Comparison of the solvers of systems of linear equations: FETI-DP vs BDDC

Abstract

This bachelor thesis compares the dual–primal domain decomposition methods FETI-DP and BDDC for solving systems of linear equations arising from finite element discretizations of elliptic problems. The work is based on a model Poisson equation with mixed Dirichlet–Neumann boundary conditions on a two-dimensional unit square domain. After deriving the weak formula tion and performing the finite element discretization, the discrete problem is reduced by subdomain decomposition and Schur complements to a problem in the space corresponding to the interface between subdomains, which makes it possible to describe both methods in a common framework. Within this framework, sequential implementations of both methods are developed in Octave and compared according to the spectral properties of the preconditioned operators and the convergence of the PCG method. The study is complemented by a benchmark comparison of the official parallel implementations available in the PETSc library. The results show that both methods are numerically robust and behave very similarly on the tested problems.