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Workshop on Computation of Kinetic Transport and Related Problems

The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term


Yuhua Zhu(朱裕华) , Stanford University


22 Jun, 15:20 - 16:00


We consider the Vlasov-Fokker-Planck equation with random electric field where the random field is parameterized by countably many infinite random variables due to uncertainty. At the theoretical level, with suitable assumption on the anisotropy of the randomness, adopting the technique employed in elliptic PDEs [5], we prove the best N approximation in the random space breaks the dimension curse and the convergence rate is faster than the Monte Carlo method. For the numerical method, based on the adaptive sparse polynomial interpolation (ASPI) method introduced in [2], we develop a residual based adaptive sparse polynomial interpolation (RASPI) method which is more efficient for multiscale linear kinetic equation, when using numerical schemes that are time-dependent and implicit. Numerical experiments show taht the numerical error of the RASPI t decays faster than the Monte-Carlo method and is also dimension independent.