Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

隐身隐身层中无Maxwell电磁波场的激发

No Maxwell Electromagnetic Wave Field Excited In Cloaked Concealment

采用GL电磁场模型对隐身衣中的三维电磁场进行了全波场模拟。对隐身衣外点源激发的电磁波场进行了三维GL模拟。本文对隐身装置内部点源激励的电磁波场进行了数值模拟。通过GL模型仿真，发现单层隐身层内部不存在由非零局部源激发的麦克斯韦电磁波场。本文用GL方法从理论上证明了这一现象。GL方法与传统方法完全不同。GL方法具有理论分析和数值模拟的双重能力，可以研究本文所展示的隐身材料的物理过程和特性。

数值求解麦克斯韦方程组的双势形式

Two-Potential Formalism for Numerical Solution of the Maxwell Equations

提出了一种基于两个矢量势和两个标量势的新的麦克斯韦方程组。使用这些潜在的允许电磁场方程被写在一个双曲系统的形式。与原来的麦克斯韦方程组相比，该系统只包含演化方程，不包含具有微分约束性质的方程。这一事实使得新方程特别方便的电磁过程的数值模拟，特别是，他们可以解决现代强大的冲击捕获方法的基础上近似的空间导数的迎风差异。考虑了真空和非均匀介质中的电磁场。文中给出了用现代高阶格式求解方程组模拟电磁波传播的实例。关键词：计算电动力学，双势形式，双曲方程组数值解，激波捕捉格式。

d'Alembert Digitized: A Wave Pulse Method for Visualizing Electromagnetic Waves in Matter and for Deriving the Finite Difference Time Domain Method for Numerically Solving Maxwell's Equations

An alternative way of visualizing electromagnetic waves in matter and of deriving the Finite Difference Time Domain method (FDTD) for simulating Maxwell's equations for one dimensional systems is presented. The method uses d'Alembert's splitting of waves into forward and backward pulses of arbitrary shape and allows for grid spacing and material properties that vary with position. Constant velocity of waves in dispersionless dielectric materials, partial reflection and transmission at boundaries between materials with different indices of refraction, and partial reflection, transmission, and a…

Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas

The advent of massively parallel supercomputers, with their distributed-memory technology using many processing units, has favored the development of highly-scalable local low-order solvers at the expense of harder-to-scale global very high-order spectral methods. Indeed, FFT-based methods, which were very popular on shared memory computers, have been largely replaced by finite-difference (FD) methods for the solution of many problems, including plasmas simulations with electromagnetic Particle-In-Cell methods. For some problems, such as the modeling of so-called "plasma mirrors" for the gener…

Vlasov-Maxwell系统的变分粒子网格几何积分

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

提出了一种用于求解Vlasov-麦克斯韦方程组的全变分、非结构化电磁粒子积分器。利用离散外微积分的形式，通过最小化单个离散场论作用量，导出了场求解器、插值格式和粒子推进算法。作为确保作用量在离散电磁规范变换下不变的结果，积分器精确地保持高斯定律。