Stabilized asynchronous fast adaptive composite multigrid using additive damping
Stabilized asynchronous fast adaptive composite multigrid using additive damping
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使用加性阻尼的稳定异步快速自适应复合多重网格
DOI：
10.1002/nla.2328
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发表时间：
2020
影响因子：
4.3
通讯作者：
Murray C
中科院分区：
文献类型：
--
作者：
Murray C
多重网格求解器在并行计算机上面临着多重挑战。两个基本的阅读如下：乘法求解器问题粗网格解决表现出低并发性和许多多重网格实现遭受昂贵的粗网格识别阶段加上自适应网格细化开销。我们提出了一个新的添加剂多重网格的空间树，即网格，因为它们是从八叉树和四叉树构建：这是一个添加剂的计划，即所有多重网格的分辨率水平同时更新。这确保了高并发级别，而网格级别之间的传输操作符仍然可以代数构造。加法方案的新颖之处在于通过每个顶点的每个网格级别的加法辅助阻尼参数来增强求解器，该参数又通过下一个较粗的级别来构造--这一想法利用了平滑聚合原理或AFACx背后的动机：每层，我们解决一个额外的方程，其目的是阻尼过于积极的解决方案更新每顶点，否则，与所有其他水平相结合，产生过度校正，最终产生振荡。这个附加方程也是加性构造的，也就是说，再一次与所有其他方程同时求解。这提高了稳定性，更接近乘法方案，而流水线技术帮助我们编写具有单点触摸语义的加法求解器，用于动态自适应网格。
Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an expensive coarse grid identification phase plus adaptive mesh refinement overhead. We propose a new additive multigrid variant for spacetrees, that is, meshes as they are constructed from octrees and quadtrees: It is an additive scheme, that is, all multigrid resolution levels are updated concurrently. This ensures a high concurrency level, while the transfer operators between the mesh levels can still be constructed algebraically. The novel flavor of the additive scheme is an augmentation of the solver with an additive, auxiliary damping parameter per grid level per vertex that is in turn constructed through the next coarser level—an idea which utilizes smoothed aggregation principles or the motivation behind AFACx: Per level, we solve an additional equation whose purpose is to damp too aggressive solution updates per vertex which would otherwise, in combination with all the other levels, yield an overcorrection and, eventually, oscillations. This additional equation is constructed additively as well, that is, is once more solved concurrently to all other equations. This yields improved stability, closer to what is seen with multiplicative schemes, while pipelining techniques help us to write down the additive solver with single‐touch semantics for dynamically adaptive meshes.
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在多处理器上求解偏微分方程的异步多级自适应方法：性能结果
影响因子：
1.4
作者：
S. McCormick;D. Quinlan
通讯作者：
D. Quinlan
非对称黑盒多重网格，粗化三倍
影响因子：
4.3
作者：
I. Yavneh;Marion Weinzierl
通讯作者：
Marion Weinzierl
边值问题的多重网格方法。
DOI：
--
发表时间：
1991
期刊：
影响因子：
--
作者：
W. Press;S. Teukolsky
通讯作者：
S. Teukolsky
影响因子：
4.3
作者：
J. Dendy;J. Moulton
通讯作者：
J. Moulton
DOI：
--
发表时间：
1990
期刊：
Attribute Grammars and their Applications
影响因子：
--
作者：
D. Knuth
通讯作者：
D. Knuth