Performance evaluation of the conjugate gradient method with master–slave elimination for the dual mortar method

In the mortar finite element method based on the dual Lagrange method (dual mortar method), a block matrix with respect to the slave degrees of freedom of the constraint matrix becomes a diagonal matrix due to the biorthogonal shape functions. In this paper, the dual mortar method is combined with the algorithm for the conjugate gradient (CG) method proposed by Horiuchi et al. (2002). Dependent DOFs, i.e., slave DOFs in the mortar method, of the residual vector are eliminated during the iteration of the CG method. The property of the block diagonal matrix in the constraint matrix facilitates the elimination. The computational performance of this approach is compared with that of the conjugate projected gradient (CPG) method and the balancing domain decomposition method with multi-point constraints (BDD-MPC method), which is based on the CPG method and was previously proposed and developed by the author. The possibility of developing a BDD method based on the RCG method is also discussed.