Using Kronecker products to construct mimetic gradients. Issue 10 (3rd October 2017)

• Record Type: Journal Article
• Authors: Castillo, J. E.; Grone, R. D.
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 10(2017)
• Page Start: 2031
• Page End: 2045
• Publication Date: 2017-10-03
• Subjects: Higher order mimetic discretizations -- Staggered one-dimensional grid -- Toeplitz -- algebraic graph theory -- Laplacian matrix; 15A69; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1298564
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : This paper describes how discrete versions of the derivative on the real line induce discrete version of the gradient and divergence in higher dimensions. This is geometrically motivated by results in algebraic graph theory since the grid in n dimensions is the graph Kronecker product of the path on n vertices. The resulting technique relies heavily on the matrix Kronecker product, and is an analogue of a derivation in multilinear algebra.