A Localized Version of the Dual‐Primal Finite Element Tearing and Interconnecting Method for the Partitioned Analysis of Heterogeneous Structural Systems

ABSTRACT FETI‐DP is a mature domain decomposition algorithm that has been successfully applied to different problems, demonstrating impressive performance. To be effective, the algorithm needs to be equipped with different technicalities that somewhat complicate its implementation. Examples include the treatment of constraint multiplicities at partition edges, the convergence enhancement using additional constraints, and the construction of an efficient preconditioner for heterogeneous problems. Nevertheless, we believe that it is possible to achieve the same performance as FETI‐DP with a simpler implementation. This paper applies the method of localized Lagrange multipliers to the domain decomposition problem with a combination of dual and primal constraints, formulating a localized variant of FETI‐DP named AFETI‐DP. Although the convergence of AFETI‐DP is equivalent to the basic FETI‐DP algorithm, its implementation is simpler, eliminating the constraint multiplicity problem at the partition edges. Another benefit is that the localized multipliers can be scaled independently, an advantage for heterogeneous cases where FETI‐DP needs to construct special jump operators for preconditioning. Finally, it is also demonstrated how to include additional constraints with AFETI‐DPc by using a classical deflation and balancing approach with projection. For this task, the subdomain rigid body modes are capitalized in a completely uncoupled manner to attain convergence properties equivalent to the most modern FETI‐DP methods.