标题： IGA拉普拉斯本征频率分布和估计：重新参数化对本征频率行为的影响 显示英文标题

标题： IGA Laplace Eigenfrequencies Distributions and Estimations: Impact of Reparametrization on Eigenfrequency Behavior

摘要： 这项工作解决了在有界区间上满足齐次狄利克雷边界条件的一维拉普拉斯特征值问题的Galerkin等几何离散化。 我们采用GLT理论来分析当对计算域进行重新参数化时特征频率的行为。 在对重新参数化变换做出适当假设的情况下，我们证明了当通过GLT符号分析重新表述问题时，特征频率的分布中会出现结构化的模式。 此外，我们建立了若干结果，这些结果细化并扩展了[3]中的结果，包括一个统一的离散Weyl定律。 此外，我们通过证明符号在零附近表现出渐近线性行为，得出了几个特征频率的估计。 显示英文摘要

摘要： This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the eigenfrequencies when a reparametrization is applied to the computational domain. Under suitable assumptions on the reparametrization transformation, we prove that a structured pattern emerges in the distribution of eigenfrequencies when the problem is reframed through GLT-symbol analysis. Additionally, we establish results that refine and extend those of [3], including a uniform discrete Weyl's law. Furthermore, we derive several eigenfrequency estimates by establishing that the symbol exhibits asymptotically linear behavior near zero.