Linearization or Not. A Numerical Study of Two Solution Algorithms for Quadratic PDE Eigenvalue Problems.

• Main Authors: Fu-Rung Liu, 劉馥榮
• Other Authors: Feng-Nan Hwang
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/vhjq3u

碩士 === 國立中央大學 === 數學系 === 105 === We numerically investigate the numerical performance of two solution algorithms for the quadratic eigenvalue problems (QEP's), namely the linearization approach and the polynomial Jacobi-Davidson method. Such eigenvalue computations play an important role and highly-demanded in many computational sciences and engineering applications, such as the noise control in the acoustical design, stability analysis in the structural engineering, and electronic engineering. In the linearization approach, the QEP is linearized as a companion generalized eigenvalue problems (GEVP's), and then a variety of linear eigensolvers are solved the resulting GEVP's. On the other hand, the polynomial Jacobi-Davidson method targets the eigenvalue of interests directly without any transformation. The evaluation metrics are the robustness, accuracy, and efficiency. To draw the conclusion for more general situations, we conduct intensive numerical experiments for a large number of test cases generated by a collection of Nonlinear Eigenvalue Problem (NLEPV), with a various problem size and different coefficient matrices properties.