An improved implementation of generalized Adams methods for underwater wave propagation problems
type: Item
instance of: scholarly article
title: An improved implementation of generalized Adams methods for underwater wave propagation problems
zbMATH Open document ID: 0565.76081
DOI: 10.1016/0898-1221(84)90053-1
author: Ding Lee
author: Kenneth R. Jackson
author: Stanley Preiser
publication date: 1984-01-01T00:00:00Z
review text: As previously demonstrated [the first and the third author, ibid. 7, 195- 202 (1980; Zbl 0451.76074)] the generalized Adams method (GAM) is effective for solving underwater acoustic wave-propagation problems. In this paper, we describe how to modify an earlier GAM implementation to substantially improve its efficiency. An approximation to the matrix exponential is required to implement a GAM. By using a rational approximation implicitly, the sparsity of the matrix can be exploited to produce a significantly more efficient implementation for a wide class of problems. A further improvement in efficiency can be gained by using a restricted-Padé approximation to the matrix exponential, rather than the more traditional Padé approximation. To demonstrate the effectiveness of this approach, an unerwater acoustic wave-propagation problem in a wedge-shaped region is solved by both the modified and unmodified GAM implementations.
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3902300
zbMATH Keywords: generalized Adams method
zbMATH Keywords: underwater acoustic wave-propagation
zbMATH Keywords: rational approximation
zbMATH Keywords: restricted-Padé approximation
MaRDI profile type: Publication
full work available at URL: 0898-1221(84)90053-1
OpenAlex ID: W2080321787
cites work: Generalized Adams methods for solving underwater wave propagation problems
cites work: Q4064972
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix
cites work: Restricted Padé Approximations to the Exponential Function
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3902300