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Balancing domain decomposition by constraints (BDDC) algorithms with adaptiveprimal constraints are developed in a concise variational framework for theweighted plane wave least-squares (PWLS) discritization of Helmholtz equationswith high and various wave numbers. The unknowns to be solved in thispreconditioned system are defined on elements rather than vertices or edges,which are different from the well-known discritizations such as the classicalfinite element method. Through choosing suitable "interface" and appropriateprimal constraints with complex coefficients and introducing some localtechniques, we developed a two-level adaptive BDDC algorithm for the PWLSdiscretization, and the condition number of the preconditioned system is provedto be bounded above by a user-defined tolerance and a constant which is onlydependent on the maximum number of interfaces per subdomain. A multilevelalgorithm is also attempted to resolve the bottleneck in large scale coarseproblem. Numerical results are carried out to confirm the theoretical resultsand illustrate the efficiency of the proposed algorithms.

Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations