Tetsuji Matsuo | Searcharxiv

arXiv2026

Estimation of Condition Number of Quasi-static Darwin Model

This study discusses the estimation of the condition number of the quasi-static Darwin model, which is shown to be a nearly singular system of equations with a large kernel derived from the gauge invariance of full Maxwell's equations. Inequality evaluations for a minimum nonzero singular value, maximum singular value, and condition number for a nearly singular system of equations and its augmented system are provided. This discussion reveals the nearly singular nature of the Darwin model and proves the effectiveness of the augmented system method for solving the Darwin model.

cs.CE↗

arXiv2026

Electro-Magnetic Decoupling Preconditioner for Eddy Current Problems with External Circuit Coupling

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.

cs.CE↗