Computationally Efficient Locally One-Dimensional Algorithm for Open Region Ground Penetrating Radar Problem With Improved Absorption

Abstract

By incorporating higher order formulation with perfectly matched layer (PML) implementation, unconditionally stable computationally efficient locally one-dimensional (LOD) algorithm with improved absorption is proposed for simulating ground penetrating radar and its open region problems in finite-difference time-domain (FDTD) algorithm. To take advantages of these methods, the proposed implementation shows characteristics of maintaining considerable accuracy, enhancing computational efficiency and improving the entire absorption. These above-mentioned advantages are illustrated through the ground penetrating radar related problem in open regions. It can be concluded from the calculation results that the proposal shows advantages of higher order formulation, PML implementation and LOD procedure which are efficient in remarkable accuracy, considerable efficiency and improved absorption with increment of CFLNs. Meanwhile, the simulation results also indicate that the proposal is an unconditionally stable procedure with the dissatisfaction of Courant-Friedrichs-Levy stability condition. INDEX TERMS Finite-difference time-domain (FDTD), Locally One-Dimensional (LOD), Perfectly matched layer (PML), Ground penetrating radar (GPR).

Introduction to the FDTD method and its application to implicit locally one-dimensional calculations

“…As a result, the LOD-FDTD method has been improved and extended by many researchers round the world. The application of the LOD-FDTD method is still spreading in various fields [67][68][69]. In addition to conventional electromagnetic problems, the LOD scheme is expected to be further utilized for computational techniques to analyze other physical phenomena.…”

An explicit and absolutely stable FDTD method for electromagnetic analysis

“…The explicit algorithm is free of solving matrix equations, while it is limited by the Courant-Friedrich-Levy (CFL) stability condition and inefficient for numerical problem with fine structures in that high temporal resolution means heavy burden of operation time. In recent years, various methods have been proposed such as the hybrid implicit-explicit (HIE) FDTD method [3,4], magnetically-mixed Newmark-Leapfrog (MNL) FDTD method [5,6,7,8], weakly conditionally stable (WCS) FDTD method [9,10], FDTD method with filtering scheme [11,12], Crank-Nicolson (CN) FDTD method [13,14,15], alternatingdirection-implicit (ADI) FDTD method [16,17,18,19], locally-one-dimensional (LOD) FDTD method [20,21,22,23] and the Weighted-Laguerre-Polynomial (WLP) FDTD method [24,25,26,27]. Among the methods above, the method in [11,12] is an explicit and unconditionally stable FDTD method by filtering part of high frequency components to extend the time step size.…”