论文标题
简单支撑的振动板特征值的dirichlet光谱 - 盖尔金近似方法
Dirichlet spectral-Galerkin approximation method for the simply supported vibrating plate eigenvalues
论文作者
论文摘要
在本文中，我们分析并实施了Dirichlet光谱 - 盖尔金方法，用于近似使用具有可变系数的振动板特征值。这是一个使用典型的近似空间，该近似空间是laplacian的许多dirichlet eigenfunctions的跨度。对该方法的收敛性和误差分析提出了两个维度和三个维度。在这里，我们将假设该域具有光滑的或Lipschitz的边界，而没有重入角。误差分析的一个重要组成部分是Dirichlet特征值的Weyl定律。提供了用于计算单位磁盘和正方形的简单支持的振动板特征值的数值示例。为了测试近似值的准确性，我们将光谱 - 盖尔金方法与单位磁盘的变量分离进行比较。而对于单位正方形，我们将数值测试可变系数问题的收敛速率。
In this paper, we analyze and implement the Dirichlet spectral-Galerkin method for approximating simply supported vibrating plate eigenvalues with variable coefficients. This is a Galerkin approximation that uses the approximation space that is the span of finitely many Dirichlet eigenfunctions for the Laplacian. Convergence and error analysis for this method is presented for two and three dimensions. Here we will assume that the domain has either a smooth or Lipschitz boundary with no reentrant corners. An important component of the error analysis is Weyl's law for the Dirichlet eigenvalues. Numerical examples for computing the simply supported vibrating plate eigenvalues for the unit disk and square are presented. In order to test the accuracy of the approximation, we compare the spectral-Galerkin method to the separation of variables for the unit disk. Whereas for the unit square we will numerically test the convergence rate for a variable coefficient problem.
