面向对象的偏微分方程并行有限元计算方法的设计与实现
An object oriented parallel finite element scheme for computations of PDEs: Design and implementation
摘要：
提出了基于面向对象概念的并行有限元算法。此外，所提出的数据结构的设计和实现被用于实现并行几何多重网格方法。在所提出的并行方案中，ParFEMapper和ParFEMapper是数据结构的关键组件。这些类是基于所使用的有限元类型（连续或非连续或不连续）构建的。建议的求解器相比，与开源的直接求解器，MUMPS和PasTiX。此外，并行多重网格求解器的性能进行了分析高达1080处理器。求解器显示了一个非常好的加速到960个处理器和问题的大小必须增加，以保持良好的加速时，处理器的数量进一步增加。因此，并行求解器能够在大规模并行超级计算机上处理大规模问题。所提出的并行有限元算法和多重网格求解器在我们的内部软件包ParMooN中实现。
英文摘要：
Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and the ParFECommunicator are the key components of the data structure in the proposed parallel scheme. These classes are constructed based on the type of finite elements (continuous or nonconforming or discontinuous) used. The proposed solver is compared with the open source direct solvers, MUMPS and PasTiX. Further, the performance of the parallel multigrid solver is analyzed up to 1080 processors. The solver shows a very good speedup up to 960 processors and the problem size has to be increased in order to maintain the good speedup when the number of processors are increased further. As a result, the parallel solver is able to handle large scale problems on massively parallel supercomputers. The proposed parallel finite element algorithms and multigrid solver are implemented in our in-house package ParMooN.
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