论文标题
非对角线线性部分的刚性系统的指数时间差异的高阶方案
High-Order Schemes of Exponential Time Differencing for Stiff Systems with Nondiagonal Linear Part
论文作者
论文摘要
指数时间差异方法是用于对凝结物理学，流体动力学，化学和生物物理学中计算挑战性问题进行高性能数值模拟的功率工具，在这种情况下，数学模型通常具有快速的振荡或衰减模式 - 换句话说，换句话说，是僵硬的系统。这些方法的实际实施是对方程式无线性部分的系统的实际实现，这是由于对非辅助线性运算符的指数的分析计算的不可行而加剧了。在这种情况下，不能通过分析计算指数时间差异方案的系数。我们建议一种方法，其中这些系数是通过辅助问题计算的。我们根据解决这些辅助问题的解决方案来重写高级Runge - KUTTA类型方案，并实际上检查了这些方法的准确性和计算性能，用于异质的Cahn--Hilliard方程，第六阶空间衍生方程式的模式在其他方程式中，在额外的保存法律和fokkkemiss和fokkkers-forecation and overration and fokkkemiss and of okkemiss and of okkerancip and-fornation-forecration-groughiard cahn-hilliard方程式和计算方程式形式。神经元网络。
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models often possess fast oscillating or decaying modes -- in other words, are stiff systems. Practical implementation of these methods for the systems with nondiagonal linear part of equations is exacerbated by infeasibility of an analytical calculation of the exponential of a nondiagonal linear operator; in this case, the coefficients of the exponential time differencing scheme cannot be calculated analytically. We suggest an approach, where these coefficients are numerically calculated with auxiliary problems. We rewrite the high-order Runge--Kutta type schemes in terms of the solutions to these auxiliary problems and practically examine the accuracy and computational performance of these methods for a heterogeneous Cahn--Hilliard equation, a sixth-order spatial derivative equation governing pattern formation in the presence of an additional conservation law, and a Fokker--Planck equation governing macroscopic dynamics of a network of neurons.
