Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson-Dirac Operator
Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson-Dirac Operator
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DOI：
10.1137/130919507
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发表时间：
2013-03
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影响因子：
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通讯作者：
A. Frommer;K. Kahl;S. Krieg;B. Leder;M. Rottmann
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文献类型：
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作者：
A. Frommer;K. Kahl;S. Krieg;B. Leder;M. Rottmann
在格子量子色动力学(QCD)计算中，需要花费大量的工作来求解离散形式的狄拉克方程。传统的Krylov解算器显示，对于较大的系统规模和物理上感兴趣的参数区域，速度会变慢。我们提出了一种区域分解自适应代数多重网格法作为预条件来求解Dirac方程的“三叶草改进”的Wilson离散化。该方法结合并改进了以往在格子QCD中分别使用的区域分解和自适应代数多重网格两种方法。我们用并行产品代码实现进行的大量数值测试表明，与传统的Krylov子空间方法、区域分解方法和其他分层方法相比，对于真实的系统大小，可以获得相当大的加速比。
In lattice quantum chromodynamics (QCD) computations a substantial amount of work is spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers show critical slowing down for large system sizes and physically interesting parameter regions. We present a domain decomposition adaptive algebraic multigrid method used as a preconditioner to solve the “clover improved” Wilson discretization of the Dirac equation. This approach combines and improves two approaches, namely domain decomposition and adaptive algebraic multigrid, that have been used separately in lattice QCD before. We show in extensive numerical tests conducted with a parallel production code implementation that considerable speedup can be achieved compared to conventional Krylov subspace methods, domain decomposition methods, and other hierarchical approaches for realistic system sizes.