Numerical methods for the QCD overlap operator: III. Nested iterations
Numerical methods for the QCD overlap operator: III. Nested iterations
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QCD重叠算子的数值方法：III．
DOI：
10.1016/j.cpc.2004.10.005
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
K. Schafer
中科院分区：
文献类型：
--
作者：
N. Cundy;A. Frommer;J. V. D. Eshof;T. Lippert;Stephan Krieg;K. Schafer
晶格量子色动力学中手性费米子的数值和计算方面要求极高。在重叠框架中，费米子传播器的计算导致嵌套迭代，其中外迭代的每一步中的矩阵向量乘法必须通过内迭代来完成；后者近似厄米威尔逊费米子矩阵的符号函数与向量的乘积。在本文中，我们研究了这种嵌套范式的各个方面。我们研究了几种用作传播器计算和混合蒙特卡罗方案的外部迭代的 Krylov 子空间方法。我们建立了内部迭代准确性的标准，允许为整体计算保留先验给定的精度。事实证明，随着外部迭代的进行，符号函数的精度可以放宽。此外，我们考虑预处理策略，其中预处理器建立在符号函数的不准确近似之上。正如我们的数值实验所示，松弛与预处理相结合可以节省高达 4 倍的计算量。我们还讨论了将平方重叠算子投影到一个手性扇区的可能性。
The numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector multiplications in each step of an outer iteration have to be accomplished by an inner iteration; the latter approximates the product of the sign function of the hermitian Wilson fermion matrix with a vector. In this paper we investigate aspects of this nested paradigm. We examine several Krylov subspace methods to be used as an outer iteration for both propagator computations and the Hybrid Monte-Carlo scheme. We establish criteria on the accuracy of the inner iteration which allow to preserve an a priori given precision for the overall computation. It will turn out that the accuracy of the sign function can be relaxed as the outer iteration proceeds. Furthermore, we consider preconditioning strategies, where the preconditioner is built upon an inaccurate approximation to the sign function. Relaxation combined with preconditioning allows for considerable savings in computational efforts up to a factor of 4 as our numerical experiments illustrate. We also discuss the possibility of projecting the squared overlap operator into one chiral sector.