【源码】Equation-Free工具箱：使用微型仿真器高效地执行宏尺度系统级任务和模拟
这个“无方程工具箱”使计算机辅助分析复杂的多尺度系统成为可能。
This ‘equation-free toolbox’ empowers the computer-assisted analysis of complex, multiscale systems.
它的目的是使您能够使用微观模拟器来执行系统级任务和分析，因为微型模拟通常是对系统的最佳可用描述。
Its aim is to enable you to use microscopic simulators to perform system level tasks and analysis, because microscale simulations are often the best available description of a system.
这种方法绕过了宏观演化方程的推导，只计算微尺度模拟器的短突发，而且通常只计算空间域的小块区域。
The methodology bypasses the derivation of macroscopic evolution equations by computing only short bursts of of the microscale simulator, and often only computing on small patches of the spatial domain.
这套函数允许用户开始在自己的应用程序中实现这些方法。
This suite of functions empowers users to start implementing such methods in their own applications.
为了快速入门，请改编其中一个示例。
For a quick start, adapt one of the included examples.
许多主函数在一开始就包括它们使用的示例代码，即，在不带任何参数的情况下调用函数时执行的代码。
Many of the main functions include, at their beginning, example code of their use—code which is executed when the function is invoked without any arguments.
为了随着时间的推移投射式地集成多尺度、慢-快odes系统，可以使用PIRK2()或PIRK4()来获得更高阶的精度：在PIRK2.m的开头修改Michaelis–Menten示例
- To projectively integrate over time a multiscale, slow-fast, system of odes you could use PIRK2(), or PIRK4() for higher-order accuracy: adapt the Michaelis–Menten example at the beginning of PIRK2.m
您可以使用模拟的前向突发，以便在时间上向后模拟慢动态，如在egPIMM.m程序中
- You may use forward bursts of simulation in order to simulate the slow dynamics backward in time, as in egPIMM.m
为了只解决投影积分中的慢动力学问题，在PIG.m开头采用了奇异摄动ode例子，使用了提升函数和约束函数
- To only resolve the slow dynamics in the projective integration, use lifting and restriction functions by adapting the singular perturbation ode example at the beginning of PIG.m
在时空系统中，考虑一个在大空间域上演化的系统，而你所拥有的只是一个微尺度的代码。
In space-time systems, consider an evolving system over a large spatial domains when all you have is a microscale code.
为了有效地模拟大区域，我们可以在适当耦合的小区域内进行模拟。
To efficiently simulate over the large domain, one can simulate in just small patches of the domain, appropriately coupled.
在1D中，将configPatches1.m开头的代码改编为Burger的pde，或者在waterWaveExample.m中调整一维波动方程的交错片段
- In 1D adapt the code at the beginning of configPatches1.m for Burgers’ pde, or the staggered patches of 1D water wave equations in waterWaveExample.m
在2D中，将configPatches2.m开头的代码用于非线性扩散，或者将wave2D.m的二维波动方程的规则片段进行修改
- in 2D adapt the code at the beginning of configPatches2.m for nonlinear diffusion, or the regular patches of the 2D wave equation of wave2D.m
以上两种方法适用于在微尺度上具有平滑空间结构的系统：当微尺度具有已知周期的“粗糙”时（到目前为止，仅在1D中），可以采用示例：HomogenisationExample.m
- The above two are for systems that have smooth spatial structures on the microscale: when the microscale is ‘rough’ with a known period (so far only in 1D), then adapt the example of HomogenisationExample.m
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