A semi-implicit spectral method for stochastic nonlocal phase-field models

43. Tina Hartley, Thomas Wanner:
    A semi-implicit spectral method for stochastic nonlocal phase-field models
    Discrete and Continuous Dynamical Systems, Series A 25(2), pp. 399-429, 2009.

Abstract

The classical phase-field model has been introduced as a model for non-isothermal phase separation processes in materials. In order to overcome some of the model’s shortcomings, a variety of extensions have recently been proposed which include nonlocal interactions as well as stochastic noise terms. In this paper, we study these extensions from a functional-analytic and numerical point of view. More precisely, we present a functional-analytic framework for establishing existence, uniqueness, and qualitative dynamical results, and then propose a spectral method for solving stochastic nonlocal phase-field models. In particular, we establish convergence properties of our method and study the effects of noise regularity and of the nonlocal interaction term on these convergence properties. Finally, numerical studies relating to the associated phase separation process are presented.

Links

The published version of the paper can be found at https://doi.org/10.3934/dcds.2009.25.399.

Bibtex

@article{hartley:wanner:09a,
   author = {Tina Hartley and Thomas Wanner},
   title = {A semi-implicit spectral method for stochastic nonlocal
            phase-field models},
   journal = {Discrete and Continuous Dynamical Systems, Series A},
   year = 2009,
   volume = 25,
   number = 2,
   pages = {399--429},
   doi = {10.3934/dcds.2009.25.399}
   }