![]() ![]() The deep region is still freely discretized by the tetrahedral elements. In this research, second-order shape functions are used to discretize near-surface prismatic elements. ![]() However, the accuracy of the numerical solution will be reduced when the stretched grid extension is too long. Triangular prism elements can be used to build the stretched grid in the near surface area 20. However, some elements of the stretched grid with hanging nodes cannot share just one whole edge or face 13, 14, and the convenience and flexibility of mesh generation are not as good as traditional tetrahedral elements. In addition, the longer the element is stretched, the more elements are saved, and the decrease in numerical accuracy caused by element stretching can be compensated by a higher-order element processing scheme 18, 19. The stretching grid obtained from this multiresolution approach can help to improve calculation accuracy with fewer elements in the near-surface area. 13 allows grid refinement only in the horizontal directions and keeps the degree of refinement in the vertical direction constant. A multiresolution approach suggested by Cherevatova et al. It helps to reduce the degrees of freedom (DoF) and is suitable for large-scale 3-D geophysical EM forward problems, such as MT forward modeling. This kind of regular grid, whose element quality is not restricted by the aspect ratio of the element, has a variable scale and stable local refinement capabilities 16, 17. To reduce the number of required elements, a scheme of nonconforming grids has been used to discretize the geoelectric model 14, 15. The refinement often results in too many redundant elements and reduces the computational efficiency of the FEM forward modeling. However, unstructured grids often need to be refined into extremely small elements to avoid ill-conditioning 12, 13. This type of grid has become a useful tool for discretizing the geoelectric model in the numerical simulation of three-dimensional geophysical electromagnetic (EM) fields using the finite element method (FEM) 6, 7, 8 and has been widely used in magnetotelluric (MT) forward modeling 9, 10, 11. Unstructured grids with tetrahedral elements are suitable for dividing complex underground anomalous bodies in terms of topography and bathymetry because they can fit arbitrary shapes of geological bodies well 1, 2, 3, 4, 5. Usage of the hybrid mesh can be easily adapted to complex geoelectric models with strong terrain fluctuations, which requires less computational cost than using conventional unstructured elements. The accuracy of the modeling using the hybrid mesh is significantly higher than that of the tetrahedral mesh with a similar DoF. The results show that the modeling efficiency has been improved, especially for high-frequency data. ![]() The superiority of this hybrid mesh has been tested on a layered model, the DTM1 model and terrain relief models. The deep area is discretized by tetrahedral elements to ensure the flexibility of the unstructured grids. The required elements in the near-surface area are reduced because the quality of the triangular prism is not limited by the element aspect ratio. To reduce the computational cost, we have developed a hybrid mesh based on triangular prisms and tetrahedrons. However, high-quality results require an extreme refinement of the near-surface area, which leads to excessive meshes and an increased degree of freedom (DoF) of the governing equation of the finite element system. Unstructured tetrahedral grids have been applied in magnetotelluric (MT) forward modeling using the finite element (FE) method because of their adaptability to complex anomalies. ![]()
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