Parallel Implementation of the Biorthogonal MRTD Method

The three-dimensional biorthogonal multi-resolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly-supported wavelet functions as the basis, where here we employ the CohenDaubechies-Fouveau (CDF) biorthogonal wavelets. Using a CDF-wavelet expansion, the spatial sampling rate can be reduced considerably compared with the conventional finite difference time domain (FDTD) method − implying that larger targets can be simulated without sacrificing accuracy. The Bi-MRTD is implemented here on a cluster of allocated-memory machines, using the message-passing interface (MPI), such that very large targets can be modeled. Numerical results are compared with analytical ones and with those obtained via the traditional FDTD method.