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首页> 外文期刊>Journal of Computational Physics >Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients
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Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

机译：基于高级算子分裂的半隐式谱方法求解变系数二元相场晶体方程

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摘要

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. B 75 (2007) 064107] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed. Crown Copyright (c) 2008 Published by Elsevier Inc. All rights reserved.
机译：我们提出一种有效的方法来数值求解Elder等人提出的二元相场晶体模型的耗散动力学方程。 [K.R. Elder，M。Katakowski，M。Haataja，M.Grant，物理学。 Rev.B 75（2007）064107]的特征在于可变系数。使用算子拆分方法，该问题已分解为子问题，可以更有效地解决该问题。非平凡分裂与频谱半隐式解的组合导致对角矩阵形式的代数方程组。已经对该方法进行了广泛的测试，以找到与时间积分，空间离散化和分割相关的误差之间的最佳平衡。我们表明，相对于传统的显式有限差分方案，我们的方法将计算速度提高了几个数量级，而每个时间步的逐点隐式解决方案的成本仍然较低。我们还表明，由于其数值耗散，有限差分在准确性方面无法与频谱差分竞争。此外，我们证明了我们的方法可以有效地并行化用于分布式存储系统，在分布式存储系统中可以观察到随CPU数量的出色可伸缩性。 Crown版权所有（c）2008，由Elsevier Inc.发行。保留所有权利。

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