Preamble
  • In this module, we learn how to use Jacobi-Davidson methods to solve quadratic eigenvalue problems. The methods can be efficient in the case studies.

Slides
  • Jacobi-Davidson Methods for quadratic eigenvalue problems (QEP)(s01)

Hands-On Labs
  1. Get familiar with the QEP.
    (a) Worksheet B1,
    (b) Files for Problem 2: box_0.650_0.000_40.mat, run_box_0.650_0.000_40.m, LS_shift_invert.m
    (c) Files for Problem 3: run_displacement.m, displacement.rar (contains the problem generators mtx_QEP.m, Construct_mass_mtx.m, Construct_mtx, and Construct_stiff_mtx.m)


References
  • S.-H. Chou, T.-M. Huang, W.-Q. Huang and W.-W. Lin (To appear). "Efficient Arnoldi-type algorithms for rational eigenvalue problems arising in fluid-solid systems". J. Comput. Phys