Energy-minimizing domain decomposition

arXiv (Cornell University)

Abstract

We propose a novel domain decomposition framework based on energy minimization, applicable to a wide class of linear and nonlinear partial differential equations. This energy-minimizing domain decomposition (EMDD) method addresses problems whose solutions are minimizers of an energy functional, either unconstrained or constrained to a manifold, and thus covers source and eigenvalue problems in a single formulation. Besides introducing the general framework, we derive the algorithmic realization of the method for four classes of model problems, namely linear and nonlinear source and eigenvalue problems, and derive the computational complexity of the method. Numerical experiments demonstrate the robustness and efficiency of the method across all four model problems and show that it compares favourably against existing model-specific domain decomposition methods.

Authors 3

1. Muhammad Hassan

   Technical University of Munich

   Affiliation as printed

   Technische Universität München , Department of Mathematics , Boltzmannstrasse 3 , Garching 85748 , Germany

2. Benjamin Stamm

   Stuttgart Technical University of Applied Sciences

   Affiliation as printed

   Department of Mathematics , University of Stuttgart , Germany

3. Lambert Theisen Aachen Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Applied and Computational Mathematics , RWTH Aachen University , Germany