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Hello,

I've been working for a while with the following wave equation PDE:

[tex]

\[

\frac{{\partial ^2 p}}{{\partial x^2 }} + \frac{{\partial ^2 p}}{{\partial y^2 }} = A\frac{{\partial ^2 p}}{{\partial t^2 }} + B\frac{{\partial p}}{{\partial t}}

\]

[/tex]

In preparation for the application of a Perfectly Matched Layer (PML), I need to be able to split the equation into x-components and y-components. This means that I would like to write down two equations. One equation is the x-projection of the equation above, and the other equation is the y-projection.

In the PML literature, examples are shown of Ampere's Law being written in two equations. One equation is for the x-projection, and the other is for the y-projection. I would like to do the same for the equation above. Where do I begin?

Then once I numerically solve the equation using a Finite-Difference Time-Domain method, I would like to combine the pressure components [tex]p_x [/tex] and [tex]p_y[/tex] to get [tex]p[/tex] again. How would I do this?

I've been working for a while with the following wave equation PDE:

[tex]

\[

\frac{{\partial ^2 p}}{{\partial x^2 }} + \frac{{\partial ^2 p}}{{\partial y^2 }} = A\frac{{\partial ^2 p}}{{\partial t^2 }} + B\frac{{\partial p}}{{\partial t}}

\]

[/tex]

In preparation for the application of a Perfectly Matched Layer (PML), I need to be able to split the equation into x-components and y-components. This means that I would like to write down two equations. One equation is the x-projection of the equation above, and the other equation is the y-projection.

In the PML literature, examples are shown of Ampere's Law being written in two equations. One equation is for the x-projection, and the other is for the y-projection. I would like to do the same for the equation above. Where do I begin?

Then once I numerically solve the equation using a Finite-Difference Time-Domain method, I would like to combine the pressure components [tex]p_x [/tex] and [tex]p_y[/tex] to get [tex]p[/tex] again. How would I do this?

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