An element-free Galerkin method for ground penetrating radar numerical simulation

FENG De-shan(冯德山)^{1, 2}, GUO Rong-wen(郭荣文)^{1, 2}, WANG Hong-hua(王洪华)^{1, 2}

(1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education
(Central South University), Changsha 410083, China)

Abstract:An element-free Galerkin method (EFGM) is used to solve the two-dimensional (2D) ground penetrating radar (GPR) modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method (FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.

Key words:element-free Galerkin method; moving least-squares method; ground penetrating radar; forward simulation