4 papers
On the Gram matrix of standard inner products of asymmetrically-weighted Hermite functions
Ruiyang Dai
Let A denote the infinite Gram matrix associated with the standard L2 inner product of asymmetrically-weighted (AW) Hermite functions. We derive an explicit representation of its e…
A stable and efficient Galerkin spectral method with asymmetrically-weighted Hermite functions for the Vlasov-Poisson system
Ruiyang Dai
We analyze a Galerkin spectral method applied to the Vlasov-Poisson (VP) system based on time-independent asymmetrically-weighted (AW) Hermite functions in velocity. The VP system…
Galerkin method for asymmetrically-weighted Hermite approximations applied to the Vlasov-Poisson system
Ruiyang Dai
We investigate a numerical method for the Vlasov-Poisson (VP) system utilizing asymmetrically-weighted (AW) Hermite bases in velocity space, which is an hyperbolic system. In parti…
On the quadratic stability of asymmetric Hermite basis with application to plasma physics with oscillating electric field
Ruiyang Dai, Bruno Després
We analyze why the discretization of linear transport with asymmetric Hermite basis functions can be instable in quadratic norm. The main reason is that the finite truncation of th…