz']))

and so on for the other components and required quantities. In this example \(g_{xx} = 1\), but you can pass any numpy array; it can be of numerical relativity simulation data, or an array generated from an analytical expression.

With everything defined, you can call any entity listed in the descriptions list. Just call it as:

rel["name_of_the_entity"]

Aurel will automatically do its best to calculate any relativistic term you ask for.

Now if you want calculations over multiple moments in coordinate time, you can use the aurel.over_time() function. First, create a dictionary containing the spacetime and matter fields over time:

# Define the spacetime metric gxx over time
data = {
    'gxx': [np.ones((param['Nx'], param['Ny'], param['Nz'])),
            np.ones((param['Nx'], param['Ny'], param['Nz']))],
    ...
}

That is a data dictionary with keys the names of the quantities, and values a list of numpy arrays, one for each time step. Calculations will be performed for each of these time steps as:

data = aurel.over_time(
   data, fd,
   vars=['name_of_the_entity', ..., {'custom_quantity': custom_quantity}],
   estimates=['name_of_estimate', ..., {'custom_estimate': custom_estimate}],
   **kwargs)

where vars is a list of entities to calculate at each time step, available terms are in descriptions but you can also pass custom functions to calculate your own quantities. Likewise estimates is a list of estimates to calculate at each time step, available functions are in estimates but you can also pass custom functions to calculate your own estimates. See the examples.

Contents:

Advice:

Examples: