Scalable solutions to integral-equation and finite-element simulations
Scalable solutions to integral-equation and finite-element simulations
复制标题
积分方程和有限元模拟的可扩展解决方案
DOI：
10.1109/8.558670
复制
发表时间：
1997
影响因子：
5.7
通讯作者：
J. Patterson
中科院分区：
文献类型：
--
作者：
T. Cwik;D. Katz;J. Patterson
在开发数值方法或将其应用于工程组件的模拟和设计时，不可避免地需要检查该方法与问题的电气尺寸的比例。缩放是原始数学发展的结果；例如，稠密方程组中积分方程的解，以及具体的数值实现。数值实现的缩放取决于许多因素；例如，线性系统求解的直接或迭代方法，以及模拟中使用的计算机体系结构。可扩展性分为两个部分——特别是在并行计算机系统上的数值算法的可扩展性和算法或顺序可扩展性。首先介绍顺序实现和扩展，然后介绍并行实现。这一进展旨在说明使用当前并行平台和顺序机器的差异以及由此产生的节省。不同问题规模的解决时间（挂钟时间）是绘制或制成表格的关键参数。详细考虑了时间调和曲面积分方程形式的顺序和并行可扩展性以及偏微分方程的有限元解。
When developing numerical methods, or applying them to the simulation and design of engineering components, it inevitably becomes necessary to examine the scaling of the method with a problem's electrical size. The scaling results from the original mathematical development; for example, a dense system of equations in the solution of integral equations, as well as the specific numerical implementation. Scaling of the numerical implementation depends upon many factors; for example, direct or iterative methods for solution of the linear system, as well as the computer architecture used in the simulation. Scalability is divided into two components-scalability of the numerical algorithm specifically on parallel computer systems and algorithm or sequential scalability. The sequential implementation and scaling is initially presented, with the parallel implementation following. This progression is meant to illustrate the differences in using current parallel platforms and sequential machines and the resulting savings. Time to solution (wall-clock time) for differing problem sizes are the key parameters plotted or tabulated. Sequential and parallel scalability of time harmonic surface integral equation forms and the finite-element solution to the partial differential equations are considered in detail.