Basis Function Transformations for Numerical Relativity

The numerical relativity code SpEC uses a mixture of both Cartesian and spherical coordinates for efficiency, and must treat coordinate transformations carefully to avoid instabilities. However, converting Cartesian tensor components expanded in spherical harmonics to spherical components expanded in spin-weighted spherical harmonics--and vice versa--is a major speed and memory bottleneck for simulating black hole binaries. We find an analytic expression for the tensor spherical harmonic transform and implement it for fast, memory-efficient basis function transformation.