论文标题
声学振动问题的不连续的galerkin方法
Discontinuous Galerkin methods for the acoustic vibration problem
论文作者
论文摘要
在两个维度和三个维度中，我们分析了声学问题的不连续的盖尔金方法。我们在本文中考虑的声流式是无关的，导致了线性特征值问题。声学问题首先是在流离失所方面写的。在非压缩操作者理论的方法下，当考虑位移配方时，我们证明了该方法的收敛性和误差估计。我们分析了稳定参数对频谱计算的影响，当未正确选择此参数时，出现虚假的特征模式。另外，我们仅根据压力提出配方，将DG方法的性能与纯粹的位移配方进行比较。在计算上，我们研究了计算频谱时稳定参数对伪造特征值产生的影响。此外，我们报告了两个和三个维度的测试，其中报道了收敛速率，以及所提出的DG方法的位移和压力配方之间的比较。
In two and three dimension we analyze discontinuous Galerkin methods for the acoustic problem. The acoustic fluid that we consider on this paper is inviscid, leading to a linear eigenvalue problem. The acoustic problem is written, in first place, in terms of the displacement. Under the approach of the non-compact operators theory, we prove convergence and error estimates for the method when the displacement formulation is considered. We analyze the influence of the stabilization parameter on the computation of the spectrum, where spurious eigenmodes arise when this parameter is not correctly chosen. Alternatively we present the formulation depending only on the pressure, comparing the performance of the DG methods with the pure displacement formulation. Computationally, we study the influence of the stabilization parameter on the arising of spurious eigenvalues when the spectrum is computed. Also, we report tests in two and three dimensions where convergence rates are reported, together with a comparison between the displacement and pressure formulations for the proposed DG methods.
