Parallel Spectral Numerical Methods
简介：
本书介绍了傅立叶频谱方法的原理，它们在求解偏微分方程中的实用性以及如何在代码中实现它们。讨论了几种傅立叶频谱实现的性能考虑，并解释了在并行计算机上有效缩放的方法。首先快速了解有限精度算术。然后讨论了如何使用变量分离来求解常微分方程 (ODE) 和偏微分方程 (PDE)。接下来，它介绍了可用于求解ode和pde的数值时间步长方案。接下来通过对离散傅里叶变换 (DFT) 和用于快速计算DFT的快速傅里叶变换 (FFT) 算法的概述来介绍伪频谱方法。最后，它将结合所有这些来解决几个不同的pde，首先在串行设置中，然后在并行设置中。该程序将使用Matlab1和Fortran。还提供了一些Matlab程序的Python2实现。
英文简介：
This book teaches the principals of Fourier spectral methods, their utility in solving partial differential equation and how to implement them in code. Performance considerations for several Fourier spectral implementations are discussed and methods for effective scaling on parallel computers are explained.
It starts by taking a quick look at finite precision arithmetic. It then discusses how to solve ordinary differential equations (ODE) and partial differential equations (PDE) using separation of variables. Next, it introduces numerical time-stepping schemes that can be used to solve ODEs and PDEs. This is followed by an introduction to pseudo spectral methods through an overview of the discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) algorithm that is used to quickly calculate the DFT. Finally it will combine all of these to solve a couple of different PDEs first in a serial setting and then in a parallel setting.
The programs will use Matlab1 and Fortran. A Python2 implementation of some of the Matlab programs is also provided.
- 书名
- Parallel Spectral Numerical Methods
- 译名
- 并行谱数值方法
- 语言
- 英语
- 年份
- 2012
- 页数
- 348页
- 大小
- 1.83 MB
- 下载
Parallel Spectral Numerical Methods.pdf- 密码
- 65536
最后更新：2025-04-12 23:54:37
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