Research On Mixed-Order DGTD Method Based On Hierarchical Basis Function

Among electromagnetic numerical calculation methods,the Discontinuous Galerkin Time Domain(DGTD)method has attracted extensive attention due to its advantages such as accurate fitting of complex and fine structures and easy parallelism.In the analysis of complex electromagnetic problems,the choice of higher order basis functions,conformal PML and non-uniform mesh can effectively reduce the computational degrees of freedom(DoF),which is of great significance in solving electromagnetic problems efficiently.In order to ensure the accuracy of calculation,The DGTD method based on low-order vector basis function needs to use smaller mesh to divide the target area,which leads to high resource consumption and time-consuming calculation.In order to solve the above problems,a 2.5-order hierarchical vector basis functions are constructed.When the 2.5-order hierarchical vector basis functions are used in this method,the large-scale mesh can be used to divide the target region,so as to reduce the number of tetrahedral meshes,which can effectively improve the computational efficiency and ensure the computational accuracy.In the electromagnetic numerical calculation,the perfect matching layer(PML)boundary conditions can be introduced through the complex coordinate stretching technology to simulate the open-field problem in a finite region.The realization scheme of conformal PML with curved interface is proposed,which reduces the buffer space and has advantages in solving the electromagnetic scattering and radiation problems of specific targets such as spheres or ellipsoids.On this basis,due to the nesting characteristics of the constructed hierarchical basis functions,a mixed order DGTD method using 2.5 order basis functions in the physical region and low order basis functions in the PML region is proposed,which can effectively solve the problems of high memory consumption and time-consuming in the calculation of pure high-order basis functions.The DGTD method is applied to the analysis of microstrip antennas,the method of non-uniform mesh division further saves computing resources.In the case of equivalent accuracy,the number of tetrahedron generated by non-uniform mesh is 39.7%of that generated by uniform mesh,and the memory consumption is reduced by half.When analyzing rectangular microstrip antennas based on the mixed-order DGTD method,the mixed-order calculation reduces the unknowns by 51.3%and the memory consumption by 46.7%compared with the pure high-order basis function calculation.The numerical simulation results fully verify the accuracy and efficiency of the proposed method in dealing with electromagnetic radiation problems.