A new unconditionally stable FDTD method for time-reversed wave simulation

In this work, a new unconditionally stable finite-difference time-domain (FDTD) method based on the Newmark-Beta algorithm is proposed. Temporal derivatives are discretized with the Newmark-Beta algorithm and a large banded matrix equation is produced. The lower-upper (LU) decomposition with reordering operation of the reverse Cuthill-Mckee (RCM) technique is used to solve the implicit equation quickly, and the LU decomposition needs to be performed only once in the beginning of the calculation. A numerical example to obtain super-resolution in time-reversed wave focusing is included to validate the accuracy and efficiency of the proposed method.