"A strongly convergent primal–dual method for nonoverlapping domain decomposition"

Research areas:
  • Uncategorized
Year:
2015
Type of Publication:
Article
Authors:
  • H. Attouch
  • Luis M. Briceño
  • Patrick L. Combettes
Journal:
Numerische Mathematik
Month:
July
ISSN:
0945-3245
Abstract:
We propose a primal–dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling constraints which model various properties of the solution at the interfaces. The proposed method can handle a wide range of linear and nonlinear problems, with flexible, possibly nonlinear, transmission conditions across the interfaces. Strong convergence in the energy spaces is established in this general setting, and without any additional assumption on the energy functions or the geometry of the problem. Several examples are presented