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It is not possible to write down closed form expressions for generic solutions to nonlinear partial differential equations. To understand their solution space we must instead resort to the combined use of sophisticated mathematics and numerical approximation. In gravitation, as described in particular by Einstein's theory of general relativity, this is called numerical relativity. In this presentation I will give an introduction to this topic. I will describe the theoretical considerations, the practical work-flow and the most exciting applications, covering both gravitational wave astronomy and our attempts to correspond with the cosmic censor.
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