case_cpml_2d_rz_tez_wavepacket_ref

测试目标

本测试验证 2D RZ TEz 分量组 Ephi,Hr,Hz 的 CPML 吸收效果。它把 compact CPML 域和更长的 reference 域在 probe 点的波形相减，估计 late reflection error。CPML 总体说明见 CPML wave-packet 测试总览。

覆盖子程序

mod_E01_cpml_2d_rz_tez
sub_E01_cpml_2d_rz_tez_E 和 sub_E01_cpml_2d_rz_tez_H
对应的 E01 TEz FDTD 更新核

文件说明

文件	作用
`test_rz_tez_wavepacket_cpml.f90`	主程序：构造 TEz 波包、运行 compact/reference 对照并输出 probe 数据。
`plot_results.py`	生成快照图和 probe error dB 曲线。
`make_gifs.py`	可选生成 `Ephi` 动画。
`run_wavelength_sweep.sh` / `run_equal_lambda_npml_sweep.sh`	扫描波长或 CPML 厚度的辅助脚本。

运行方式

source ~/.venv/bin/activate
cd tests/005_maxwell/case_cpml_2d_rz_tez_wavepacket_ref
./run.sh 12 output_lambda12mm_npml12_weak_ephi_gif 12 3 0.02 3.5 0.012 all 136 36 450 260 200 10

主流程

初始化有限宽度 TEz 波包。
用相同初值分别推进 compact CPML 域和更长 reference 域。
按 z_plus,z_minus,r_plus,r_minus 方向测试出射。
在主波后方 probe 记录 Ephi 波形。
用 reference 峰值归一化 compact-reference 差值。
late gate 后取最大值作为 late reflection error。

典型例子：z_plus 入射的 TEz 波包

test_rz_tez_wavepacket_cpml.f90 默认在 dr=dz=1 mm 网格上生成有限宽度 TEz 波包，并依次检查 z_plus、z_minus、r_plus、r_minus 四个出射方向。以 z_plus 为例，compact 域在右侧放置 CPML，reference 域加长同一传播方向，然后比较同一 probe 上的 Ephi 波形。

real(dp), parameter :: dr = 1.0d-3
real(dp), parameter :: dz = 1.0d-3
real(dp), parameter :: dt = 0.99d0/(c0*sqrt(1.0d0/dr**2 + 1.0d0/dz**2))
real(dp) :: lambda0 = 12.0d-3
integer :: nstep = 450
integer :: late_gate = 260
integer :: npml = 12

character(len=16), dimension(4), parameter :: cases = (/ &
    'z_plus          ', 'z_minus         ', 'r_plus          ', 'r_minus         ' /)

每个方向都运行两次：一次打开 CPML 并写快照，一次使用更长 reference 域作为近似无反射基准。 late reflection error 由 compact/reference probe 差值归一化得到。

call run_one_sim(cname, nr_cpml, nz_cpml, npml, rmin_cpml, zmin_cpml, &
    .true., probe_cpml, e0, e1)
call run_one_sim(cname, nr_ref, nz_ref, npml_ref, rmin_ref, zmin_ref, &
    .false., probe_ref, e0, e1)

ref_norm = max(maxval(abs(probe_ref)), 1.0d-300)
err_db = 20.0d0*log10(max(abs(probe_cpml-probe_ref), 1.0d-300)/ref_norm)
late_error_db = maxval(err_db(late_gate:nstep))

单步推进中先做内部 FDTD 更新，再把四条 CPML 带补上记忆变量修正。TEz 例子主要观察 Ephi；Hr 和 Hz 提供磁场半步更新。

重点调用方式

call sub_E01_fdtd_2d_rz_tez_H(...)
call sub_E01_cpml_2d_rz_tez_H(...)
call sub_E01_fdtd_2d_rz_tez_E(...)
call sub_E01_cpml_2d_rz_tez_E(...)
call record_probe_error(...)

结果和图像

当前参考 lambda0=12 mm, npml=12 的 late reflection error 约为 -49 到 -50 dB。

第一张快照图用来检查波包传播形态。应看到 Ephi 波包向 z_plus 边界移动，进入右侧 CPML 后迅速衰减；如果 CPML 区域附近出现明显返回波前，说明吸收边界或参数可能有问题。

../../_images/2d_rz_tez_ephi_snapshots_z_plus.png — `z_plus` 方向 `Ephi` 波包快照。波包进入右侧 CPML 后应快速衰减。

第二张误差图才是定量判据。曲线表示 compact CPML 域和 longer reference 域在 probe 点的归一化差异，单位为 dB；越负表示反射越小。应重点看 late gate 之后的峰值，而不是主波包经过 probe 时的早期瞬态。

../../_images/2d_rz_tez_probe_error_db.png — 四个方向的 probe error dB 曲线；late gate 后的峰值用于判定反射水平。

常见误读

late reflection error 是一个 probe 点上的幅值误差，不是全局反射能量系数。TEz 的主观测量是 Ephi，不要把它和 TMz 的 Ez 图混用。

Test Goal

This test checks CPML absorption for the 2D RZ TEz field group Ephi,Hr,Hz. It subtracts probe waveforms from a compact CPML domain and a longer reference domain to estimate late reflection error. See also the CPML wave-packet overview.

Covered Routines

mod_E01_cpml_2d_rz_tez
sub_E01_cpml_2d_rz_tez_E and sub_E01_cpml_2d_rz_tez_H
The matching E01 TEz FDTD kernels

Files

File	Role
`test_rz_tez_wavepacket_cpml.f90`	Main program for TEz packet generation, compact/reference runs, and probe output.
`plot_results.py`	Creates snapshots and probe-error dB plots.
`make_gifs.py`	Optionally creates `Ephi` animations.
Sweep scripts	Optional wavelength or equal-wavelength/CPML-thickness sweeps.

Run Command

source ~/.venv/bin/activate
cd tests/005_maxwell/case_cpml_2d_rz_tez_wavepacket_ref
./run.sh 12 output_lambda12mm_npml12_weak_ephi_gif 12 3 0.02 3.5 0.012 all 136 36 450 260 200 10

Main Flow

Initialize a finite-width TEz packet.
Propagate the same initial state in compact and longer reference domains.
Test z_plus,z_minus,r_plus,r_minus outgoing directions.
Record Ephi at a probe behind the main packet.
Normalize compact-reference error by the reference peak.
Use the late-gate maximum as late reflection error.

Example: z_plus TEz Packet

test_rz_tez_wavepacket_cpml.f90 builds a finite-width TEz packet on a dr=dz=1 mm grid and checks z_plus, z_minus, r_plus, and r_minus outgoing directions. For z_plus, the compact domain places CPML on the right side, while the reference domain extends the same propagation direction. The two Ephi probe traces are then compared.

real(dp), parameter :: dr = 1.0d-3
real(dp), parameter :: dz = 1.0d-3
real(dp), parameter :: dt = 0.99d0/(c0*sqrt(1.0d0/dr**2 + 1.0d0/dz**2))
real(dp) :: lambda0 = 12.0d-3
integer :: nstep = 450
integer :: late_gate = 260
integer :: npml = 12

character(len=16), dimension(4), parameter :: cases = (/ &
    'z_plus          ', 'z_minus         ', 'r_plus          ', 'r_minus         ' /)

Each direction is run twice: once in the compact CPML domain, with snapshots, and once in the longer reference domain. The late reflection error is the normalized compact/reference probe difference.

call run_one_sim(cname, nr_cpml, nz_cpml, npml, rmin_cpml, zmin_cpml, &
    .true., probe_cpml, e0, e1)
call run_one_sim(cname, nr_ref, nz_ref, npml_ref, rmin_ref, zmin_ref, &
    .false., probe_ref, e0, e1)

ref_norm = max(maxval(abs(probe_ref)), 1.0d-300)
err_db = 20.0d0*log10(max(abs(probe_cpml-probe_ref), 1.0d-300)/ref_norm)
late_error_db = maxval(err_db(late_gate:nstep))

A time step first advances the interior FDTD region, then applies memory variable corrections in the CPML strips. The TEz example mainly monitors Ephi; Hr and Hz are the staggered magnetic components.

Core Call Pattern

call sub_E01_fdtd_2d_rz_tez_H(...)
call sub_E01_cpml_2d_rz_tez_H(...)
call sub_E01_fdtd_2d_rz_tez_E(...)
call sub_E01_cpml_2d_rz_tez_E(...)
call record_probe_error(...)

Results and Figures

For lambda0=12 mm, npml=12, reference late reflection error is about -49 to -50 dB.

The snapshot figure is for reading the packet shape. Ephi should move toward the z_plus boundary and decay rapidly once it enters the right-side CPML. A clear returning wavefront near the CPML side would indicate a boundary or parameter problem.

The probe-error figure is the quantitative diagnostic. It plots the normalized compact-domain/reference-domain probe difference in dB; more negative values mean lower reflection. Focus on the peak after the late gate, not on the early transient while the main packet passes the probe.

Common Pitfall

Late reflection error is a probe amplitude error, not a global reflected energy coefficient. TEz is monitored mainly through Ephi; do not mix it with TMz Ez plots.