Tensor spherical harmonic filtering for numerical relativity

SpEC, the Spectral Einstein Code, solves Einstein's equations using multidomain spectral methods on cylindrical, cubical, and spherical subdomains. SpEC chooses Cartesian components of tensors as the variables on all subdomains, so the equations are the same everywhere and variables can be directly compared wherever subdomains touch. However, the use of Cartesian components on spherical subdomains causes an instability in the highest angular modes. This instability can be resolved by expanding tensors in a spherical basis with spin-weighted spherical harmonic expansion coefficients, truncating the highest modes, and transforming back to a Cartesian basis. We describe a new implementation of this filtering operation.