Seminars on Numerical Algorithms, Analyses, and Applications：Structure-preserving spectral methods with exact curl/divergence-free constraints for plasma simulations-Tianyuan Mathematical Center in Southeast China (TMSE)

Speaker：Zhiguo Yang（Shanghai Jiao Tong University）

Time：2022-12-16, 10:00

Location：Tencent Meeting ID：795-762-597（No Password）

Abstract:

In this talk, we present H^1-, H(div) and H(curl)-conforming spectral method with exact preservation of the curl/divergence-free constraints for two typical PDEs arising from plasma simulations. One is the incompressible visco-resistive MHD system and the other one is the Vlasov-Ampere system. Two key ingredients, i.e. exact de Rham complexes and their commuting diagram, and the derivative property of the generalized Jacobi polynomials are essential for the derivation of the desired basis functions. Besides, several novel second-order energy-stable or energy-conserving time discretization schemes are proposed. Ample 2D and 3D numerical examples illustrate both the accuracy of the structure-preserving basis functions and the efficiency of the proposed schemes.