Electromagnetic Forward Modeling Of Underground Pipeline Based On DGTD

Underground pipeline is the lifeline of urban life and the effective guarantee of urban safety and stability.Electromagnetic detection is an effective means to study the state of underground complex targets.Therefore,the research on the health status of underground pipeline based on electromagnetic forward simulation is of great significance to urban management.Based on the basic theory of low-order three-dimensional discontinuous Galerkin(DGTD)time domain method,the spatial and temporal discrete sch eme of DGTD algorithm and the implementation method of boundary conditions are studied.Different order hierarchical vector basis functions are constructed and introduced into the DGTD method to expand the electric field and magnetic field instead of the original low-order basis functions,so th at higher computational accuracy can be obtained under the same or rougher grid.Since the hierarchical vector basis functions are nested,a static adaptive DGTD method based on the hierarchical vector basis functions was proposed.According to certain precision requirements,the tetrahedral elements were assigned to different regions by the size of the mesh,and the hybrid calculation of different order elements under the same mesh division was realized.In order to capture the dynamic change of the distribution of unknown physical quantity in space and time,the dynamic P-adaptive DGTD method is further proposed.The order of the basis functions can be adjusted dynamically according to the change of the electromagnetic field.Low order basis functions are used in some areas where the the electromagnetic field waves oscillate gently,such as the areas where the waves have not arrived or have passed.The higher order basis functions are selected in the region where the oscillations change violently.In this way,the number of high-order elements can be reduced as much as possible,so as to ensure the accuracy of forward simulation and reduce the cost of calculation.Dynamic DGTD method based on hierarchical vector basis functions is used to simulate single and double underground pipeline models.The electromagnetic response characteristics of underground pipeline model in different materials,different buried depth,different pipe diameter and layered terrain are studied.The influence of DGTD method based on different orders basis functions on calculation accuracy is analyzed,and the memory consumption of dynamic adaptive DGTD method and traditional non-adaptive DGTD method is compared.The results show that the introduction of high order hierarchical vector basis functions can effectively improve the accuracy of forward simulation.The relative error of DGTD method based on high order hierarchical vector basis functions is about 20 dB lower than that of DGTD method based on low order edge-based vector basis functions;Compared with the traditional DGTD method,the dynamic P-adaptive DGTD method can reduce the calculation memory by about 50%while ensuring the accuracy of calculation,which provides a more efficient numerical calculation method for the forward simulation of underground pipeline.