Abstract
We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 834-844 |
| Number of pages | 11 |
| Journal | Procedia Computer Science |
| Volume | 80 |
| DOIs | |
| State | Published - Jun 2 2016 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: The work of MW, MS, MP, RS presented in this paper concerning the development of Cahn-Hilliard scheme has been supported by National Science Centre, Poland grant no. DEC-2012/07/B/ST6/01229. The visit of AC and his work concerning the PETIGA solver interface has been supported by National Science Centre, Poland grant no. DEC-2012/06/M/ST1/00363.