The paper presents a model order reduction (MOR) approach for the real-time estimation of structural deformations in large-scale conductive structures, such as the vacuum vessel (VV) of thermonuclear fusion devices, due to electromagnetic (EM) forces.
The key highlights are:
The EM problem is solved using either the Finite Element Method (FEM) or the Volume Integral Equation (VIE) method, with the latter accelerated by hierarchical matrices (H-matrices) to efficiently handle the fully populated matrices.
The structural problem is solved using the FEM, with the EM loads serving as the forcing term.
Proper Orthogonal Decomposition (POD) is employed to develop Reduced Order Models (ROMs) for both the EM and structural problems, minimizing the computational expense associated with coupling the two physics.
The time-dependent analysis is resolved efficiently by solving the linear DAE system representing the EM-ROM, and then computing the forcing term for the Structural-ROM.
Numerical results demonstrate the accuracy of the approach and its compatibility with real-time execution, even for realistic 3D VV models of thermonuclear fusion devices like ITER, in contrast to the prohibitive computational cost of the full-order models.
The proposed methodology enables the construction of a Digital Twin of the machine, serving as a virtual sensor for real-time monitoring of critical structural displacements, which is essential for the safe operation of current and future thermonuclear fusion devices.
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