Efficient Asymptotic-Preserving Method Based on Characteristics for Kinetic Equations

Kinetic equations serve as fundamental mathematical models for describing the dynamic behavior of particle systems. Their intrinsic multiscale structure, however, poses significant challenges in developing efficient and robust numerical schemes. A popular approach is to design asymptotic preserving (AP) schemes. It aims to create a unified solver across the computational domain that captures the correct asymptotic limits at a discrete level. In recent years, we have developed a class of unconditionally stable AP schemes based on characteristic backtracking. These methods feature low computational complexity, high parallel efficiency, and excellent scalability, making them particularly suitable for long-time simulations of high-dimensional, multiscale transport phenomena. Owing to these advantages, the proposed framework holds great potential for applications in national defense engineering, astrophysics, semiconductor, and biochemistry.