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arXiv · 2009.01596

A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements

Efthymios N. Karatzas·Gianluigi Rozza
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Abstract

In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We manage to tackle the instability issues of such methods whenever strong nonlinearities appear and to utilize their flexibility of the fixed background geometry -- and mesh -- characteristic, through which, one can avoid e.g. in parametrized geometries the remeshing on the full order level, as well as, transformations to reference geometries on the reduced level. As a final goal, we manage to find an efficient global, concerning the geometrical manifold, and independent of geometrical changes, reduced order basis. The POD-Galerkin approach exhibits its strength even with pseudo-random discontinuous initial data verified by numerical experiments.

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Efthymios N. Karatzas, Gianluigi Rozza. 2021-08-09. A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements. https://arxiv.org/abs/2009.01596

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