A Reduced Order Model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements

09/03/2020
by   Efthymios N. Karatzas, et al.
0

In the present work, we investigate for the first time with a cut finite element method, a parameterized 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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset