论文标题
弗拉索夫 - 马克斯韦方程的不连续的盖尔金解决方案的超级会议和准确性增强
Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations
论文作者
论文摘要
本文考虑了解决vlasov-Maxwell（VM）系统的不连续的Galerkin（DG）方法，Vlasov-Maxwell（VM）系统是无碰撞磁化等离子体的基本模型。 DG方法提供了具有保护和稳定性属性的准确数值描述。但是，为了解决高维概率分布函数，即使对于现代超级计算机来说，计算成本也是主要的瓶颈。这项工作研究了后处理技术对DG解决方案的适用性，以增强其对VM系统的准确性和分辨率。特别是，当使用分段多项式$ k $时，我们在负顺序范围内证明了$ $ $（2K+\ frac {1} {2}）$的超偏见。数值测试包括Landau阻尼，两流不稳定性和流媒体微小的不稳定性，被视为后处理器的性能。
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and stability properties. However, to resolve the high dimensional probability distribution function, the computational cost is the main bottleneck even for modern-day supercomputers. This work studies the applicability of a post-processing technique to the DG solution to enhance its accuracy and resolution for the VM system. In particular, we prove the superconvergence of order $(2k+\frac{1}{2})$ in the negative order norm for the probability distribution function and the electromagnetic fields when piecewise polynomial degree $k$ is used. Numerical tests including Landau damping, two-stream instability and streaming Weibel instabilities are considered showing the performance of the post-processor.
