论文标题
对心脏力学的可扩展多层预处理的比较研究
A comparative study of scalable multilevel preconditioners for cardiac mechanics
论文作者
论文摘要
在这项工作中，我们在结构化和非结构化有限元网格上，通过约束（BDDC）（BDDC）（BDDC）（BDDC）的平衡域分解（BDDC）（AMG）预处理器之间进行了性能比较。心肌的机械行为可以通过三维有限弹性的方程来描述，这些弹性由空间中的有限元素离散，并产生大型非线性代数系统的解决方案。牛顿 - 克里洛夫方法解决了这个问题，其中jacobian线性系统的解决方案由BDDC/AMG预处理加速。我们彻底探讨了BDDC预处理的主要参数，以使比较公平。我们关注：对于BDDC算法的局部和粗糙问题，不同直接求解器的性能； BDDC原始自由度的不同选择的影响；以及有限元程度的影响。可伸缩性测试是在最多1024个处理器的Linux簇上进行的，我们以对现实机电模拟的性能研究结论。
In this work, we provide a performance comparison between the Balancing Domain Decomposition by Constraints (BDDC) and the Algebraic Multigrid (AMG) preconditioners for cardiac mechanics on both structured and unstructured finite element meshes. The mechanical behavior of myocardium can be described by the equations of three-dimensional finite elasticity, which are discretized by finite elements in space and yield the solution of a large scale nonlinear algebraic system. This problem is solved by a Newton-Krylov method, where the solution of the Jacobian linear system is accelerated by BDDC/AMG preconditioners. We thoroughly explore the main parameters of the BDDC preconditioner in order to make the comparison fair. We focus on: the performance of different direct solvers for the local and coarse problems of the BDDC algorithm; the impact of the different choices of BDDC primal degrees of freedom; and the influence of the finite element degree. Scalability tests are performed on Linux clusters up to 1024 processors, and we conclude with a performance study on a realistic electromechanical simulation.
