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The FDTD method was first introduced by Yee in 1966 and has since become a popular choice for solving electromagnetic problems. The method discretizes both space and time, dividing the solution domain into a grid of cells. By approximating the derivatives in Maxwell's equations using finite differences, FDTD solves for the electric and magnetic fields at each grid point and time step.

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This paper presents a numerical FDTD study on the detection of cracks in concrete using ultrasonic waves. The authors propose a fixed-grid FDTD method to model the ultrasonic wave propagation and investigate the effects of crack size, shape, and location on the ultrasonic signal. The FDTD method was first introduced by Yee

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