1 research outputs found
Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations
Balancing domain decomposition by constraints (BDDC) algorithms with adaptive
primal constraints are developed in a concise variational framework for the
weighted plane wave least-squares (PWLS) discritization of Helmholtz equations
with high and various wave numbers. The unknowns to be solved in this
preconditioned system are defined on elements rather than vertices or edges,
which are different from the well-known discritizations such as the classical
finite element method. Through choosing suitable "interface" and appropriate
primal constraints with complex coefficients and introducing some local
techniques, we developed a two-level adaptive BDDC algorithm for the PWLS
discretization, and the condition number of the preconditioned system is proved
to be bounded above by a user-defined tolerance and a constant which is only
dependent on the maximum number of interfaces per subdomain. A multilevel
algorithm is also attempted to resolve the bottleneck in large scale coarse
problem. Numerical results are carried out to confirm the theoretical results
and illustrate the efficiency of the proposed algorithms