Abstract
Abstract
The spectrally discretized parabolic equation model provides high-accuracy numerical solutions for underwater acoustic propagation. However, its global discretization strategy yields a nonsymmetric, locally dense block-structured system with sparse interface and boundary coupling, creating computational and memory bottlenecks for direct solvers. To overcome these limitations, this paper proposes an efficient solver based on preconditioned Krylov subspace iterations. This strategy introduces two preconditioners optimized for the distinct structure of the spectral matrix to accelerate iterative convergence. These include a structure-aware variant of the incomplete LU factorization with threshold and pivoting (SA-ILUTP) and an upper triangular block preconditioner (UTBP). By employing a partial fraction expansion of the high-order Padé approximation, the solver effectively utilizes multi-core architectures to parallelize the simulation process. Numerical experiments on representative cases, including a plane-parallel waveguide, a warm-core eddy, and a measured deep-sea waveguide, demonstrate that the proposed strategy significantly accelerates computation while preserving the inherent high accuracy of the spectral method. Evaluations with eight threads at the Beijing Supercomputing Center indicate both customized strategies deliver considerable performance gains over direct methods. The SA-ILUTP solver accelerates computation by a factor of up to 28 and reduces peak memory from 13.7 GB to 4.6 GB, whereas the UTBP strategy extends the maximum speedup to a factor of 35 and reduces the memory footprint to 2.6 GB. Overall, this iterative framework effectively balances computational speed and memory overhead, providing practical numerical support for high-resolution ocean acoustic field simulations.