Costabel FEM-BEM耦合的算子预处理用于时谐Maxwell传输问题
Operator preconditioning of the Costabel FEM-BEM coupling for the time-harmonic Maxwell transmission problem
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中文总结 AI 辅助
本文为时谐Maxwell传输问题的Costabel FEM-BEM耦合推导等价形式并构造块对角预处理器，证明其谱条件数一致有界，数值实验验证了有效性。
中文摘要 AI 辅助
本文针对具有Lipschitz界面的时谐Maxwell传输问题，推导了Costabel FEM-BEM耦合的等价形式，并为所得离散系统构造了一个块对角预处理器。重新表述的耦合定义在迹空间的乘积上，通过引入迹提升算子和Steklov-Poincaré算子获得。在代数层面，这对应于消除内部FEM未知量，得到一个涉及内部FEM块的Schur补的离散系统。假设频率位于共振集之外，我们证明了重新表述的耦合在连续和离散层面上均等价于Costabel耦合。利用算子预处理框架，我们从Maxwell单层边界积分算子诱导的Galerkin矩阵构建了一个预处理器。预处理矩阵的谱条件数被证明是一致有界的。数值实验展示了所提方法的实际有效性。
英文摘要
This paper derives an equivalent formulation of the Costabel FEM-BEM coupling for the time-harmonic Maxwell transmission problem with a Lipschitz interface, and constructs a block-diagonal preconditioner for the resulting discrete system. The reformulated coupling is posed on a product of trace spaces and is obtained by introducing a trace lifting operator and the Steklov--Poincar{\' e} operator. At the algebraic level, it corresponds to eliminating the interior FEM unknowns, resulting in a discrete system that involves the Schur complement of the interior FEM block. Assuming that the frequency lies outside the resonance sets, we prove that the reformulated coupling is equivalent to the Costabel coupling at both the continuous and discrete levels. Using the operator preconditioning framework, we build a preconditioner from the Galerkin matrix induced by the Maxwell single layer boundary integral operator. The spectral condition number of the preconditioned matrix is shown to be uniformly bounded. Numerical experiments illustrate the practical effectiveness of the proposed approach.
发表机构
- Ghent University - imec（根特大学-imec）
- Hanoi University of Science and Technology（河内理工大学）
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