Search Results (3)

Ground penetrating radar (GPR) forward modeling is one of the core geophysical research topics and also the primary task of simulating ground penetrating radar system. It is a process of simulating the propagation laws and characteristics of electromagnetic waves in simulated space when the distribution of internal parameters in the exploration region is known. And the finite-difference-time-domain (FDTD) method has the characteristics of simulating the space-time transient evolution of electromagnetic wave, whose numerical method is simple and easy to program, so it has become one of the most extensively utilized methods in GPR forward modeling. It is generally known that the conventional FDTD approach requires finer uniform Yee cell all the time to produce satisfactory accuracies from numerical simulations of the GPR. However, the smaller temporal incremental has to be adopted due to the lower spatial incremental, which would dramatically weaken the advantage of the FDTD method. To solve this issue, the subgridding-technique-based hybrid local-one-dimensional FDTD (LOD-FDTD) is applied in this work to modeling the classical GPR scenarios. In this method, the unconditional-stable LOD-FDTD is employed in the fine-grid domain, while the traditional FDTD is used in the coarse-grid domain, which could avoid the oversampling problem in the local domain if the uniform fine-grid scheme is adopted. Meanwhile due to the unconditional stability of the LOD-FDTD, the larger time step, derived from the coarse grid which satisfies the Courant-Friedrichs-Lewy (CFL) stability condition, could be utilized in the whole domain so that the long-time interpolation process could be circumvented. Additionally, the proposed approach could be arbitrarily adjusted by means of different ratio of both coarse- and fine-grid, and hence it holds much higher generality. As compared with the auxiliary differential equation (ADE) technique, the Z-transform method is integrated into FDTD methods for modeling multi-pole Debye-based dispersive media in this method, resulting in more direct numerical implementations and fewer computing steps. Finally, three different classical GPR problems are carried out to validate accuracies and efficiencies of the proposed method. Full article

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date. Full article

This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods. Full article