摘要
对周期复合域的二次特征值问题(Quadratic Eigenvalue Problem,QEP),本文提出了一种二阶双尺度(Second-Order Two-Scale,SOTS)渐近分析和计算方法.该方法考虑一种包含速度阻尼的典型QEP,对特征函数进行渐近展开并设计了有限元算法,采用线性化方法求解均匀化二次特征值问题.数值算例表明,该方法可以有效处理此类非线性特征值问题,且二阶校正器在描述特征函数的局部行为和高效获得特征值的逼近值等方面起着重要作用.
Abstract
A second-order two-scale(SOTS)asymptotic analysis and computational method are developed for solving the quadratic eigenvalue problem(QEP)in periodic composited domain.A typical QEP involving the velocity-damping is considered and asymptotic expansions for the eigenfunctions are performed.Then a finite el-ement procedure is proposed and the homogenized QEPs are solved by the linearized method.Numerical ex-amples demonstrate the accuracy and efficiency of the method.It is shown that the method can effectively be ap-plied to such nonlinear eigenvalue problems in which the second-order correctors play an important role for de-scribing the local behavior of eigenfunctions and obtaining better approximation of the eigenvalues at lower cost.
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