发表机构
Technische Universität München; University of Stuttgart; RWTH Aachen University（慕尼黑工业大学; 斯图加特大学; 亚琛工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于能量最小化的区域分解框架，统一处理线性和非线性源与特征值问题，推导算法实现与复杂度，数值实验验证其鲁棒性和高效性。
AI 中文摘要
我们提出了一种基于能量最小化的新型区域分解框架，适用于广泛的线性和非线性偏微分方程。这种能量最小化区域分解（EMDD）方法处理其解为能量泛函极小值的问题，无论是无约束的还是受限于流形的，从而在单一公式中涵盖了源问题和特征值问题。除了引入一般框架外，我们还推导了该方法在四类模型问题上的算法实现，即线性和非线性源问题及特征值问题，并推导了该方法的计算复杂度。数值实验证明了该方法在所有四类模型问题上的鲁棒性和效率，并表明它与现有的特定模型区域分解方法相比具有优势。
英文摘要
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.
