Model order reduction of parametrized nonlinear reaction-diffusion systems

Abstract We present a model order reduction technique for parametrized nonlinear reaction–diffusion systems. In our approach we combine the reduced basis method – a computational framework for rapid evaluation of functional outputs associated with the solution of parametrized partial differential equations – with the empirical interpolation method – a tool to construct “affine” coefficient-function approximations of nonlinear parameter dependent functions. We develop an efficient offline–online computational procedure for the evaluation of the reduced basis approximation: in the offline stage, we generate the reduced basis space; in the online stage, given a new parameter value, we calculate the reduced basis output. The operation count for the online stage depends only on the dimension of the reduced order model and the parametric complexity of the problem. The method is thus ideally suited for the many-query or real-time contexts. We present numerical results for a non-isothermal reaction–diffusion model to confirm and test our approach.

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