Parameter optimization for explicit parallel peer two-step methods
type: Item
instance of: scholarly article
title: Parameter optimization for explicit parallel peer two-step methods
zbMATH Open document ID: 1163.65051
published in: Applied Numerical Mathematics
publication date: 2009-03-20T00:00:00Z
review text: The authors discuss the parameter optimization for explicit parallel peer two-step methods for initial-value problems. Due to a two-step structure certain explicit peer methods with \(s\) stages have a parallel implementation on \(s\) processors. By the peer property all stages have essentially identical properties and the authors constructed a class of zero-stable methods with order \(p = s\) in all stages. Two approaches are discussed for choosing the free parameters. In a certain subclass the stability polynomial depends only linearly on a new set of parameters and by employing tailored root locus bounds a linear program can be formulated and solved exactly for stable and accurate methods. The second approach uses Monte-Carlo simulation in a wider class of methods. The two approaches are compared in realistic numerical tests on a parallel computer.
reviewed by: Srinivasan Natesan
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 5530713
zbMATH Keywords: Explicit two-step peer methods
zbMATH Keywords: parallel methods
zbMATH Keywords: linear programming
zbMATH Keywords: numerical examples
zbMATH Keywords: parameter optimization
zbMATH Keywords: initial-value problems
zbMATH Keywords: stability
zbMATH Keywords: Monte-Carlo simulation
author: B. A. Schmitt
author: R. Weiner
author: Stefan Jebens
MaRDI profile type: Publication
full work available at URL: j.apnum.2008.03.013
OpenAlex ID: W2076456542
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DOI: 10.1016/J.APNUM.2008.03.013
description: scientific article; zbMATH DE number 5530713