分层紧缩共轭梯度
Hierarchically deflated conjugate gradient
摘要：
提出了一种求解五维手征费米子方程的多层算法，包括畴壁和Mobius费米子。该算法对红-黑预处理厄米特算子进行运算，直接加速法方程组上的共轭梯度。该矩阵的粗网格表示是下一个到最近的邻居，并引入了多个算法的进步，这有助于最大限度地减少粗网格的开销。粗网格的处理是纯四维的，并且粗网格操作的大部分是最近邻的。因此，大多数粗网格操作的内在成本与威尔逊情况下的成本相当。我们还记录了该算法在BAGEL/Bfm软件包中的实现，并报告了该算法在IBM BlueGene/Q硬件上的物理点上模拟的实测性能增益。
英文摘要：
We present a multi-level algorithm for the solution of five dimensional chiral fermion formulations, including domain wall and Mobius Fermions. The algorithm operates on the red-black preconditioned Hermitian operator, and directly accelerates conjugate gradients on the normal equations. The coarse grid representation of this matrix is next-to-next-to-next-to-nearest neighbour and multiple algorithmic advances are introduced, which help minimise the overhead of the coarse grid. The treatment of the coarse grids is purely four dimensional, and the bulk of the coarse grid operations are nearest neighbour. The intrinsic cost of most of the coarse grid operations is therefore comparable to those for the Wilson case. We also document the implementation of this algorithm in the BAGEL/Bfm software package and report on the measured performance gains the algorithm brings to simulations at the physical point on IBM BlueGene/Q hardware.
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