Preamble
  • Solving a large-scale eigenvalue problem may not be as easy, nor as boring, as you think. We will see how some sophisticated eigenvalue techniques can reduce the computational time dramatically and turn a mission impossible to a piece of cake.

Slides
  • Power and Inverse Power Methods (s01)
  • Lanczos Method (s02)

Hands-On Labs
  1. Test Problem Generator
    Worksheet A1, Problem generator (see README.txt first)

  2. The Eigensolvers in MATLAB
    Worksheet A2

  3. Power Method
    Worksheet A3,   GEP2SEP.m,   PowerMethod_Norm.m,   PowerMethod_LinFun.m,
    plot_3d_ev.m,   run_eig_solver.m

  4. Inverse Power Method
    Worksheet A4,   InversePower.m

  5. Lanczos Method
    Worksheet A5,   run_Lanczos_solver.m,   Lanczos_basic.m,   Lanczos_with_IR_Reorth.m,   Lanczos_Steps_with_Reorth.m,   Implicit_Restart_for_Lanczos.m,   Lanczos_.m,   Lanczos_.m,   Lanczos_.m


References
  • Tsung-Ming Huang, Wei-Jen Chang, Yin-Liang Huang, Wen-Wei Lin, Wei-Cheng Wang, and Weichung Wang (2010). "Preconditioning Bandgap Eigenvalue Problems in Three Dimensional Photonic Crystals Simulations.”Journal of Computational Physics, 229:8684-8703. http://dx.doi.org/10.1016/j.jcp.2010.08.003

  • Photonic Crystals