Practical considerations in the MRTD modeling of microwave structures

This paper focuses on details often overlooked in papers discussing the multiresolution time-domain (MRTD) method. Specifically, a non-uniform Cartesian grid and a uniaxial perfectly matched layer (UPML) implementation for arbitrary levels of wavelet resolution are discussed. The details of implementing the non-uniform grid are simple but non-trivial, allowing a variation of grid size that maintains the orthogonality of the wavelet basis functions. The discussion of the UPML demonstrates issues that arise for arbitrary wavelet resolution UPML and the resulting complexity of the code for arbitrary wavelet functions. An example is presented that compares the Haar-MRTD method with finite-difference time-domain (FDTD) when both UPML and a variable grid are used.