Fully nonorthogonal higher-order FDTD schemes for the systematic development of 3-D PML's in general curvilinear coordinates

The efficient construction of reflectionless PML's in 3-D curvilinear coordinates via a new higher-order FDTD methodology, is presented in this paper. By accurately treating the div-curl problem, the technique introduces a higher-order rendition of the covariant/contravariant vector theory with generalized conventional and nonstandard schemes. Moreover, a mesh expansion algorithm decreases the absorbers' thickness. In the time domain, the four-stage Runge-Kutta integrator is also invoked, while the wider spatial stencils are effectively limited by self-adaptive compact operators. Numerical verification indicates that the novel PML's offer a serious suppression of dispersion errors and significant savings in the computational burden.