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Hello--

I'm in the process of implementing a PML for FDTD modeling.

I would like to take the derivative of the partial derivative shown below, but I am uncertain with respect to how I might proceed.

[tex]

\[

\frac{\partial }{{\partial x}} \to \frac{1}{{1 + \frac{{i\sigma \left( x \right)}}{\omega }}}\frac{\partial }{{\partial x}}

\]

[/tex]

Essentially what I would like to do is take the derivative of a partial derivative, and also deal with the [tex]\[{i\sigma \left( x \right)}\] [/tex] term, which is a function of position [tex]x[/tex].

This would result in the calculation of [tex] \[\frac{{\partial ^2 }}{{\partial x^2 }}\][/tex]

I'm in the process of implementing a PML for FDTD modeling.

I would like to take the derivative of the partial derivative shown below, but I am uncertain with respect to how I might proceed.

[tex]

\[

\frac{\partial }{{\partial x}} \to \frac{1}{{1 + \frac{{i\sigma \left( x \right)}}{\omega }}}\frac{\partial }{{\partial x}}

\]

[/tex]

Essentially what I would like to do is take the derivative of a partial derivative, and also deal with the [tex]\[{i\sigma \left( x \right)}\] [/tex] term, which is a function of position [tex]x[/tex].

This would result in the calculation of [tex] \[\frac{{\partial ^2 }}{{\partial x^2 }}\][/tex]

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