Parallel implementation of the biorthogonal multiresolution time-domain method.
The three-dimensional biorthogonal multiresolution 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, whereas we employ the Cohen-Daubechies-Fouveau (CDF) biorthogonal wavelets. When a CDF-wavelet expansion is used, the spatial-sampling rate can be reduced considerably compared with that of the conventional finite-difference time-domain (FDTD) method, implying that larger targets can be simulated without sacrificing accuracy. We implement the Bi-MRTD 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 by use of the traditional FDTD method.