A method is presented for application of the perfectly matched layer ͑PML͒ absorbing boundary condition ͑ABC͒ to the P-SV velocity-stress finite-difference method. The PML consists of a nonphysical material, containing both passive loss and dependent sources, that provides ''active'' absorption of fields. It has been used in electromagnetic applications where it has provided excellent results for a wide range of angles and frequencies. In this work, numerical simulations are used to compare the PML and an ''optimal'' second-order elastic ABC ͓Peng and Toksöz, J. Acoust. Soc. Am. 95, 733-745 ͑1994͔͒. Reflection factors are used to compare angular performance for continuous wave illumination; snapshots of potentials are used to compare performance for broadband illumination. These comparisons clearly demonstrate the superiority of the PML formulation. Within the PML there is a 60% increase in the number of unknowns per grid cell relative to the velocity-stress formulation. However, the high quality of the PML ABC allows the use of a smaller grid, which can result in a lower overall computational cost.

A Monte-Carlo finite-difference time-domain (FDTD) technique is developed for wave scattering from randomly rough, one-dimensional surfaces satisfying the Dirichlet boundary condition. Both single-scale Gaussian and multiscale Pierson-Moskowitz surface roughness spectra are considered. Bistatic radar cross sections are calculated as a function of scattering angle for incident angles of 0, 45, 70, and 80 degrees measured from the vertical. The contour path FDTD method is shown to improve accuracy for incident angles greater than 45 degrees. Results compare well with those obtained using a Monte-Carlo integral equation technique.

A Monte-Carlo finite-difference time-domain (FDTD) technique is developed for wave scattering from randomly rough, one-dimensional surfaces satisfying the Dirichlet boundary condition. Both single-scale Gaussian and multiscale Pierson-Moskowitz surface roughness spectra are considered. Bistatic radar cross sections are calculated as a function of scattering angle for incident angles of 0, 45, 70, and 80 degrees measured from the vertical. The contour path FDTD method is shown to improve accuracy for incident angles greater than 45 degrees. Results compare well with those obtained using a Monte-Carlo integral equation technique.

The finite-difference time-domain ͑FDTD͒ method is a numerical technique that makes no explicit physical approximations to the underlying problem. The quality of a FDTD-based solution typically is determined by the discretization of the computational domain-the smaller the spacing, the more accurate the solution. Unfortunately, for large computational domains, i.e., ones spanning many wavelengths, the small spatial step size needed to obtain a high-fidelity solution may lead to a prohibitively large number of unknowns. Here it is shown how the FDTD method can be used to model accurately scattering from pressure-release surfaces above a homogeneous water column. To keep the computational cost manageable, a number of enhancements to the standard FDTD algorithm are employed. These enhancements include correcting for numerical dispersion along the specular direction of the incident insonification, using locally conformal cells at the pressure-release boundary, and propagating the field through the homogeneous water column via an analytic method. The accuracy of the FDTD approach is demonstrated by comparison with an integral equation-based reference solution to the same rough surface scattering problem ͓Thorsos,

To demonstrate the relationship between physical reality and the equations used in electromagnetics, we have created interactive software using Mathematica' with its "notebook" capability. This software is composed of different notebooks, each covering a specific topic, which are collectively called EM Notebooks. The notebooks are used in a workstation laboratory of 12 NeXT2 computers in conjunction with our two required junior-level courses in electromagnetics. Each notebook consists of text, equations, and graphics. The equations are actually Mathematica commands which are used to evaluate electromagnetic formulas found in a typical undergraduate electromagnetics textbook Equation parameters can be changed by a student permitting examination of an unlimited number of examples. In addition, much of the graphics can be animated. The animations provide a pedagogic tool unavailable in traditional textbooks; they have proven valuable in illustrating dynamic processes and parametric dependence in a function. EM Notebooks are not restricted to NeXT workstations; however, they must be used on a computer that runs Mathematica with the notebook facility.