论文标题
在2D中，适用于大波数的helmholtz方程的适应性泡沫的应用
Application of adapted-bubbles to the Helmholtz equation with large wave numbers in 2d
论文作者
论文摘要
提出了一种适用于2D中Helmhotz问题的无残留气泡（RFB）方法的修饰的气泡方法。引入了一种新的两级有限元方法，以实现气泡函数的近似值。与其他方程式（例如对流扩散方程）不同，将RFB方法应用于Helmholtz方程时，不取决于另一种稳定方法，以获得对亚问题的溶液的近似值。通过简单修改子问题，可以获得适应的气泡（AB）。这种修改令人印象深刻地提高了数值解决方案的准确性。 AB方法能够在2D中有效地求解Helmholtz方程至CH = 3.5，其中C为波数，H是网格大小。我们提供分析以显示AB方法如何减轻污染误差。
An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions. Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation, does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems. Adapted bubbles (AB) are obtained by a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. The AB method is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size. We provide analysis to show how the AB method mitigates the pollution error.
