This paper proposes a simple yet efficient mortar-type method to couple independent finite element subdomains with intersecting interfaces. In this method, we split the subdomain interfaces into several contact patches. Different patches are allowed to have the same master/slave nodes. To eliminate the over-constrained behavior that often occurs in conventional mortar methods, we divide the constraint matrix into two categories: pure and cross constraint systems. In this way, all over-constrained equations are concentrated in the cross constraint system. Then, an efficient submatrix condensation algorithm is proposed to remove the linearly dependent equations in cross constraint systems. The over-constrained behavior can thus be avoided. Using the dual Lagrange scheme, the proposed method can implement the matrix condensation at a minimal computational cost and ensure the positive definiteness of the system matrix. The robustness and effectiveness of the proposed method are studied by comparing the theoretical and numerical solutions. Several numerical examples show that our method has an optimal convergence rate and high computational efficiency.

本文提出了一种简单而有效的砂浆型方法来将独立的有限元子域与相交界面耦合。在这种方法中，我们将子域接口拆分为几个联系补丁。允许不同的补丁具有相同的主/从节点。为了消除传统砂浆方法中经常出现的过度约束行为，我们将约束矩阵分为两类：纯约束系统和交叉约束系统。这样，所有过约束方程都集中在交叉约束系统中。然后，提出了一种有效的子矩阵凝聚算法来去除交叉约束系统中的线性相关方程。因此可以避免过度约束的行为。使用对偶拉格朗日方案，所提出的方法可以以最小的计算成本实现矩阵压缩，并保证系统矩阵的正定性。通过比较理论和数值解来研究所提出方法的鲁棒性和有效性。几个数值例子表明我们的方法具有最优的收敛速度和较高的计算效率。