Parallel integration of ODEs based on convolution algorithms
type: Item
instance of: scholarly article
title: Parallel integration of ODEs based on convolution algorithms
zbMATH Open document ID: 0789.65057
DOI: 10.1007/BF02238533
published in: Computing
publication date: 1994-06-13T00:00:00Z
review text: A method for parallel computing of ordinary differential equations (ODE's) is introduced. The method is based on the potential parallelism of convolution algorithms. Initial value problems for a system of nonlinear ODE's are considered. The solution of the problems is presented in convolution form. The idea of the proposed approach is to discretize the continuous convolution and after that to apply any existing parallel convolution algorithms, e.g. FFT algorithms, circle convolution by segmenting, direct convolution etc. The opportunity of applying convolution algorithms in finite fields which supplies new properties and additional speedup with special parallel signal processors using number theoretic transformations is discussed. The author's approach is considered on the example of the well-known Lorenz model of liquid convection. A connection between properties of shift operators on trajectories, the convolution, and ODE parallelism across time is shown. In this way there is an easy explanation for \textit{C. W. Gear's} observation [Calcolo 25, No. 1/2, 1-20 (1988; Zbl 0675.65068)] about high parallelism across time for equations with ``large'' and ``small'' Jacobians. An estimation for the norm of the shift operator derivative gives some information about a signal transmission from one point of time to another along trajectories. The parallel convolution algorithms: optical digital filtration, direct convolution on systolic arrays, circle convolution by segmenting, FFT algorithms are considered.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 490617
zbMATH Keywords: parallel signal processing
zbMATH Keywords: parallel computing
zbMATH Keywords: convolution algorithms
zbMATH Keywords: FFT algorithms
zbMATH Keywords: circle convolution by segmenting
zbMATH Keywords: direct convolution
zbMATH Keywords: Lorenz model of liquid convection
zbMATH Keywords: optical digital filtration
zbMATH Keywords: systolic arrays
author: Yuri P. Boglaev
reviewed by: I. Dimov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02238533
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description: scientific article; zbMATH DE number 490617