Numerical methods for high-dimensional kinetic equations

High-dimensionality is one of the major challenges in kinetic modeling and simulation of realistic physical systems. The most appropriate numerical scheme needs to balance accuracy and computational complexity, and it also needs to address issues such as multiple scales, lack of regularity, and long-term integration. In this chapter, we review state-of-the-art numerical techniques for highdimensional kinetic equations, including low-rank tensor approximation, sparse grid collocation, and ANOVA decomposition.