TOWARD AN EFFICIENT PARALLEL IN TIME METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS
TOWARD AN EFFICIENT PARALLEL IN TIME METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS
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DOI：
10.2140/camcos.2012.7.105
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发表时间：
2012-01-01
影响因子：
2.1
通讯作者：
Minion, Michael L.
中科院分区：
文献类型：
--
作者：
Emmett, Matthew;Minion, Michael L.
提出了一种在时间方向上实现偏微分方程数值方法并行化的新方法。该方法是迭代的，每次迭代由延迟校正扫描交替进行精细和粗时空离散。粗网格的问题，制定使用时空模拟的全近似计划流行的多重网格方法的非线性方程。当前的方法旨在为空间维度已经饱和的PDE模拟提供额外的并行化途径。在一个，两个和三个空间维度上的偏微分方程的数值结果和时间证明了该方法在时间方向上提供有效的并行化的潜力。
A new method for the parallelization of numerical methods for partial differential equations (PDEs) in the temporal direction is presented. The method is iterative with each iteration consisting of deferred correction sweeps performed alternately on fine and coarse space-time discretizations. The coarse grid problems are formulated using a space-time analog of the full approximation scheme popular in multigrid methods for nonlinear equations. The current approach is intended to provide an additional avenue for parallelization for PDE simulations that are already saturated in the spatial dimensions. Numerical results and timings on PDEs in one, two, and three space dimensions demonstrate the potential for the approach to provide efficient parallelization in the temporal direction.