In this work, we consider large-scale finite element modeling on voxel grids. We are targeting the IBM Blue Gene/P computer, which features a 3D torus interconnect. Our previous parallelization approach was to divide the domain in one spatial direction only, which lead to limited parallelism. Here, we extend it to all three spatial directions in order to match the interconnect topology. As a sample problem, we consider the simulation of the thermal and electrical processes, involved in the radio-frequency (RF) ablation procedure. RF ablation is a low invasive technique for the treatment of hepatic tumors, utilizing AC current to destroy the tumor cells by heating. A 3D voxel approach is used for finite element method (FEM) approximation of the involved partial differential equations. After the space discretization, the backward Euler scheme is used for the time stepping. We study the impact of the domain partitioning on the performance of a parallel preconditioned conjugate gradient (PCG) solver for the arising large linear systems. As a preconditioner, we use BoomerAMG - a parallel algebraic multigrid implementation from the package Hypre, developed in LLNL, Livermore. The implementation is tested on the IBM Blue Gene/P massively parallel computer.
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机译：在这项工作中，我们考虑在体素网格上进行大规模有限元建模。我们的目标是具有3D圆环互连功能的IBM Blue Gene / P计算机。我们以前的并行化方法是仅在一个空间方向上划分域，这导致有限的并行性。在这里，我们将其扩展到所有三个空间方向，以匹配互连拓扑。作为一个样本问题，我们考虑了射频和消融过程中涉及的热和电过程的仿真。射频消融是一种用于治疗肝肿瘤的低侵入性技术，它利用交流电通过加热破坏肿瘤细胞。 3D体素方法用于所涉及的偏微分方程的有限元方法（FEM）逼近。在空间离散化之后，将后向欧拉方案用于时间步进。我们研究了域划分对出现的大型线性系统的并行预条件共轭梯度（PCG）求解器性能的影响。作为先决条件，我们使用BoomerAMG-来自Livermore LLNL开发的Hypre软件包中的并行代数多重网格实现。该实现已在IBM Blue Gene / P大规模并行计算机上进行了测试。
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