PARALLEL ALGORITHMS FOR FLUID-STRUCTURE INTERACTION PROBLEMS IN HAEMODYNAMICS
PARALLEL ALGORITHMS FOR FLUID-STRUCTURE INTERACTION PROBLEMS IN HAEMODYNAMICS
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DOI：
10.1137/090772836
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发表时间：
2011-01-01
影响因子：
3.1
通讯作者：
Quarteroni, Alfio
中科院分区：
文献类型：
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作者：
Crosetto, Paolo;Deparis, Simone;Quarteroni, Alfio
在过去的几十年里，大多数应用程序所需的不断增加的计算负载和影响科学计算的硬件性能的限制促进了并行软件和体系结构的发展。在血流动力学应用的流固耦合（FSI）中，并行化和可扩展性是关键问题。Formaggia， A. Quarteroni和A. Veneziani编。，心血管数学：循环系统的建模与仿真，建模、仿真与应用1，bbb，米兰，2009])。在本文中，我们引入了一类利用线性系统的块结构得到的FSI问题的并行预调节器。我们强调了将该方法推广到具有块结构的一般线性系统的可能性，然后根据预条件对角块的条件给出了预条件系统条件数的一个界，最后证明了所设计的预条件的构造和评价是模块化的。在粗糙网格和精细网格的基准三维（3D）几何图形以及两种生理主动脉几何图形上对预调节器进行了测试。仿真结果表明，所引入的块预调节器具有一定的优势，并证实了我们的理论结果。
The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In fluid-structure interaction (FSI) for haemodynamic applications, parallelization and scalability are key issues (see [L. Formaggia, A. Quarteroni, and A. Veneziani, eds., Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, Modeling, Simulation and Applications 1, Springer, Milan, 2009]). In this work we introduce a class of parallel preconditioners for the FSI problem obtained by exploiting the block-structure of the linear system. We stress the possibility of extending the approach to a general linear system with a block-structure, then we provide a bound in the condition number of the preconditioned system in terms of the conditioning of the preconditioned diagonal blocks, and finally we show that the construction and evaluation of the devised preconditioner is modular. The preconditioners are tested on a benchmark three-dimensional (3D) geometry discretized in both a coarse and a fine mesh, as well as on two physiological aorta geometries. The simulations that we have performed show an advantage in using the block preconditioners introduced and confirm our theoretical results.