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M should be same timestep as E

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Jan Petykiewicz 2024-01-16 23:17:05 -08:00
parent 24da3f673b
commit 5c3b3532a9
1 changed files with 2 additions and 2 deletions
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meanas/fdtd/__init__.py
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@ -48,12 +48,12 @@ $$
\\tilde{E}_{l, \\vec{r}} \\cdot \\hat{\\nabla} \\times \\hat{H}_{l', \\vec{r} + \\frac{1}{2}} \\\\ \\tilde{E}_{l, \\vec{r}} \\cdot \\hat{\\nabla} \\times \\hat{H}_{l', \\vec{r} + \\frac{1}{2}} \\\\
&= \\hat{H}_{l', \\vec{r} + \\frac{1}{2}} \\cdot &= \\hat{H}_{l', \\vec{r} + \\frac{1}{2}} \\cdot
(-\\tilde{\\partial}_t \\mu_{\\vec{r} + \\frac{1}{2}} \\hat{H}_{l - \\frac{1}{2}, \\vec{r} + \\frac{1}{2}} - (-\\tilde{\\partial}_t \\mu_{\\vec{r} + \\frac{1}{2}} \\hat{H}_{l - \\frac{1}{2}, \\vec{r} + \\frac{1}{2}} -
\\hat{M}_{l-1, \\vec{r} + \\frac{1}{2}}) - \\hat{M}_{l, \\vec{r} + \\frac{1}{2}}) -
\\tilde{E}_{l, \\vec{r}} \\cdot (\\hat{\\partial}_t \\tilde{\\epsilon}_{\\vec{r}} \\tilde{E}_{l'+\\frac{1}{2}, \\vec{r}} + \\tilde{E}_{l, \\vec{r}} \\cdot (\\hat{\\partial}_t \\tilde{\\epsilon}_{\\vec{r}} \\tilde{E}_{l'+\\frac{1}{2}, \\vec{r}} +
\\tilde{J}_{l', \\vec{r}}) \\\\ \\tilde{J}_{l', \\vec{r}}) \\\\
&= \\hat{H}_{l'} \\cdot (-\\mu / \\Delta_t)(\\hat{H}_{l + \\frac{1}{2}} - \\hat{H}_{l - \\frac{1}{2}}) - &= \\hat{H}_{l'} \\cdot (-\\mu / \\Delta_t)(\\hat{H}_{l + \\frac{1}{2}} - \\hat{H}_{l - \\frac{1}{2}}) -
\\tilde{E}_l \\cdot (\\epsilon / \\Delta_t )(\\tilde{E}_{l'+\\frac{1}{2}} - \\tilde{E}_{l'-\\frac{1}{2}}) \\tilde{E}_l \\cdot (\\epsilon / \\Delta_t )(\\tilde{E}_{l'+\\frac{1}{2}} - \\tilde{E}_{l'-\\frac{1}{2}})
- \\hat{H}_{l'} \\cdot \\hat{M}_{l-1} - \\tilde{E}_l \\cdot \\tilde{J}_{l'} \\\\ - \\hat{H}_{l'} \\cdot \\hat{M}_{l} - \\tilde{E}_l \\cdot \\tilde{J}_{l'} \\\\
\\end{aligned} \\end{aligned}
$$ $$