论文标题
El-Waveholtz：时间域的迭代求解器，用于时谐波波
El-WaveHoltz: A Time-Domain Iterative Solver for Time-Harmonic Elastic Waves
论文作者
论文摘要
我们考虑将Waveholtz迭代应用于具有能量保护边界条件的时谐波弹性波方程。原始的helmholtz问题的原始WaveHoltz迭代是一种定点迭代，它可以通过时谐波强迫和边界数据过滤波程的解。与原始的WaveHoltz方法一样，我们将固定点迭代重新制定为通过Krylov方法迭代求解的正定方程式的正定义线性系统。我们提出了两个时间稳定的方案，一个显式和一个（新颖的）隐式，通过对初始数据和时间stepping方案进行简单修改，从Waveholtz解决方案中完全消除了时间离散误差。数值实验表明迭代缩放与原始Waveholtz方法相似，并且收敛速率取决于问题的最短（剪切）波速。我们还表明，对于具有不同元素大小的网格，隐式方案在实践中可能是有利的。
We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acoustic Helmholtz problems is a fixed-point iteration that filters the solution of the wave equation with time-harmonic forcing and boundary data. As in the original WaveHoltz method, we reformulate the fixed point iteration as a positive definite linear system of equations that is iteratively solved by a Krylov method. We present two time-stepping schemes, one explicit and one (novel) implicit, which completely remove time discretization error from the WaveHoltz solution by performing a simple modification of the initial data and time-stepping scheme. Numerical experiments indicate an iteration scaling similar to that of the original WaveHoltz method, and that the convergence rate is dictated by the shortest (shear) wave speed of the problem. We additionally show that the implicit scheme can be advantageous in practice for meshes with disparate element sizes.
