A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard discontinuous Galerkin scheme with upwind numerical fluxes and high-order polynomial bases. Auxiliary unknowns corresponding to characteristic variables are defined at the interface between the elements, and the physical fields are eliminated to obtain a reduced system. The reduced system can be written as a fixed-point problem that can be solved with stationary iterative schemes. Numerical results with 2D benchmarks are presented to study the performance of the approach. Compared to the standard HDG approach, the properties of the reduced system are improved with CHDG, which is more suited for iterative solution procedures. The condition number of the reduced system is smaller with CHDG than with the standard HDG method. Iterative solution procedures with CGN or GMRES required smaller numbers of iterations with CHDG.
翻译：一种名为 CHDG 方法的新的可混合不连续的 Galerkin 方法, 用于解决时间- 调和卡路里波传播问题。 这种方法依赖于一种标准不连续的 Galerkin 方法, 具有上风数字通量和高阶多式基基。 元素之间的界面上定义了与特性变量相应的辅助未知, 并且消除了物理字段以获得一个缩小的系统。 降低的系统可以写成一个固定的迭代方案可以解决的固定点问题。 使用 2D 基准的数值结果, 用于研究该方法的性能。 与标准 HDG 方法相比, 降低的系统特性与 CHD 方法相比得到了改进, 后者更适合迭代解决方案程序。 降低的系统条件小于 CHDG 标准 HDG 方法。 与 CGN 或 GMRES 的循环解决方案要求与 CHDG 进行较少的重复。
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