Advancing Industrial Finite Element Software through Model Order Reduction for Nonlinear Transient Thermal Problems

  • Malleval, Pierre-Eliot (Ecole normale Supéreure Paris-Saclay)
  • Scanff, Ronan (Siemens)
  • Néron, David (Ecole normale Supéreure Paris-Saclay)

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Over the past two decades, non-intrusive techniques have been widely employed to construct reduced-order models for nonlinear structural problems in industrial contexts. These approaches predominantly rely on a posteriori strategies, which typically require solutions obtained from computationally demanding full-order models. In contrast, a priori methods that do not depend on full-order simulations are attractive, as they significantly reduce the computational cost at the outset. However, the intrusive nature of the algorithms underlying such approaches has hindered their adoption within commercial finite element software. For these methods to achieve widespread industrial use, they must be integrated into certified products through robust and reliable implementations. In this context, the present work pursues this objective by extending a weakly intrusive implementation of the LATIN-PGD method [1] within commercial finite element software to nonlinear transient thermal problems. The originality of the proposed approach lies in its broad applicability: the PGD framework is not restricted to specific applications but is capable of handling arbitrary nonlinearities, a wide range of element types, diverse boundary conditions, and other intrinsic features of industrial finite element platforms. This development leads to a comprehensive industrial nonlinear solver incorporating a priori model order reduction, enabling the efficient treatment of parametrized problems [2,3].