Efficient assembly for high order unstructured FEM meshes
Efficient assembly for high order unstructured FEM meshes
复制标题
高阶非结构化有限元网格的高效组装
DOI：
10.1109/fpl.2015.7293749
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
W. Luk
中科院分区：
文献类型：
--
作者：
P. Burovskiy;Paul Grigoras;S. Sherwin;W. Luk
有限元法（FEM）是一种常用的数值技术，用于求解复杂区域几何形状上的偏微分方程（PDE）。大型非结构化有限元网格用于表示计算域，这使得有限元方法到FPGA的有效映射特别具有挑战性。本文的重点是装配映射，有限元的核心，它导致了稀疏和非结构化的性质的问题。我们将FEM向量汇编映射转化为数据访问调度，直接在FPGA上执行向量汇编，作为硬件流水线的一部分。我们展示了如何有效地划分成密集和稀疏的子问题映射到FPGA的问题。在单个FPGA上实现的所提出的方法可以优于在两个Xeon E5-2640处理器上运行的高度优化的FEM软件。
The Finite Element Method (FEM) is a common numerical technique used for solving Partial Differential Equations (PDEs) on complex domain geometries. Large and unstructured FEM meshes are used to represent the computation domains which makes an efficient mapping of the Finite Element Method onto FPGAs particularly challenging. The focus of this paper is on assembly mapping, a key kernel of FEM, which induces the sparse and unstructured nature of the problem. We translate FEM vector assembly mapping into data access scheduling to perform vector assembly directly on the FPGA, as part of the hardware pipeline. We show how to efficiently partition the problem into dense and sparse sub-problems which map well onto FPGAs. The proposed approach, implemented on a single FPGA could outperform highly optimised FEM software running on two Xeon E5-2640 processors.