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.
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Foundation item: Project(41074085) supported by the National Natural Science Foundation of China; Project(NCET-12-0551) supported by the Funds for New Century Excellent Talents in University, China; Project supported by Shenghua Yuying Program of Central South University, China
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Feng, Ds., Guo, Rw. & Wang, Hh. An element-free Galerkin method for ground penetrating radar numerical simulation. J. Cent. South Univ. 22, 261–269 (2015). https://doi.org/10.1007/s11771-015-2517-7
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DOI: https://doi.org/10.1007/s11771-015-2517-7