  In this paper, we are concerned with the weighted plane wave least-squares
(PWLS) method for three-dimensional Helmholtz equations, and develop the
multi-level adaptive BDDC algorithms for solving the resulting discrete system.
In order to form the adaptive coarse components, the local generalized
eigenvalue problems for each common face and each common edge are carefully
designed. The condition number of the two-level adaptive BDDC preconditioned
system is proved to be bounded above by a user-defined tolerance and a constant
which is dependent on the maximum number of faces and edges per subdomain and
the number of subdomains sharing a common edge. The efficiency of these
algorithms is illustrated on a benchmark problem. The numerical results show
the robustness of our two-level adaptive BDDC algorithms with respect to the
wave number, the number of subdomains and the mesh size, and illustrate that
our multi-level adaptive BDDC algorithm can reduce the scale of the coarse
problem and can be used to solve large wave number problems efficiently.
