论文标题
vlasov-Poisson模拟和GPU实施Python的张量产品不续止的galerkin操作员
Analysis of tensor-product discontinous Galerkin operators for Vlasov-Poisson simulations and GPU implementation on Python
论文作者
论文摘要
不连续的Galerkin（DG）有限元方法是保守的，它非常适合并行化，并且由于其与正交和正交多项主义的理论的亲密关系而具有高度准确性。当使用正交离散化（\ textit {i.e。}直流网格）时，DG方法可以在GPU上有效地实现，仅在几行高级语言（例如Python）中。这项工作通过以张量产生形式编写DG半混凝土方程，然后使用开源GPU库来计算产品，从而证明了这种实现。通过模拟等离子体物理学的问题来说明结果，即磁化vlasov-Poisson系统中的不稳定性。此外，由于DG通过其正交基础与光谱方法密切相关，因此有可能将转换转换为替代的全局本本特征函数，以进行分析或执行其他操作。这种转换也被作为张量产品构成，并且可能会被GPU加速。在这项工作中，例如计算一个傅立叶系列（尽管这不会超过离散的傅立叶变换），并用于将Vlasov-Poisson系统的泊松部分求解到$ \ Mathcal {o}（ΔX^{n+1/2}）$ - 准确性。
The discontinuous Galerkin (DG) finite element method is conservative, lends itself well to parallelization, and is high-order accurate due to its close affinity with the theory of quadrature and orthogonal polynomials. When applied with an orthogonal discretization (\textit{i.e.} a rectilinear grid) the DG method may be efficiently implemented on a GPU in just a few lines of high-level language such as Python. This work demonstrates such an implementation by writing the DG semi-discrete equation in a tensor-product form and then computing the products using open source GPU libraries. The results are illustrated by simulating a problem in plasma physics, namely an instability in the magnetized Vlasov-Poisson system. Further, as DG is closely related to spectral methods through its orthogonal basis it is possible to calculate a transformation to an alternative set of global eigenfunctions for purposes of analysis or to perform additional operations. This transformation is also posed as a tensor product and may be GPU-accelerated. In this work a Fourier series is computed for example (although this does not beat discrete Fourier transform), and is used to solve the Poisson part of the Vlasov-Poisson system to $\mathcal{O}(Δx^{n+1/2})$-accuracy.
