Gravitational waves and Reduced Basis

Manuel Tiglio

April 26, 2012

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Abstract: I will give an introduction to some aspects of Reduced Basis and its applications to gravitational waves, discussing results that we have obtained so far and our roadmap for the future. Essentially, the core issue is how to choose the most relevant points in parameter space, in a nearly optimal way, to select which configurations (of, say, binary black holes or binary compact objects in general) are the “most representative ones”. This applies to the case in which the emitted gravitational waves can be simply evaluated using closed form approximations or obtained by solving simple equations but, most important, when deciding which configurations to solve for in numerical simulations of the full Einstein equations. The approach also provides a way of interpolating between these selected configurations to obtain other ones with high accuracy. We have so far found that the representation error decays exponentially with the number of elements in the reduced basis, providing dramatic savings (sometimes of several orders of magnitude) compared to traditional methods. The techniques are generic (i.e. not restricted to General Relativity) and fall within the area of reduced order modeling, approximation theory, and parametrized problems/partial differential equations.