关于声学振动问题虚拟元方法的稳定化

Discontinuous Galerkin methods for the acoustic vibration problem

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 c…

声学问题非协调虚拟元离散的误差分析

Error analysis for a non-conforming virtual element discretization of the acoustic problem

本研究针对二维声振动问题，引入适用于$\rm H^1$空间的非协调虚拟元离散其压强公式，借助非紧算子理论证明方法的收敛性与谱正确性，并通过多组多边形网格数值实验验证了谱近似精度。

Fast multipole accelerated boundary element methods for room acoustics

The direct and indirect boundary element methods, accelerated via the fast multipole method, are applied to numerical simulation of room acoustics for large rooms of volume $\sim 150$ $m^{3}$ and frequencies up to 5 kHz on a workstation. As the parameter $kD$ (wavenumber times room diameter) is large, stabilization of the previously developed FMM algorithms is required for accuracy. A stabilization scheme is one of the key contribution of this paper. The computations are validated using well-known image source solutions for shoebox shaped rooms. Computations for L-shaped rooms are performed to…

混合高阶方法用于时域弹性-声波传播

Hybrid high-order methods for elasto-acoustic wave propagation in the time domain

本文提出一种混合高阶方法求解时域弹性-声波耦合问题，通过O(1)稳定化避免CFL限制，实现最优收敛率，并验证了在对比材料介质中的有效性。

变分多尺度稳定化与细尺度修正器的指数衰减

Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors

本文研究了线性偏微分方程多尺度特征的变分多尺度稳定化方法，通过Petrov-Galerkin型稳定化消除高振荡问题中的尺度依赖预渐进行为。

允许小边的声学问题虚拟元方法

VEM allowing small edges for the acoustic problem

本文提出一种允许小边的多边形网格上的虚拟元方法，用于逼近声学特征值问题的自然频率，并证明了收敛性与误差估计，数值测试验证了方法的性能与准确性。

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods

Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems. Such models typically exhibit a second-order structure and their material properties as well as their excitation may be depending on the driving fr…