An efficient patch-to-patch method for coupling independent finite element subdomains with intersecting interfaces

Abstract

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.