Efficient Parallel Adaptive BDDC Algorithm For Mortar Discretization Of Second-order Elliptic Problem In Three Dimension

A BDDC(balancing domain decomposition by constraints)algorithm with adaptive primal constraints is designed to solve the Schur complement system of Mortar discretization of second-order elliptic problem in three dimension.Compared with the conforming finite element method,the construction of coarse space is simpler because the multiplier degree of freedom is only defined in the interior nodes of interfaces which are shared by only two subdomains.Numerical results show that when deluxe scaling matrix is chosen for the case of complex random coefficient,the average number of primal unknowns on each interface is almost independent of the subdomain partition,and the iteration counts of PCG method remains stable.Then,corresponding classification algorithm are designed separately for the local Schur complement matrix sequence and the matrix sequence of the generalized eigenvalue problems with a specific algebraic structure,further we obtain the corresponding parallel optimization algorithm and implement it based on OpenMP environment.Numerical results show that the parallel algorithm has a good speedup.