Modeling of ultrasonic waves by the finite-difference method in the time domain: A two-dimensional problem: Optimal algorithms, analysis of errors, and absorbing ranges near the grid boundaries

Reconstruction of reflector images using the C-SAFT method with account for the anisotropy of the material of the test object

“…To test the program for calculating ray trajectories, calculations of the ultrasound propagation were performed using the finite difference method in the time domain (FDTD) [11], which solves the wave equation in the vector variant and, consequently, reproduces the specific features of the ultrasound propagation in an anisotropic solid. We modulated the field that was emitted by a transducer with one 4 mm wide piezoelectric (PE) element, which was excited by a force that was perpendicular to the sur face of a plate positioned on a rexolite wedge with an angle of 35 deg.…”

“…The PE plate and the speci men boundaries are shown with black lines. To increase the accuracy of the calculation, the spatial derivatives were calculated over a square of 16 points, and the time derivatives were estimated through their values at four points [11]. Figure 4 shows the magnitude of the particle vibration velocity for (upper picture) an isotropic medium at a moment of 3.95 μs and (lower picture) an anisotropic material with the properties: (C 11 = 2.4, C 12 = 1.09, and C 44 = 0.83 × 10 11 N/m 2 ), ρ = 7800 kg/m 3 , and θ = 0 deg.…”