Giada Lorenzo, Giacometti Achille, Rossi Maurice
International School for Advanced Studies (SISSA) and INFM Unità di Trieste, Via Beirut 2-4, Trieste I-34014, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):036134. doi: 10.1103/PhysRevE.65.036134. Epub 2002 Mar 5.
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudospectral approximation of the nonlinear term. The method is tested in (1+1) and (2+1) dimensions, where it is shown to reproduce the current most reliable estimates of the critical exponents based on restricted solid-on-solid simulations. In particular, it allows the computations of various correlation and structure functions with high degree of numerical accuracy. Some deficiencies that are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.
我们讨论了一种用于求解一般空间维度下连续 Kardar-Parisi-Zhang 方程的数值方案。它基于连续方程的动量空间离散化以及非线性项的拟谱近似。该方法在（1 + 1）维和（2 + 1）维中进行了测试，结果表明它能够重现基于受限固-固模拟得出的当前最可靠的临界指数估计值。特别是，它能够以高精度数值计算各种关联函数和结构函数。指出了所有先前使用的有限差分方案共有的一些缺陷，并讨论了本方法在这方面的实用性。
