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 CGNR or GMRES required smaller numbers of iterations with CHDG.

翻译：本文提出了一种新的混合化间断伽辽金方法，称为CHDG方法，用于求解时谐标量波传播问题。该方法基于标准的间断伽辽金格式，采用迎风数值通量和高阶多项式基函数。在单元交界处定义了与特征变量相对应的辅助未知量，并通过消去物理场获得一个降阶系统。该降阶系统可表述为一个不动点问题，从而能够通过稳态迭代格式求解。通过二维基准算例的数值结果，分析了该方法的性能。与标准HDG方法相比，CHDG方法改善了降阶系统的性质，使其更适用于迭代求解过程。采用CHDG方法时，降阶系统的条件数小于标准HDG方法。使用CGNR或GMRES进行迭代求解时，CHDG方法所需的迭代次数更少。