An iterative asymptotic expansion method for elliptic eigenvalue problems with oscillating coefficients

作者：Mehraeen Shafigh; Chen Jiun Shyan^*; Hu Wei

来源：Computational Mechanics, 2010, 46(2): 349-361.

DOI：10.1007/s00466-009-0435-y

• Multi-scale
• Asymptotic expansion
• Eigen-value problems
• Inverse iteration

In this work we propose a method for obtaining fine-scale eigensolution based on the coarse-scale eigensolution in elliptic eigenvalue problems with oscillating coefficient. This is achieved by introducing a 2-scale asymptotic expansion predictor in conjunction with an iterative corrector. The eigensolution predictor equation is formulated using the weak form of an auxiliary problem. It is shown that large errors exist in the higher eigenmodes when the 2-scale asymptotic expansion is used. The predictor solution is then corrected by the combined inverse iteration and Rayleigh quotient iteration. The numerical examples demonstrate the effectiveness of this approach.

• 出版日期2010-7