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Fast and Stable Schemes for Phase Fields Models

Matthieu Brachet 1 Jean-Paul Chehab 2 
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to semi-implicit schemes for which the linear part is simplified using sparse pre-conditioners. The new methods allow to significant obtain a gain of CPU time. The numerical illustrations we give concern applications on pattern dynamics and on image processing (inpainting, segmentation) in two and three dimension cases.
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Matthieu Brachet, Jean-Paul Chehab. Fast and Stable Schemes for Phase Fields Models. Computers & Mathematics with Applications, Elsevier, 2020, 80 (6), pp.1683-1713. ⟨10.1016/j.camwa.2020.07.015⟩. ⟨hal-02301006v2⟩

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