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Application of FPGAs in acceleration of numerical solution of differential equations.

机译：FPGA在加速微分方程数值解中的应用。

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摘要

This thesis proposes a new application for Field Programmable Gate Array in the acceleration of the numerical solution of differential equations. By using the FPGA as a coprocessor that can be integrated with the system main processor, certain tasks that represent a computational bottleneck can be offloaded to the FPGA coprocessor and carried out more efficiently. More specific, the domain of differential equations considered in this thesis arises during the transient simulation of nonlinear circuits. The work in this thesis investigates the various computational tasks involved in the numerical solution of differential equations. A recent approach to solve differential equations numerically has been studied that requires the computation of high-order derivatives of circuit variables (e.g. node voltages, charges) with respect to a single parameter such as time. However, complex nonlinear devices, are typically characterized by complex nonlinear functions with mathematical expressions that render such computations on conventional computing platforms very time-consuming.;It is shown that this scheme has the potential of relieving the central processing unit in the conventional platforms from having to fetch the tree structure from the system memory and process it in computing the derivatives and will thus lead to significant acceleration.;This thesis demonstrates that using a computational platform with hardware-enabled accelerator can speed up the task of computing high-order derivatives by at least one-order-of-magnitude. The main idea of the thesis is based on using some recently derived formulas representing the high-order derivatives in terms of the lower-order ones to configure a Field Programmable Gate Arrays (FPGA) in a tree-like structure that represent the non-linear expression. The nodes of this tree will represent common non-linear terms such as exponential or logarithmic functions, which will programmed to propagate their own derivatives from the knowledge of their "children" nodes derivatives.
机译：本文提出了现场可编程门阵列在微分方程数值解加速中的新应用。通过将FPGA用作可以与系统主处理器集成的协处理器，可以将代表计算瓶颈的某些任务转移到FPGA协处理器上，并可以更高效地执行。更具体地说，本文所考虑的微分方程域出现在非线性电路的瞬态仿真过程中。本文的工作研究了微分方程数值解中涉及的各种计算任务。已经研究了一种新的数值求解微分方程的方法，该方法要求针对诸如时间的单个参数计算电路变量（例如，节点电压，电荷）的高阶导数。但是，复杂的非线性设备通常以具有数学表达式的复杂非线性函数为特征，这些复杂的非线性函数使常规计算平台上的此类计算非常耗时。;表明该方案具有缓解常规平台中的中央处理单元的潜力必须从系统内存中获取树结构并对其进行处理以计算导数，从而导致明显的加速。；本论文证明，使用具有硬件加速器的计算平台可以加快计算高阶导数的任务至少一个数量级。本文的主要思想是基于使用一些最近衍生的公式来表示低阶导数的高阶导数，从而以树状结构配置现场可编程门阵列（FPGA），以表示非线性表达。该树的节点将表示常见的非线性项（例如指数或对数函数），这些项将被编程为从其“子”节点导数的知识中传播自己的导数。

著录项

  • 作者

    Ben Jamil, Watany.;

  • 作者单位

    University of Ottawa (Canada).;

  • 授予单位 University of Ottawa (Canada).;
  • 学科 Electrical engineering.
  • 学位 M.A.Sc.
  • 年度 2010
  • 页码 93 p.
  • 总页数 93
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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