A scalable elliptic solver with task-based parallelism for the SpECTRE numerical relativity code
A scalable elliptic solver with task-based parallelism for the SpECTRE numerical relativity code
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DOI：
10.1103/physrevd.105.084027
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发表时间：
2021-11
影响因子：
5
通讯作者：
Nils L. Vu;Harald Pfeiffer;G. Bonilla;N. Deppe;F. H'ebert;Lawrence E. Kidder;G. Lovelace;Jordan Moxon;M. Scheel;S. Teukolsky;William Throwe;Nikolas A. Wittek;T. Włodarczyk
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文献类型：
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作者：
Nils L. Vu;Harald Pfeiffer;G. Bonilla;N. Deppe;F. H'ebert;Lawrence E. Kidder;G. Lovelace;Jordan Moxon;M. Scheel;S. Teukolsky;William Throwe;Nikolas A. Wittek;T. Włodarczyk
对于数值相对论中的许多问题，例如黑洞和中子星合并的每次模拟的初始数据，都必须数值求解椭圆型偏微分方程组。现有的椭圆求解器在高分辨率和涉及物质的情况下可能需要数天时间来求解这些问题，因为它们要么很难并行化，要么需要大量的计算资源。在这里，我们提出了一个新的线性和非线性椭圆问题的求解器，它被设计成随分辨率缩放并在计算集群上并行化。为了实现这一点，我们使用了不连续的Galerkin离散化，迭代的多重网格-Schwarz预条件牛顿-Krylov算法，以及基于任务的并行范例。为了加快椭圆求解器的收敛速度，我们开发了新的子域预条件技术。我们fi发现，我们的多重网格-Schwarz预条件椭圆解实现了与分辨率无关的迭代计数，并且我们的基于任务的并行程序将200多万个自由度扩展到至少数千个核心。我们的新代码解决了一个经典的二进制黑洞初始数据问题，当只分发到八个内核时，速度比光谱代码规范快，而且在更多内核上的时间要短得多。它可以在下一代SPECTE数值相对论代码中公开访问。我们的结果为数值相对论中及以后的高度并行的椭圆解铺平了道路。
Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple days to solve these problems at high resolution and when matter is involved, because they are either hard to parallelize or require a large amount of computational resources. Here we present a new solver for linear and nonlinear elliptic problems that is designed to scale with resolution and to parallelize on computing clusters. To achieve this we employ a discontinuous Galerkin discretization, an iterative multigrid-Schwarz preconditioned Newton-Krylov algorithm, and a task-based parallelism paradigm. To accelerate convergence of the elliptic solver we have developed novel subdomain-preconditioning techniques. We find that our multigrid-Schwarz preconditioned elliptic solves achieve iteration counts that are independent of resolution, and our task-based parallel programs scale over 200 million degrees of freedom to at least a few thousand cores. Our new code solves a classic initial data problem for binary black holes faster than the spectral code SpEC when distributed to only eight cores, and in a fraction of the time on more cores. It is publicly accessible in the next-generation SpECTRE numerical relativity code. Our results pave the way for highly parallel elliptic solves in numerical relativity and beyond.