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Unstructured-grid spectral method for 3D Maxwell's equations with well-posed PML

A spectral penalty method for the solution of 3D Maxwell's equations with a well-posed PML (perfectly matched layer) has been developed to model the electromagnetic waves in an unbounded physical region. Numerical results of the radiation of an electric dipole source located at a sphere center show an excellent agreement with the analytical solution. Other numerical results also illustrate the high accuracy and geometric flexibility of the spectral penalty method. The well-posed PML can be successfully introduced into the spectral penalty methods and works very well in absorbing outgoing waves.