摘要翻译:
本文比较了有限差分格式和伪谱方法在模拟表面生长的随机偏微分方程数值积分中的应用。我们在1+1维中研究了Kardar、Parisi和Zhang模型(KPZ)和Lai、Das Sarma和Villain模型(LDV)。在给定的时间步长下,伪谱方法对两种模型都是最稳定的。这意味着,对于伪谱方法,我们可以跟踪给定系统的时间演化的时间更长。此外,对于KPZ模型,伪谱格式比有限差分方法得到的结果更接近于连续介质模型的预测。另一方面,在进行伪谱积分时,不存在用有限差分方法对LDV模型所出现的一些数值不稳定性。这些数值不稳定性引起了数值模拟中观察到的近似多尺度。在伪谱方法中,没有多尺度与连续体模型一致。
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英文标题:
《Pseudospectral versus finite-differences schemes in the numerical
integration of stochastic models of surface growth》
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作者:
Rafael Gallego (Univ de Oviedo), Mario Castro (Universidad Pontificia
Comillas), and Juan M. L\'opez (Instituto de Fisica de Cantabria)
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最新提交年份:
2007
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分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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英文摘要:
We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi and Zhang model (KPZ) and the Lai, Das Sarma and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in the numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.
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PDF链接:
https://arxiv.org/pdf/707.2469