Self-consistent field theory simulations of polymers on arbitrary domains
| Autor: | Glenn H. Fredrickson, Frederic Gibou, Nabil Laachi, Gaddiel Ouaknin, Kris T. Delaney |
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| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis Degrees of freedom (statistics) Finite difference Boundary (topology) 010103 numerical & computational mathematics Mixed boundary condition 01 natural sciences Domain (mathematical analysis) Computer Science Applications 010101 applied mathematics Computational Mathematics Boundary conditions in CFD Modeling and Simulation Neumann boundary condition Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Journal of Computational Physics. 327:168-185 |
| ISSN: | 0021-9991 |
| Popis: | We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refine the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables. |
| Databáze: | OpenAIRE |
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