Abstract:
The discontinuous Galerkin time-domain (DGTD) method exhibits great geometric adaptability and parallel computing capability for electromagnetic simulations involving complex structures. For large-scale unstructured tetrahedral meshes, the evaluation of spatial adjacency relationships over discretely allocated memory addresses leads to extensive non-contiguous memory accesses during the solution process. This issue becomes particularly pronounced in time-marching computations, where frequent cache misses significantly constrain solver performance. To address this problem, a high-efficiency Hilbert-curve-based element reordering method utilizing bitwise operations is proposed. By combining a finite-state machine with bitwise manipulation, the proposed approach rapidly generates spatial state codes and constructs one-dimensional continuous Hilbert indices. These indices are then employed to reorganize the storage layouts of elements and nodes, enabling the data arrangement to better match the memory access characteristics associated with local flux exchanges and element integrations in DGTD computations. Numerical results demonstrate that the proposed method improves data access patterns with only a small preprocessing overhead and effectively reduces accesses to main memory. The reordered data layout enhances spatial memory locality and yields a significant improvement in overall solver efficiency without compromising computational accuracy.