Efficient Evolution of Self-Gravitating Spherical Dark-Matter Halos with and without New Physics

We discuss NSphere, a new numerical algorithm for evolving spherically symmetric self-gravitating systems that reduces the six-dimensional phase space to three, providing orders-of-magnitude efficiency gains over full N-body methods. NSphere enables rapid exploration of halo evolution both in the collisionless case and when new physics, such as self-interacting dark matter (SIDM), is included. I will describe the method, its recent extension to SIDM, and applications to halos with anisotropic velocity distributions. These results show that anisotropy can alter gravothermal collapse timescales by more than a factor of two, underscoring the importance of velocity structure. For isotropic velocity distributions, our findings are consistent with existing work