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arXiv · 2608.25041

Rapidly Convergent Finite-Element Domain Decomposition Method With Two-Channel Transmission Conditions

Furkan Şık·Fernando L. Teixeira·Balasubramaniam Shanker
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Abstract

A novel dual-primal finite element tearing and interconnecting (FETI-DP) domain decomposition method (DDM) is introduced for solving Maxwell's equations. The proposed method is built upon a two-channel transmission condition (TC) enforcing both tangential-field and normal-flux continuity across subdomain interfaces. Two interface channels are separately constructed from the Faraday and Ampere-Maxwell equations. Simultaneously enforcing tangential-field and normal-flux continuity reduces interface jumps by several orders of magnitude relative to the widely used Robin TC. The resulting global interface equation exhibits markedly improved iterative convergence. Numerical experiments across different partitioning strategies, subdomain counts and volumes, mesh resolutions, and geometries demonstrate drastic reductions in iteration counts, while accuracy, massive parallelism, and scalability are preserved.

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Furkan Şık, Fernando L. Teixeira, Balasubramaniam Shanker. 2026-08-25. Rapidly Convergent Finite-Element Domain Decomposition Method With Two-Channel Transmission Conditions. https://arxiv.org/abs/2608.25041

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