科研之友
微信
新浪微博
Facebook
分享链接
摘要
In this article, we derive a semi-Lagrangian scheme for the solution of the Vlasov equation represented as a low-parametric tensor. Grid-based methods for the Vlasov equation have been shown to give accurate results but their use has mostly been limited to simulations in two-dimensional phase space due to extensive memory requirements in higher dimensions. Compression of the solution via high-order singular value decomposition can help in reducing the storage requirements and the tensor train (TT) format provides efficient basic linear algebra routines for low-rank representations of tensors. In this paper, we develop interpolation formulas for a semi-Lagrangian solver in TT format. In order to efficiently implement the method, we propose a compression of the matrix representing the interpolation step and an efficient implementation of the Hadamard product. We show numerical simulations for standard test cases in two-, four-, and six-dimensional phase space. Depending on the test case, the memory requirements reduce by a factor 10(2)-10(3) in four and a factor 10(5)-10(6) in six dimensions compared to the full-grid method.
- 出版日期2015
