论文标题
具有特征变量的Helmholtz问题的杂交不连续的Galerkin方法
A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems
论文作者
论文摘要
提出了一种名为CHDG方法的新型杂交不连续的Galerkin方法，用于解决时间谐波标量波传播问题。此方法依赖于具有上风数值通量和高阶多项式碱基的标准不连续的盖尔金方案。与特征变量相对应的辅助未知数是在元素之间的接口处定义的，并且消除了物理场以获得还原的系统。还原系统可以写成一个定点问题，可以通过固定的迭代方案解决。提出了具有2D基准测试的数值结果，以研究该方法的性能。与标准HDG方法相比，使用CHDG改善了还原系统的特性，CHDG更适合迭代溶液程序。用墨西哥动物学杂志（CHDG）使用的还原系统的状况数量小于标准HDG方法。使用CGNR或GMRE的迭代溶液程序需要使用CHDG数量较少的迭代。
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.
