The FDTD (Finite Difference Time Domain) method is a simple and high-precision numerical method in the underwater acoustic field. For large-scale underwater acoustic field simulations with the FDTD method, it is necessary to use vector and parallel computations. One method of parallel computation is to use a PC cluster; this method has already been reported at this society. Another way is to perform vector and parallel calculations using a supercomputer. In this work, we used a supercomputer to attempt vector and parallel computations, which were possible to achieve by making small changes to an existing program. We adjusted the program to optimize the vector and parallel computations, and found that the speed was improved by a factor of 32 for vector computation and 6 for parallel computation.
An acoustic aplanatic lens is designed by the optical method. It can remove spherical and coma aberrations in the paraxial area. Sound pressure fields of the bi-concave aplanatic lens and a spherical lens 160 mm in diameter are calculated for the frequency of 500 kHz by the two-dimensional finite difference time domain (2-D FDTD) method. The aplanatic lens shows better convergence than the spherical lens. Two biconcave lenses made by acrylic resin are compared in a water tank experiment to confirm the results of the calculation. The aplanatic lens could focus with higher sound pressure than the spherical one within 10 degrees incidence. Then, aplanatic lenses with various apertures and focal lengths are designed to improve the maximum pressure and resolution. Sound pressure fields are compared by the 2-D FDTD method. These are evaluated from the standpoint of the numerical aperture (NA). Lenses with large NA could focus higher sound pressure than the small-NA lenses. In lenses with the same NA, the maximum sound pressure depended on the aperture and the resolution depended on the focal length.