Numerical black hole perturbation theory

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On-site: Room 11.2.21
Lidia Gomes da Silva (QMUL, London)
Extreme-Mass-Ratio-Inspirals (EMRIs) modelling in time-domain has been anything but trivial due to the challenges associated with resolving the discontinuity emerging from the point-particle model of the smaller BH and the slow long-term evolution.  
In this talk I will review two novel highly accurate hyperboloidal numerical algorithms in the time-domain designed to address the issues faced by previous attempts. In the first algorithm, arXiv:2306.13153, we use collocation methods with higher order jumps in combination with novel implicit-turned-explicit IMTEX time integrators; In the second algorithm, (arXiv: 1402.7343, 2202.01794) we will show how we can return high accuracies from a fully-spectral implementation with multidomain spectral decomposition and an implicit spectral time integrator. Both of our time-integrators show long-term stability, preserve symplectic structure and conserver energy.