Numerical relativity for LISA with spectral methods

The upcoming space-based LISA mission will require numerical relativity simulations of merging supermassive black hole binaries at higher accuracy and across a larger parameter space of mass-ratios, spins, and orbital eccentricities than currently possible. In this talk, I present progress by the SXS collaboration to make these simulations computationally feasible using spectral methods, which can achieve high accuracy for binary black hole simulations with low computational cost. I explore the limits of our current numerical relativity code SpEC in tackling these simulations and our prospect of surpassing these limits by massive parallelization of spectral methods with our new code SpECTRE. I present a suite of our highest-accuracy simulations so far that are available to inform waveform modeling and data analysis efforts for LISA.