A Pade approximate linearization algorithm for solving the quadratic eigenvalue problem with low-rank damping

作者：Lu, Ding; Huang, Xin; Bai, Zhaojun^*; Su, Yangfeng

来源：International Journal for Numerical Methods in Engineering, 2015, 103(11): 840-858.

DOI：10.1002/nme.4919

• quadratic eigenvalue problem
• low-rank damping
• linearization
• Pade approximation

The low-rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low-rank damping property, we propose a Pade approximate linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only n + lm, which is generally substantially smaller than the dimension 2n of the linear eigenvalue problem produced by a direct linearization approach, where n is the dimension of the quadratic eigenvalue problem, and l and m are the rank of the damping matrix and the order of a Pade approximant, respectively. Numerical examples show that by exploiting the low-rank damping property, the PAL algorithm runs 33-47% faster than the direct linearization approach for solving modest size quadratic eigenvalue problems.

• 出版日期2015-9-14
• 单位复旦大学