An exact PML to truncate lattices with unstructured-mesh-based adaptive finite element method in frequency domain for ground penetrating radar simulation

Abstract

We present a new approach of unstructured grid adaptive finite element in the frequency domain (AFEFD) based on exact perfect matching layer (EPML) boundary condition for Ground penetrating radar (GPR) simulation. The discrete equations of transverse magnetic mode are derived by using the unstructured Delaunay mesh coupled with linear interpolation basis functions. For the trade off between the computational efficiency and the accuracy of simulation, an h-type adaptive finite element method (AFEM) is employed and, in particular, with less layer thickness and fewer parameters setting, an EPML boundary condition is developed to truncate the AFEM lattices. In addition, the Zienkiewicz-Zhu posterior error estimation, the mesh refinement scheme and the implementation process of AFEM are also elaborated in detail. To testify the validity and practicability of this methodology, a homogeneous medium model of line current radiation field with analytical solution and a complex model of lining fracture disease are considered. The results of frequency-domain slices, transformed time-domain forward profile, together with wavefield snapshots demonstrated that the reflections, diffractions and other codas caused by non-physical factors at the boundary are effectively absorbed, subsequently, the absorbing performance of simulation with AFEM in frequency domain is greatly improved. More importantly, the proposed methodology can automatically control its mesh density according to the features of the complex object, which significantly economize the computing resource of simulation when AFEM is employed.