Adaptive-multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems

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