Domain Decomposition with Lagrange Multipliers

9. Iterative Substructuring with Lagrange Multipliers for Coupled Fluid-Solid Scattering

A Nonoverlapping Domain Decomposition Method for Incompressible Stokes Equations with Continuous Pressures

A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressur...

A hybrid domain decomposition method based on one-level FETI and BDDC algorithms

A three-level domain decomposition is considered. Bodies in contact with each other are divided into subdomains, which in turn are the union of elements. Using an approach based purely on FETI (finite element tearing and interconnecting) algorithms with only Lagrange multipliers as unknowns, which has been developed by the engineering community, does not lead to a scalable algorithm with respec...

Mortar Finite Elements with Dual Lagrange Multipliers: Some Applications

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We consider mortar techniques with dual Lagrange multiplier spaces to couple different discretization schemes. It is well known that the discretization error for linear mortar finite elements in the energy norm is of order h. Here, we apply these techniques to curvilinear b...

A numerically scalable domain decomposition method for the solution of frictionless contact problems

We present a domain decomposition method with Lagrange multipliers for solving iteratively frictionless contact problems. This method, which is based on the FETI method and therefore is named here the FETIC method, incorporates a coarse contact system that guides the iterative prediction of the active zone of contact. We demonstrate numerically that this method is numerically scalable with resp...