Total FETI-an easier implementable variant of the FETI method for numerical solution of elliptic PDE

Abstract

SUMMARYA new variant of the FETI method for numerical solution of elliptic PDE is presented. The basic idea is to simplify inversion of the stiffness matrices of subdomains by using Lagrange multipliers not only for gluing the subdomains along the auxiliary interfaces, but also for implementation of the Dirichlet boundary conditions. Results of numerical experiments are presented which indicate that the new method may be even more efficient then the original FETI.

Solving Contact Mechanics Problems with PERMON

“…The basic idea of the TFETI method [5,7,32] is to keep all the subdomains floating and enforce the Dirichlet boundary conditions by means of a constraint matrix and Lagrange multipliers, similarly to the gluing conditions along subdomain interfaces. This simplifies the implementation of the stiffness matrix pseudoinverse.…”

“…PERMON extends PETSc [3] with support for quadratic programming (QP) and non-overlapping domain decomposition methods (DDM), namely of the FETI (Finite Element Tearing and Interconnecting) [13,12,5,24] type. This paper presents the process of solving contact problems using PERMON (Section 3).…”

Discretization and numerical realization of contact problems for elastic‐perfectly plastic bodies. PART II – numerical realization, limit analysis

“…To make computations more efficient, the TFETI domain decomposition method ( [12,14]) was used. A typical decomposition of 1 and 2 into subdomains is shown in Fig.…”

Scalable algorithm for solving 3D contact problems with friction

“…The elastic behavior of the brick is described by Lamé equations that, after FETI discretization, lead to a symmetric positive semidefinite stiffness matrix K ∈ R 3nc×3nc and to a load vector f ∈ R 3nc . As the FETI procedure divides the brick into subbricks, we interconnect corresponding parts of the solution by a "gluing" matrix B g ∈ R mg×3nc and, moreover, we enforce the Dirichlet boundary condition by B d ∈ R m d ×3nc [2]. Finally we introduce full rank matrices N and T 1 , T 2 ∈ R mc×3nc projecting displacements at contact nodes to normal and tangential directions, respectively, and we denote B = B d , B g , N , T 1 , T 2 ∈ R m d +mg +3mc×3nc .…”