On finite-difference time-domain sub-gridding algorithms for efficient modelling of ground-penetrating radar
Hartley, John Matthew
Introducing finely detailed models of GPR antennas into finite-difference time-domain forward models often results in large computation overheads. In many cases the solution becomes intractable. The overhead increases due to the larger size of the model. This is as a result of the increase in spatial and temporal sampling required by the antenna geometry and the conditionally stable nature of the FDTD method respectively. This problem is compounded for predictive applications where the model-parameter space is non-linear and solutions derived from heuristic optimisation schemes require multiple simulation runs. To overcome this issue this work presents a novel sub-gridded FDTD approach to model for the first time realistic descriptions of GPR antennas in half-space type problems. The sub-gridding is performed using Huygens Sub-Gridding (HSG). This method does not limit the sub-gridding ratio and therefore a wide range of applications are possible. Also, a new method is developed called the Switched Huygens Sub-Gridding (SHSG). This method significantly improves upon the stability of the HSG, and has a superior computational performance. In addition, it is simpler to implement and optimise its performance owing to the simple nature of its stabilisation mechanism. In resonant problems, stability is shown to increase by a factor of 5.6. And computational speed is increased by a factor of 28 and 17 for a realistically modelled antenna over a buried water-filled plastic pipe using the SHSG and HSG respectively. Furthermore, a novel effective permittivity scheme is developed for Debye media that can be applied to dielectric-dispersive and dispersive-dispersive interfaces. This technique resolves the issue of reduction in accuracy at material interfaces outside sub-gridded regions. And it can be used to increase the accuracy of the FDTD method for dispersive materials generally. The relative error is reduced from 5% to 0.6% for the field transmitted and received by a Hertzian dipole over a dispersive half-space containing a water pipe. In addition, analytical results confirm a significant increase in accuracy for a range of soil types. Moreover, these advances are implemented in open-source package gprMax and will be made available in a forthcoming release. The implementations take advantage of parallel architectures and are therefore very efficient. In addition, these advances are general and can be applied to several problems in GPR and to many problems in computational electrodynamics.