TITLE:
Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar
AUTHORS:
Zhi Zhang, Honghua Wang, Minling Wang, Xi Guo, Guihong Guo
KEYWORDS:
Non-Split Perfectly Matched Layer (NPML), Ground Penetrating Radar (GPR), Second Order Wave Equation, Finite Element Time Domain (FETD)
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.5,
May
23,
2019
ABSTRACT: As a highly efficient absorbing
boundary condition, Perfectly Matched Layer (PML) has been widely used in
Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar
(GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite
Element Time Domain (FETD) simulation based on the second order electromagnetic
wave equation. This paper developed a non-split perfectly matched layer (NPML)
boundary condition for GPR FETD simulation based on the second order
electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived
according to the definition of complex extending coordinate transformation.
Then it transformed into time domain by means of auxiliary differential
equation method, and its FETD equation is derived based on Galerkin method. On
this basis, a GPR FETD forward program based on NPML boundary condition is
developed. The merits of NPML boundary condition are certified by compared with
wave field snapshots, signal and reflection errors of homogeneous medium model
with split and non-split PML boundary conditions. The comparison demonstrated
that the NPML algorithm can reduce memory occupation and improve calculation
efficiency. Furthermore, numerical simulation of a complex model verifies the
good absorption effects of the NPML boundary condition in complex structures.