High-order GPU-DGTD method based on unstructured grids for GPR simulation

The finite element time-domain (FETD) method is an appealing electromagnetic (EM) field-solving procedure for the derivation of high-resolution field distribution of complex geological models. However, the arising computational burden has become a main bottleneck restricting the efficient implementation of ground penetrating radar (GPR) simulation at a high speed and large scale. In this research, we developed a high-efficiency EM solver to discretize the partial differential equations on unstructured triangular meshes, using a high-order graphics processing unit (GPU)-finite element discontinuous Galerkin time-domain (DGTD) method. By introducing a semi-discrete strong format instead of solving large stiffness matrices, and by employing the Runge-Kutta temporal integration scheme, the DGTD method can effectively overcome the problem of memory shortage and thereby solves the issue of instability. Besides, the uniaxial perfectly matched layer (UPML) is extended to match the lossy medium and used as an absorbing boundary condition to simulate an open space. Three models were manufactured to compare the DGTD method with the state-of-art methods (FDTD, FETD) of different grids in terms of computing accuracy, the dispersion degree of the rough interface, and memory occupied. To be specific, we explored the detailed effect of both the grid sizes and the order of basis functions on the modeling accuracy for the proposed GPU-DGTD method. We finally verified the numerical solution and demonstrated its applications by simulating a complex model for tunnel geological forecast. The experimental results reveal the order of basic function N and the size of the grid d are closely concerned with the wavelength lambda of EM waves, for example, an appropriate definition is d/N approximate to lambda/15.