A Fast Grid Correspondence Judgment Algorithm between Tetrahedrons for the DGTD Method

The discontinuous Galerkin time-domain (DGTD) method used for the computation of electromagnetic fields in 3-D structures obtains the weak solution form of the Maxwell’s equations through spatial semidiscrete approximation and integration of test function. Numerical flux needs to be added between unstructured tetrahedral elements to compensate for boundary conditions. The establishment of corresponding surface mapping between mesh elements is a prerequisite for the numerical flux transfer between meshes. Based on fast sorting algorithm, this paper designs a grid correspondence judgment algorithm called ‘Sorting and Querying’, which reduces computational complexity from O(n^2) to O(nlogn). The numerical results show that the algorithm is faster than the similar algorithms and easier to program even in the case of a large number of grids.