Energy-minimizing domain decomposition

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.