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**1 - 1**of**1**### PROPER ORTHOGONAL DECOMPOSITION FOR NONLINEAR RADIATIVE HEAT TRANSFER PROBLEMS

"... Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques fo ..."

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Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques for such nonlin-ear multiphysical systems. The paper focuses on Proper Orthog-onal Decomposition (POD), a multivariate statistical method that obtains a compact representation of a data set by reducing a large number of interdependent variables to a much smaller number of uncorrelated variables. A fully coupled, thermomechanical model consisting of a multilayered, cantilever beam is described and analysed. This linear benchmark is then extended by adding nonlinear radiative heat exchanges between the beam and an enclosing box. The ra-diative view factors, present in the equations governing the heat fluxes between beam and box elements, are obtained with a ray-tracing method. A reduction procedure is proposed for this fully coupled non-linear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic ap-proach incorporating a scaling factor to the equations, and a partitioned approach that treats the individual physical modes ∗Address all correspondence to this author. separately. The paper builds on previous work presented previ-ously by the authors. The results are given for the RMS error between either approach and the original, full solution.