Volume 55, pp. 187-212, 2022.

Hierarchical model reduction driven by a proper orthogonal decomposition for parametrized advection-diffusion-reaction problems

Massimiliano Lupo Pasini and Simona Perotto


This work combines the Hierarchical Model (HiMod) reduction technique with a standard Proper Orthogonal Decomposition (POD) to solve parametrized partial differential equations for the modeling of advection-diffusion-reaction phenomena in elongated domains (e.g., pipes). This combination leads to what we define as HiPOD model reduction, which merges the reliability of HiMod reduction with the computational efficiency of POD. Two HiPOD techniques are presented and assessed by an extensive numerical verification.

Full Text (PDF) [4.9 MB], BibTeX

Key words

hierarchical model reduction, proper orthogonal decomposition, parametric partial differential equations, finite elements, spectral methods

AMS subject classifications

65N30, 65N35, 65T40

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