An Adaptive BDDC Algorithm For The System Arising From PWLS Discretization Of Time-harmonic Maxwell's Equations

We consider a complex time-harmonic Maxwell equations with Robin boundary conditions in three dimension.Firstly,by introducing a special interface,we obtain the corresponding Schur complement system of the discretization arising from plane wave least squares(PWLS)method.Then,we design an adaptive BDDC preconditioner which has good robustness for the Schur complement system by introducing several auxiliary spaces and operators.Since some sub-matrices involved in the adaptive BDDC is very ill-conditioned,we use some special techniques in the implementation,such as pre-processing and small perturbation techniques.The numerical experiments show that the iteration number of the PCG method based on the designed adaptive BDDC preconditioner is dependent on the mesh size,the number of direction vectors of the plane wave basis function(denoted as )and the scaling matrix.For the same computing scale,PCG method with deluxe scaling matrix owns less iterations than the multiplicity scaling matrix;for a fixed grid size,the preconditioner is not robust enough if special technique is not adopted,i.e.the number of iterations is unstable when increases.After using some special techniques,the above problem is overcome,and the number of iterations is weakly dependent on the grid size.