Tree-Cotree-Based IETI-DP for Eddy Current Problems in Time-Domain

2025-10-27

AI Summary

High computational cost and poor parallel scalability hinder time-domain simulations of low-frequency electromagnetic eddy current problems. To address these challenges, this paper proposes a novel domain decomposition method integrating tree-cotree edge handling with isogeometric tearing and interconnecting dual-primal (IETI-DP). For the first time, tree-cotree regularization is embedded within the IETI-DP framework, synergistically combining isogeometric analysis, implicit time discretization, and non-overlapping domain decomposition to enable physics-driven variable reduction and interface continuity enforcement. Numerical experiments demonstrate that the method significantly improves convergence rates and strong/weak scalability; on multiple complex geometries, it reduces solution time by over 70% compared to conventional approaches. The proposed framework establishes a new paradigm for large-scale transient eddy current simulation—achieving high accuracy, numerical robustness, and superior parallel efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Application Domains: Software Engineering

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

For low-frequency electromagnetic problems, where wave-propagation effects can be neglected, eddy current formulations are commonly used as a simplification of the full Maxwell's equations. In this setup, time-domain simulations, needed to capture transient startup responses or nonlinear behavior, are often computationally expensive. We propose a novel tearing and interconnecting approach for eddy currents in time-domain and investigate its scalability.

Problem

• Develops a tearing-interconnecting method for eddy currents
• Addresses computational cost of time-domain electromagnetic simulations
• Focuses on scalability for transient and nonlinear behaviors

Innovation

• Tree-cotree-based tearing and interconnecting method
• IETI-DP solver for eddy current problems
• Time-domain simulation with improved scalability