Algebraic structures underneath geometric approaches

Abstract

Purpose

The purpose of this paper is to study algebraic structures that underlie the geometric approaches. The structures and their properties are analyzed to address how to systematically pose a class of boundary value problems in a pair of interlocked complexes.

Design/methodology/approach

The work utilizes concepts of algebraic topology to have a solid framework for the analysis. The algebraic structures constitute a set of requirements and guidelines that are adhered to in the analysis.

Findings

A precise notion of “relative dual complex”, and certain necessary requirements for discrete Hodge‐operators are found.

Practical implications

The paper includes a set of prerequisites, especially for discrete Hodge‐operators. The prerequisites aid, for example, in verifying new computational methods and algorithms.

Originality/value

The paper gives an overall view of the algebraic structures and their role in the geometric approaches. The paper establishes a set of prerequisites that are inherent in the geometric approaches.

Citation

Kangas, J., Suuriniemi, S. and Kettunen, L. (2011), "Algebraic structures underneath geometric approaches", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 6, pp. 1715-1726. https://doi.org/10.1108/03321641111168048