A Fast Algorithm Based On Adaptive BDDC For Solving Stokes Saddle Point System With Lagrange Multiplier

This paper enfolds a two-dimensional Stokes problem.First,the Lagrange multiplier is introduced to convert its P2-P0 element saddle point system into a larger saddle point system with multiplier variables.Then the Schur complement method is used to solve the larger saddle point system.The specific steps are first use the CG method to solve the Schur complement equation corresponding to the pressure function,and then solve the vector saddle point system corresponding to the speed and multiplier function.The key involved in these two steps is how to quickly solve the latter.For the second step,by taking advantage of the characteristics of coefficient matrix,it can be transformed into two scalar(second-order elliptic problem with finite element)saddle point systems with Lagrange multipliers.As for solution to the scalar saddle point system,it can call the adaptive BDDC method.Finally,several numerical experiments under matching grid and non-matching grid verify the efficiency of the algorithm,that is,the number of iterations of the CG method hardly depends on the grid size,and the average number of iterations of the internal iterative adaptive BDDC method increases slightly as the grid size increases.