E_Maxwell

• FDTD Learning Path
• FDTD Usage Cookbook
• CPML Cookbook
• FDTD Testing Guide
• E01_Maxwell_2Drz
• E02_Maxwell_3Drtz
• E03_Maxwell_3Dxyz

中文 English

概览

E_Maxwell 记录 AlgoPlasma 中用于数值求解 Maxwell 方程组的场推进子程序和边界处理扩展。 当前主要实现基于有限差分时域法（Finite-Difference Time-Domain, FDTD）：电场 \(\mathbf{E}\) 和磁场 \(\mathbf{H}\) 在空间上交错，在时间上采用 leapfrog 半步交错。模块还提供卷积完美匹配层（Convolutional Perfectly Matched Layer, CPML） 扩展，用作有限计算区域边界处的电磁波吸收边界，以减小出射波反射。模块覆盖 2D 轴对称柱坐标、完整 3D 柱坐标和 3D Cartesian 网格。

从哪里开始

阅读和使用路线

读者目标	先看	然后看
第一次学习 FDTD / Maxwell 更新	FDTD Learning Path	从 E03 Cartesian notes 开始，再看 E01/E02。
想把 routine 接进自己的代码	FDTD Usage Cookbook	进入对应 E01/E02/E03 页面，再看具体 subroutine 参数表。
需要吸收边界	CPML Cookbook	看对应 CPML module/subroutine 页面，并运行 wave-packet reference 测试。
修改了算法，想确认没破坏实现	FDTD Testing Guide	再看 005_maxwell 测试总览。

模块关系

模块	坐标/模式	主要职责	测试/说明
E01_Maxwell_2Drz	2D (r,z) TE/TM	轴对称 FDTD 更新，包含 TE/TM 拆分和 2D RZ CPML。	2D RZ notes
E02_Maxwell_3Drtz	3D (r,phi,z)	完整柱坐标六分量 Yee-FDTD 和 CPML 吸收边界扩展，显式处理轴线和柱坐标 metric 项。	3D cylindrical notes
E03_Maxwell_3Dxyz	3D (x,y,z)	Cartesian 六分量 Yee-FDTD 和 3D CPML 扩展。	3D Cartesian notes

数值结构

所有 FDTD 内核都遵循 Maxwell curl 方程的离散形式。非 CPML 内核只负责 interior-style curl update；周期边界、外部边界填充、源项注入和诊断输出由调用方或测试程序组织。 CPML 模块额外维护 split-field memory variables，用于吸收层中的修正 curl 项。 因此，E_Maxwell 更像一组可组合的低层场推进积木，而不是包含网格管理、边界管理和 I/O 的完整求解器框架。

测试入口

Maxwell/FDTD 测试目录入口见 005_maxwell 测试总览； 更完整的公式、可视化说明和案例细节整理在 FDTD Testing Guide。 覆盖内容对应 tests/005_maxwell 下的 single-step、m=0 equivalence、MMS、稳定性、 长时间传播、CPML wave-packet reference 和可视化案例。

Overview

E_Maxwell documents AlgoPlasma field-advance subroutines and boundary extensions for numerically solving Maxwell’s equations. The current main implementation uses the finite-difference time-domain method (FDTD): electric and magnetic fields are staggered in space and advanced with leapfrog half-step staggering in time. The module also provides convolutional perfectly matched layer (CPML) extensions, which act as electromagnetic-wave absorbing boundaries at the edges of a finite computational domain to reduce outgoing-wave reflections. The module covers 2D axisymmetric cylindrical, full 3D cylindrical, and 3D Cartesian grids.

Where to Start

Reading and Usage Paths

Reader goal	Start with	Then read
Learn FDTD / Maxwell updates for the first time	FDTD Learning Path	Start from E03 Cartesian notes, then move to E01/E02.
Integrate routines into your own code	FDTD Usage Cookbook	Open the matching E01/E02/E03 page and then the subroutine parameter table.
Add absorbing boundaries	CPML Cookbook	Read the matching CPML module/subroutine pages and run wave-packet reference tests.
Validate changes after editing kernels	FDTD Testing Guide	Then use 005_maxwell Tests.

Module Map

Module	Coordinates / mode	Main responsibility	Tests / notes
E01_Maxwell_2Drz	2D (r,z) TE/TM	Axisymmetric FDTD updates with TE/TM splitting and 2D RZ CPML.	2D RZ notes
E02_Maxwell_3Drtz	3D (r,phi,z)	Full cylindrical six-component Yee-FDTD and CPML absorbing-boundary extension with explicit axis and metric handling.	3D cylindrical notes
E03_Maxwell_3Dxyz	3D (x,y,z)	Cartesian six-component Yee-FDTD and 3D CPML extension.	3D Cartesian notes

Numerical Structure

All FDTD kernels discretize Maxwell curl equations. Non-CPML kernels handle interior-style curl updates; periodic wrapping, external boundary fill, source injection, and diagnostics are organized by the caller or test programs. CPML modules additionally maintain split-field memory variables for corrected curl terms inside absorbing layers. In other words, E_Maxwell is a set of composable low-level field-advance building blocks, not a full solver framework with mesh management, boundary orchestration, and I/O.

Test Entry

The Maxwell/FDTD test-directory entry point is 005_maxwell Tests. Fuller formulas, visualization notes, and case details are collected in the FDTD Testing Guide. Coverage corresponds to tests/005_maxwell cases for single-step formulas, m=0 equivalence, MMS, stability, long-run pulse propagation, CPML wave-packet reference tests, and visualization.