用COLA简便十步求解大尺度结构
Solving Large Scale Structure in Ten Easy Steps with COLA
摘要：
本文提出了一种求解大尺度结构的N体方法--COmoving Lagrangian Acceleration（COLA）方法，该方法是在观测者沿拉格朗日摄动理论（LPT）计算的轨迹运动的框架内求解的。与标准的N体方法不同，COLA方法可以直接在小尺度上牺牲精度，以获得计算速度，而不会牺牲大尺度上的精度。这是特别有用的廉价产生大合奏的准确模拟晕目录需要研究星系团和弱透镜，因为这些目录是必不可少的进行详细的误差分析，为正在进行的和未来的调查LSS。作为一个例子，我们在一个大小为100 Mpc/h的盒子上运行了一个基于COLA的N体代码，其中粒子的质量为~5*10^9Msolar/h。仅用10个时间步长运行代码就足以获得晕统计的准确描述，直到晕质量至少为10^11兆太阳能/小时。与使用LPT获得的模拟相比，这只是在适度的速度损失下。一个标准的详细N体运行比我们基于COLA的代码慢几个数量级。我们使用COLA获得的加速是由于我们使用LPT精确计算大尺度动力学，同时让N体代码解决小尺度问题，而不需要它精确捕获晕的内部动力学。在没有COLA方法的情况下，在晕轮统计中实现类似水平的准确度需要比采用COLA时多至少3倍的时间步长。
英文摘要：
We present the COmoving Lagrangian Acceleration (COLA) method: an N-body method for solving for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). Unlike standard N-body methods, the COLA method can straightforwardly trade accuracy at small-scales in order to gain computational speed without sacrificing accuracy at large scales. This is especially useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing, as those catalogs are essential for performing detailed error analysis for ongoing and future surveys of LSS. As an illustration, we ran a COLA-based N-body code on a box of size 100Mpc/h with particles of mass ~5*10^9Msolar/h. Running the code with only 10 timesteps was sufficient to obtain an accurate description of halo statistics down to halo masses of at least 10^11Msolar/h. This is only at a modest speed penalty when compared to mocks obtained with LPT. A standard detailed N-body run is orders of magnitude slower than our COLA-based code. The speed-up we obtain with COLA is due to the fact that we calculate the large-scale dynamics exactly using LPT, while letting the N-body code solve for the small scales, without requiring it to capture exactly the internal dynamics of halos. Achieving a similar level of accuracy in halo statistics without the COLA method requires at least 3 times more timesteps than when COLA is employed.
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