标题： 具有传输变量的杂交izable间断Galerkin方法求解非均匀介质中的时谐声学问题 显示英文标题

标题： A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic acoustic problems in heterogeneous media

摘要： 我们考虑用混合间断伽辽金（HDG）方法求解时间谐波波传播问题在非均匀介质中的有限元解。在均匀介质的情况下，已经观察到通过使用传输变量进行混合而不是数值迹线可以加速线性系统的迭代解，这与标准方法不同。在这项工作中，我们将传输变量的HDG方法，称为CHDG方法，扩展到具有分片常数物理系数的非均匀情况。特别是，我们考虑了标准迎风和一般对称通量的公式。CHDG混合系统可以写成一个不动点问题，对于一类对称通量，可以用定常迭代方案来求解。通过一系列二维数值基准，系统地研究了标准HDG和CHDG方法的不同数值通量。使用扩展的CHDG方法时，标准迭代方案的收敛速度总是比使用标准HDG方法（迎风和标量对称通量）更快。 显示英文摘要

摘要： We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that the iterative solution of the linear system can be accelerated by hybridizing with transmission variables instead of numerical traces, as performed in standard approaches. In this work, we extend the HDG method with transmission variables, which is called the CHDG method, to the heterogeneous case with piecewise constant physical coefficients. In particular, we consider formulations with standard upwind and general symmetric fluxes. The CHDG hybridized system can be written as a fixed-point problem, which can be solved with stationary iterative schemes for a class of symmetric fluxes. The standard HDG and CHDG methods are systematically studied with the different numerical fluxes by considering a series of 2D numerical benchmarks. The convergence of standard iterative schemes is always faster with the extended CHDG method than with the standard HDG methods, with upwind and scalar symmetric fluxes.