Numerical exterior algebra and the compound matrix method
type: Item
instance of: scholarly article
title: Numerical exterior algebra and the compound matrix method
zbMATH Open document ID: 1012.65079
author: Leanne Allen
author: Thomas J. Bridges
published in: Numerische Mathematik
publication date: 2002-12-01T00:00:00Z
review text: The authors reformulate the compound matrix method in a coordinate-free way using exterior algebra spaces \(\bigwedge^k({\mathbb C}^n)\). This formulation leads to a general framework for studying systems of differential equations on \(k\)-dimensional subspaces. The framework requires the development of new ideas, namely, the role of Hodge duality and the Hodge star operator in the construction, an efficient strategy for constructing the induced differential equation on \(\bigwedge^k({\mathbb C}^n)\), a general formulation \({\mathbb C}^n)\) of \(k\)-dimesnional subspaces, and a formulation for induced systems on an unbounded interval. The numerical exterior algebra framework is most advantageous for the numerical solution of differential eigenvalue problems on unbounded domains, where there are significant difficulties in setting up matrix discretizations. The theory is applied to the stability of four differential eigenvalue problems on unbounded intervals: (1) boundary-layer flow past a compliant surface, (2) solitary waves, (3) Bickley jet in oceanography, and (4) Ekman layer in atmospheric dynamics.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 34L16
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 86A10
Mathematics Subject Classification ID: 76B25
zbMATH DE Number: 1837039
zbMATH Keywords: numerical exterior algebra
zbMATH Keywords: compound matrix method
zbMATH Keywords: systems of diffrential equations
zbMATH Keywords: Hodge duality
zbMATH Keywords: Hodge star operator
zbMATH Keywords: eigenalue problems
zbMATH Keywords: stability
zbMATH Keywords: boundary-layer flow
zbMATH Keywords: solitary waves
zbMATH Keywords: Bickley jet in oceanography
zbMATH Keywords: Ekman layer in atmospheric dynamics
MaRDI profile type: Publication
full work available at URL: s002110100365
OpenAlex ID: W2017607641
DOI: 10.1007/S002110100365
description: scientific article; zbMATH DE number 1837039