(A) dual-primal FETI domain decomposition method for the poisson problem

Abstract

In this thesis, a dual-primal FETI method is applied for one dimensional Poisson problem with Dirichlet boundary condition. The domains of the problem is decomposed into nonoverlapping subdomains and the continuity of displacement on the interfaces between subdomains is enforced by the Lagrange multiplier and the continuity at corner points of subdomains are enforced exactly. By formulating FETI-DP method, we obtained a symmetric and positive definite system for Lagrange multipliers that are defined on interfaces between subdomains except corner points. We adapt the conjugate gradient method to solve the system. From the numerical result for this problem, we show that FETI-DP method is stable for the number of subdomains and meshes. Also demonstrate the optimal order of convergence of Q(h) is demonstrated as in the standard finite element spaces.