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3.2.6 Eigenvalue problems

There is some preliminary support for solving eigenvalue problems by Wielandt’s iteration. For example, the first eigenvalue of the Laplace operator on a unit square can be approximated with

(let ((problem (cdr-model-problem 2 :evp (list :lambda (box 20.0)
                                               :mu (box 1.0)))))
  (defparameter *result*
    (solve (blackboard :problem problem
                       :success-if '(or (>= :time 5) (>= :nr-levels 5))
                       :output 1))))
(slot-value (getbb *result* :problem) 'lambda)
(plot (getbb *result* :solution))

Note that the multigrid algorithm has not yet been adapted for eigenvalue problems. Therefore, a sparse decomposition is used for solving the linear systems which does not work for large problems.