AI 中文总结
该研究比较了无粗网格校正的两类区域分解预条件子，针对三种非协调Helmholtz离散化方法，经数值实验验证其对大规模问题有良好性能。
AI 中文摘要
我们比较了无粗网格校正的加法型与乘法型区域分解预条件子，适用于Helmholtz问题的三种非协调多项式离散化方法：间断Galerkin法、嵌入Trefftz间断Galerkin法与混合间断Galerkin法。这些预条件子在定常及Krylov迭代求解器中被研究。三种离散化均导出复对称系统，且局部子问题带有继承的阻抗型边界条件；这些特性可应用共轭梯度法，且局部矩阵可通过全局矩阵的限制直接得到。二维与三维数值实验表明，其对大规模Helmholtz问题具有良好性能。
英文摘要
We compare additive and multiplicative domain decomposition preconditioners, without coarse correction, for three non-conforming polynomial discretizations of Helmholtz problems: discontinuous Galerkin, embedded Trefftz discontinuous Galerkin, and hybrid discontinuous Galerkin methods. The preconditioners are studied within stationary and Krylov iterative solvers. All three discretizations lead to complex-symmetric systems and local subproblems with inherited impedance-type boundary conditions. These properties enable the use of conjugate gradients and allow the local matrices to be obtained directly by restriction of the global matrix. Numerical experiments in two and three dimensions demonstrate promising performance for large-scale Helmholtz problems.
Comments22 pages, 9 figures, 5 tables
