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Spurred by the current development of numerous large-scale projects for detecting gravitational radiation, with the aim to open a completely new window to the observable Universe, numerical relativity has become a major field of research over the past years. Indeed, numerical relativity is the standard approach when studying potential sources of gravitational waves, where strong fields and relativistic velocities are part of any physical scenario. This book can be considered a primer for both graduate students and non-specialist researchers wishing to enter the field. Starting from the most basic insights and aspects of numerical relativity, Elements of Numerical Relativity develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism, gauge, initial and boundary conditions as well as various numerical algorithms. The tests and applications proposed in this book can be performed on a standard PC.

Relativity (Physics) --- Space and time --- Evolution equations --- Einstein field equations --- Relativité (Physique) --- Espace et temps --- Equations d'évolution --- Mathematics. --- Numerical solutions. --- Mathématiques --- Solutions numériques --- Physics. --- Computer science. --- Mathematical physics. --- Relativity (Physics). --- Mathematical and Computational Physics. --- Relativity and Cosmology. --- Computational Science and Engineering. --- Applied Physics --- Physics - General --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematics --- Numerical solutions --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Physical mathematics --- Informatics --- Natural philosophy --- Philosophy, Natural --- Computer mathematics. --- Gravitation. --- Theoretical, Mathematical and Computational Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Science --- Computer mathematics --- Electronic data processing --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties --- Space and time - Mathematics --- Evolution equations - Numerical solutions --- Einstein field equations - Numerical solutions --- Computer science