Absorbing boundary conditions are important in many applications where partial differential equations defined on infinite domains are solved numerically. A problem that has attracted interest recently is that perfectly matched layers layers (PML) for electro-magnetic FDTD simulations applied on convex surfaces may lead to instabilities. This paper shows that these problems are not restricted to electro-magnetic calculations, but common for problems described by the classical wave equation with absorbing boundary conditions on convex surfaces. It is shown that the instabilities are independent of the numerical implementation of the absorbing boundary condition, and instead a result of unphysical assumption in the formulation of the boundary condition.
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