🤖 AI Summary
This work addresses the spectral degradation and poor solver efficiency arising from discretized Laplacian operators in eddy current problems coupled with external circuits. To overcome these challenges, the authors propose an electromagnetic decoupling (EMD) preconditioner that physically separates the system into vector and scalar potential components, each treated with a tailored preconditioning strategy. The approach synergistically combines algebraic multigrid, domain decomposition, and direct solver techniques, enabling parallel computation across multiple excited conductor domains and seamless integration with mainstream solver frameworks. Numerical experiments demonstrate that, compared to conventional incomplete Cholesky preconditioning, the proposed method reduces iteration counts by up to a factor of 20 and accelerates solution times by as much as 20-fold.
📝 Abstract
This paper proposes an efficient and scalable preconditioning strategy for eddy current problems involving coupled external circuits. The approach, named Electro-Magnetic Decoupling (EMD) preconditioner, decomposes the discrete system into vector and scalar potential components and applies tailored preconditioners to each. In particular, strong preconditioning is applied to the scalar component to address the spectral degradation induced by the discrete Laplacian. The method was evaluated on four eddy current models with varying frequencies, conductor topologies, and excitation types. Compared to the conventional incomplete Cholesky preconditioner, the EMD approach achieved up to 20 times fewer iteration counts and up to 20 times faster iterative solver time. Moreover, the method supports physics-level parallelization, allowing efficient treatment of independently excited conductor domains. The EMD framework is compatible with algebraic multigrid, domain decomposition, and direct solvers, offering flexibility and robustness for large-scale electromagnetic simulations.