In-Core LU-Decomposition of Symmetrical Dense MoM Matrix in WIPL-D Multi-GPU Solver

机译：WIPL-D多GPU解算器中对称密集MoM矩阵的核内LU分解

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Acceleration of in-core LU decomposition of symmetrical dense MoM matrices by using multiple GPUs in parallel is presented in this paper. Memory limitations of GPUs are overcome by using block LU decomposition, where the entire system matrix is stored in CPU RAM, while only processed blocks are stored in GPU VRAM. The presented algorithm for LU decomposition enables highly efficient utilization of an arbitrary number of GPUs. Comparison of performance of up to 4 GTX 680 GPUs and up to 4 GTX 1080 Ti GPUs is shown. Presented results show that a symmetrical dense MoM matrix with 100 000 complex unknowns in single precision can be LU decomposed in about 3.5 minutes, on a personal computer equipped with 4 GTX 1080 Ti GPUs.

机译：本文提出了通过并行使用多个GPU来加速对称密集MoM矩阵的核内LU分解的过程。通过使用块LU分解克服了GPU的内存限制，其中整个系统矩阵存储在CPU RAM中，而只有经过处理的块存储在GPU VRAM中。所提出的用于LU分解的算法能够高效利用任意数量的GPU。显示了多达4个GTX 680 GPU和多达4个GTX 1080 Ti GPU的性能比较。呈现的结果表明，在配备有4个GTX 1080 Ti GPU的个人计算机上，可以在大约3.5分钟的时间内对具有单精度10万个复杂未知数的对称密集MoM矩阵进行LU分解。

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来源
《2018 IEEE Indian Conference on Antennas and Propogation》|2018年|1-4|共4页
会议地点 Hyderabad(IN)
作者
Branko Lj. Mrdakovic; Milan M. Kostic; Dragan I. Olcan; Branko M. Kolundzija;
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作者单位

WIPL-D d.o.o., Gandijeva 7/32, Belgrade, 11073, Serbia;

WIPL-D d.o.o., Gandijeva 7/32, Belgrade, 11073, Serbia;

Department of Electrical Engineering, University of Belgrade, Bul. King Alexander 73, Belgrade, 11120, Serbia;

Department of Electrical Engineering, University of Belgrade, Bul. King Alexander 73, Belgrade, 11120, Serbia;

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原文格式 PDF
正文语种 eng
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关键词
Graphics processing units; Matrix decomposition; Acceleration; Symmetric matrices; Method of moments; Random access memory; Atmospheric modeling;

机译：图形处理单元矩阵分解加速度对称矩阵矩量法随机存取存储器大气建模;

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专利

1. Parallel MoM Using Higher-Order Basis Functions and PLAPACK In-Core and Out-of-Core Solvers for Challenging EM Simulations [J] . Yu Zhang, van de Geijn R.A., Taylor M.C., Antennas and Propagation Magazine, IEEE . 2009,第5期

机译：使用高阶基函数和PLAPACK内核内和内核外求解器进行并行MoM挑战性的EM仿真
2. MLFMA-MoM for Solving the Scattering of Densely Packed Plasmonic Nanoparticle Assemblies [J] . Solis D.M., Araujo M.G., Landesa L., Photonics Journal, IEEE . 2015,第3期

机译：MLFMA-MoM用于解决密集堆积的等离子纳米粒子组件的散射
3. Spectral Properties of the EFIE-MoM Matrix for Dense Meshes With Different Types of Bases [J] . Vipiana F., Pirinoli P., Vecchi G. IEEE Transactions on Antennas and Propagation . 2007,第11期

机译：EFIE-MoM矩阵对具有不同基类型的密集网格的光谱性质
4. In-Core LU-Decomposition of Symmetrical Dense MoM Matrix in WIPL-D Multi-GPU Solver [C] . Branko Lj. Mrdakovic, Milan M. Kostic, Dragan I. Olcan, IEEE Indian Conference on Antennas and Propogation . 2018

机译：WIPL-D多GPU求解器对称密度母矩阵的核心LU分解
5. Large-Scale Quasi-Newton Trust-Region Methods: High-Accuracy Solvers, Dense Initializations, and Extensions [D] . Brust, Johannes J. 2018

机译：大规模拟牛顿信任区域方法：高精度求解器，密集初始化和扩展
6. NMF-mGPU: non-negative matrix factorization on multi-GPU systems [O] . Edgardo Mejía-Roa, Daniel Tabas-Madrid, Javier Setoain, 2015

机译：NMF-mGPU：多GPU系统上的非负矩阵分解
7. Highly efficient parallel direct solver for solving dense complex matrix equations from method of moments [O] . Yan Chen, Zhongchao Lin, Yu Zhang, 2017

机译：用矩量法求解密集复矩阵方程的高效并行直接求解器
8. A Fortran Subroutine Requiring Only N(N+1)/2 Matrix Locations to Invert, Solve, and Find the Determinant of a Real Symmetric Matrix [R] . Mason, J. P. 1969

机译：Fortran子程序只需要N（N + 1）/ 2个矩阵位置来反转，求解和找到实对称矩阵的行列式

In-Core LU-Decomposition of Symmetrical Dense MoM Matrix in WIPL-D Multi-GPU Solver

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