We present efficient domain decomposition solvers for a class of non-standard finite element methods (FEM). These methods utilize PDE-harmonic trial functions in every element of a polyhedral mesh, and use boundary element techniques locally in order to assemble the finite element stiffness matrices. For these reasons, the terms BEMbased FEM or Trefftz-FEM are sometimes used in connection with ...

A domain decomposition method with Lagrange multipliers for the Stokes problem is developed and analysed. A common approach to solve the Stokes problem, termed the Uzawa algorithm, is to decouple the velocity and the pressure. This approach yields the Schur complement system for the pressure Lagrange multiplier which is solved with an iterative solver. Each outer iteration of the Uzawa procedur...

Tearing and interconnecting domain decomposition methods [ 2, 3] are well established for an efficient and parallel solution of various elliptic partial differential equations by using finite and boundary element methods. But in the case of the Helmholtz equation, additional difficulties may appear. Although the global boundary value problem admits a unique solution, local subdomain solvers as ...

We show how we can exploit our recently proposed algorithms for the solution of contact problem of elasticity to the 2D analysis of the interfacial debonding of samples that consist of several fibres embedded in a homogeneous matrix, aligned in the longitudal direction. The performance of the algorithm is demonstrated on analysis of deformations of samples of the fibrous composite material.

Two popular non-overlapping domain decomposition methods, the FETI–DP and BDDC algorithms, are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal conti...

Two domain decomposition methods with Lagrange multipliers for solving iteratively quadratic programming problems with inequality constraints are presented. These methods are based on the FETI and FETI-DP substructuring algorithms. In the case of linear constraints, they do not perform any Newton-like iteration. Instead, they solve a constrained problem by an active set strategy and a generaliz...