Abstract
The analysis of complex grounding systems (GS), taking into account anisotropic soil properties, or the presence of different structures buried in the soil, requires the use of advanced numerical methods, such as FEM. Two of the main problems that FEM models must address are the small cross sectional area of the electrodes, compared with its length, and the semi-infinite space that must be modeled using a finite 3D mesh. Different solution to both problems have been proposed in the technical literature, such as the combined use of 3D elements for the solid and 1D elements for the electrodes, and spatial transformations of the semi-infinite space into a finite space domain, but these techniques introduce a great complexity in the analysis of complex GS, especially when nonhomogenous soils are to be considered. In the paper, a new approach is proposed to address these
problems. It is based on the use of the Proper Generalized Decomposition, which is able to use very fine meshes because the solution of the field is formulated as a separated representation, using just three 1D meshes (one for each dimension), instead of a full 3D mesh of the domain. Besides, different soils domains can be expressed also as separated representations, which makes it easy to analyze complex soils configurations. The problem of establishing the potential values of the electrodes in a PGD formulation is solved using a penalty approach.
