Publication

FETI-DP Domain Decomposition Method

2014
Student Projects

Abstract

FETI-DP is a dual iterative, nonoverlapping domain decomposition method. By a Schur complement procedure, the solution of a boundary value problem is reduced to solving a symmetric and positive definite dual problem in which the variables are directly related to the continuity of the solution across the interface between the subdomains. The dual problem is solved by the conjugate gradient method with a Dirichlet preconditioner. In each iteration step a relatively small number of continuity constraints are enforced by the solution of a coarse level problem. Some numerical experiments are provided for the FETI-DP method applied to a 2- and 3-dimensional Poisson problem, as well as to a 3-dimensional Navier-Stokes problem.

Official source

https://infoscience.epfl.ch/entities/publication/564b174c-7085-40f8-afa5-cf8ccc69ab92

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2014
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/564b174c-7085-40f8-afa5-cf8ccc69ab92

About this result

Related concepts (21)

Duality (optimization)

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.

Semidefinite programming

Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems.

Duality (mathematics)

In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry. In mathematical contexts, duality has numerous meanings.

Related publications (3)

FETI-DP Domain Decomposition Method

Chat with Graph Search

Freight railway network design problem

A Lagrangian relaxation technique for the demand-based benefit maximization problem

Integrated schedule planning with supply-demand interactions for a new generation of aircrafts