Wave

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In **numerical relativity**, Einstein's field equations are solved on the computer.

Numerical solving these 10 coupled, highly nonlinear partial differential equations allows the investigation of

**physical properties**of astrophysical systems such as the fusion of black holes or neutron stars**mathematical properties**of spacetimes such as geometry or horizons.

Numerical relativity complements analytical methods and perturbation theory, and allows the calculation of phenomena that cannot be investigated by other methods.

Of particular interest is the calculation of gravitational waves. While the methods of perturbation theory provide the waveforms in the phase of the spiralling in of binary black holes, it is possible in numerical relativity theory to determine waveforms of the fusion phase. These simulated gravitational wave signals are helpful in the detection of gravitational waves.

Solving Einstein's field equations on the computer is a big challenge. It is necessary to cover many different topics.

**Physics**is the goal, but also essential to understand and interpret the results of numerical simulations.**Simulations**are performed on high-performance computers so that they can be completed within a reasonable time.**Mathematics**is needed to rewrite Einstein's field equations into a well-founded initial value problem.**Numerics**provides methods of high accuracy to discretize the Einstein equations and calculate solutions.