Difference between revisions of "Sommerfeld Radiation Condition"
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(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.} | (\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.} | ||
</math> | </math> | ||
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| + | [[Category:Linear Water-Wave Theory]] | ||
Revision as of 01:41, 2 June 2006
This is a condition for the Frequency Domain Problem that the scattered wave is only outgoing at infinity.
In two-dimensions the condition is
[math]\displaystyle{ \left( \frac{\partial}{\partial|x|}-{i}k\right) (\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|x|\rightarrow\infty\mathrm{.} }[/math]
where [math]\displaystyle{ \phi^{\mathrm{{In}}} }[/math] is the incident potential and [math]\displaystyle{ k }[/math] is the wave number.
In three-dimensions the condition is
[math]\displaystyle{ \sqrt{|\mathbf{r}|}\left( \frac{\partial}{\partial|\mathbf{r}|}-{i}k\right) (\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.} }[/math]
