Efficient Adaptive-Rank Implicit Time Integrators for Stiff Nonlinear Fokker-Planck Kinetic Models

The authors propose a high-order adaptive-rank implicit integrator that leverages extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases, enabling accurate representation of solutions with significantly reduced computational costs. The approach is demonstrated on the challenging Lenard-Bernstein Fokker-Planck nonlinear equation, preserving equilibrium states and strictly conserving mass, momentum, and energy.