PML-PEC and PML-PMC grounded Green´s functions

Artificial boundary conditions (ArBC), defined as Robin boundary conditions (RBC) positioned at a complex space coordinate, are introduced in order to obtain pertinent approximations for the Green´s functions in grounded layered media. These artificial boundary conditions include perfectly matched layers (PML) backed by perfectly electric (PEC) or magnetic conductors (PMC). Since weighted sums of Green´s functions are again Green´s functions, a weighted mixture of ArBC Green´s functions of the PML-PEC and PML-PMC type can be utilized to approximate a given Green´s function. The advantage of the approach is that it yields a comprehensive eigenexpansion for the Green´s function at hand. An example illustrates the goodness of fit between the approximate Green´s function and the Green´s function for the uniform halfspace.